Muireann spain finalreport

Hierarchical Mapping of Condensation Growth on
Metallic Surfaces
Muireann Spain
15386981
MEEN30120: Mechanical Engineering Project
UCD School of Mechanical and Materials Engineering
Supervisor: Dr Kevin Nolan
23rd April 2019

0 Abstract
The purpose of this project is to expand and test an existing MATLAB condensation
tracking code provided from industry. The code tracks droplets on a surface, and returns
the location, size and shape of each droplet, assuming dropwise condensation is occurring.
As this code analyses each image separately at discrete time steps, the main objective
of this project is to add a historical storage structure to this code in order to build a
visual 3-D model of droplet merging and coalescence. This will be achieved by completing
a number of tasks. Modelled images of dropwise condensation were created to test the
function of the existing MATLAB droplet tracking code. A basic droplet historical storage
structure was also modelled on MATLAB and tested using the synthetic generated images.
An experimental rig to generate condensation droplets on a metallic surface was modelled
on CAD software and built in order to provide real data with which to test the MATLAB
droplet tracking code. Two data sets were generated on hand-polished sample plates, and a
MATLAB image processing code was designed to improve image coherence prior to loading
them into the droplet tracking code. Finally, based on the returned 3-D model from the
tracking code, qualitative characterisations of sample surfaces were discussed. Although
insuﬃcient data was collected to make a deﬁnitive conclusion, it would appear that more
polished surfaces would be better suited for use in HVAC systems for condensate collection
and a reduction in the occurrence of sick building syndrome.
I

Contents
0 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3.1 Model droplet growth to test the existing code . . . . . . . 1
1.3.2 Further develop the existing droplet detection code . . . . 1
1.3.3 Build a thermoelectric rig . . . . . . . . . . . . . . . . . . 2
1.3.4 Characterise growth of condensation and coalescence be-
haviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5 Report Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Sick Building Syndrome . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Air Conditioner Mechanics . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Causes of Condensation Formation on Air Conditioning Units . . . 6
2.4 Mechanics of Condensation Formation . . . . . . . . . . . . . . . . 7
2.5 Micro-level Condensation Nucleation . . . . . . . . . . . . . . . . . 7
2.6 Growth Dynamics on a Hydrophobic Rough Surface . . . . . . . . . 8
2.7 Condensation Formation on Microgrooved Surfaces . . . . . . . . . 9
2.8 Condensation Collection . . . . . . . . . . . . . . . . . . . . . . . . 10
2.9 Self-Propelled Dropwise Condensation . . . . . . . . . . . . . . . . 11
2.9.1 Stages of Condensation Growth . . . . . . . . . . . . . . . 11
2.10 Droplet Tracking Code . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Experimental Design and Methodology . . . . . . . . . . . . . . . . . . . . 17
3.1 Droplet Growth Modelling . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.1 First Iteration . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.2 Second Iteration . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.3 Third Iteration . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Testing the Droplet Detection Code . . . . . . . . . . . . . . . . . . 21
3.3 Creating a Historical Droplet Tracking Structure . . . . . . . . . . . 23
3.3.1 First Iteration . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.2 Second Iteration . . . . . . . . . . . . . . . . . . . . . . . 27
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3.4 Thermoelectric Rig Model . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Thermoelectric Rig Design . . . . . . . . . . . . . . . . . . 29
3.4.2 Construction of the Thermoelectric Rig . . . . . . . . . . 32
3.4.3 Sample Plate Surface Finishes . . . . . . . . . . . . . . . . 36
3.4.4 Optical Microscope Conﬁguration . . . . . . . . . . . . . . 37
3.5 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 Determining Sample Plate Temperature . . . . . . . . . . 38
3.5.2 PID Temperature Controller . . . . . . . . . . . . . . . . . 44
3.5.3 Gathering Experimental Data . . . . . . . . . . . . . . . . 46
3.5.4 Experimental Data Image Processing . . . . . . . . . . . . 51
4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
A Thermoelectric Rig Isometric Part Drawings . . . . . . . . . . . . . . . . . 66
B Code Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
B.1 Modiﬁed Droplet Detection MATLAB Code Script From Industry . 72
B.2 Third Iteration of Droplet Modelling MATLAB Script . . . . . . . 76
B.3 Historical Storage Structure MATLAB Script . . . . . . . . . . . . 80
B.4 Experimental Image Processing MATLAB Script . . . . . . . . . . 83
C Recorded Image Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
C.1 1200 Grit Finished Surface . . . . . . . . . . . . . . . . . . . . . . . 85
C.2 2500 Grit Finished Surface . . . . . . . . . . . . . . . . . . . . . . . 86
D Supplied Thermoelectric Cooler Performance Curves . . . . . . . . . . . . 87
III

List of Figures
1 Indoor Cassette Air Conditioning Unit [12] . . . . . . . . . . . . . . . . . . 5
2 Comparison of Flow Fields Surrounding the Discharge Outlet [12] . . . . . 6
3 Comparison of Condensation Formation Surrounding the Discharge Outlet
[12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4 Transition from a Cassie-Baxter State to a Wenzel regime of a Droplet Dur-
ing Evaporation [14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5 Growth, Coalescence, and Merging of Droplets on a Flat and Microgrooved
Surface with Increasing Condensation [20] . . . . . . . . . . . . . . . . . . 9
6 Schematic of a HVAC unit with a Condensation Collection Mechanism [4] . 10
7 (a) Dropwise Condensation on a Horizontal Hydrophobic Flat Surface and
(b) on a Horizontal Superhydrophobic Rough Surface [6] . . . . . . . . . . 11
8 Droplet Formation Observed Under an Optical Microscope [17] . . . . . . . 13
9 Binary Representation of Droplets [17] . . . . . . . . . . . . . . . . . . . . 13
10 Specular Reflections in Binary [17] . . . . . . . . . . . . . . . . . . . . . . 14
11 Reflections on Original Image [17] . . . . . . . . . . . . . . . . . . . . . . . 14
12 Voronoi Diagram [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
13 Droplets Approximated as Circles [17] . . . . . . . . . . . . . . . . . . . . . 16
14 MATLAB Mask Approximating Size and Shape of Droplet [17] . . . . . . . 16
15 Binary Representation of Droplet Growth . . . . . . . . . . . . . . . . . . 17
16 First Iteration Representation of Droplet Growth . . . . . . . . . . . . . . 18
17 Second Iteration Binary Representation of Droplet Growth . . . . . . . . . 19
18 Third Iteration Final Representation of Droplet Growth . . . . . . . . . . . 21
19 Random Sample of Synthetic Image . . . . . . . . . . . . . . . . . . . . . . 22
20 Droplet Detection of Synthetic Code Droplets with Over-Large Reflections 23
21 Droplet Detection of Synthetic Code Droplets . . . . . . . . . . . . . . . . 23
22 Computing the Movement of Droplets Using the Level Set Method (Provided
By Supervisor) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
23 Sample of (a) Synthetic Image, and (b) Real Image in Binary with Reflections
Filled . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
24 Sample of First Iteration of Historical Graphing Structure . . . . . . . . . 26
25 Sample of First Iteration of Historical Graphing Structure with Synthetic
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
IV

26 (a) XY and (b) XZ View of Historical Graphing Structure with Synthetic
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
27 3-D View of Historical Graphing Structure with Synthetic Data . . . . . . 28
28 (a) Second and (b) Fourth Time Step Representation of Overlapping Droplet
Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
29 Front View of Initial CAD Model of Thermoelectric Rig . . . . . . . . . . . 30
30 Front View of CAD Model of Manufactured Thermoelectric Rig . . . . . . 31
31 Parts for Building the Thermoelectric Rig . . . . . . . . . . . . . . . . . . 34
32 Front View of the Assembled Thermoelectric Rig . . . . . . . . . . . . . . 35
33 Thermoelectric Rig with Altered Duct and Fan . . . . . . . . . . . . . . . 35
34 Manufactured Sample Plates with Varying Surface Finishes . . . . . . . . . 36
35 Labelled Schematic of the Light Path Through The Optical Microscope . . 37
36 Experimental Determination of Chilled Sample Plate Temperature . . . . . 39
37 Chilled Sample Plate Temperature at Varying Initial Fan Voltages . . . . . 42
38 Chilled Sample Plate Temperature at Varying Actual Fan Voltages . . . . 43
39 Temperature Diﬀerential of TEC at Varying Fan Voltages . . . . . . . . . . 44
40 Calibrating the Arduino Thermometer with a Hand-Held Thermocouple
Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
41 Droplets on (a) 80, (b) 150 and (c) 1200 Emery Cloth Finished Metallic
Surfaces (Inverted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Surfaces with Marker Coating (Inverted) . . . . . . . . . . . . . . . . . . . 47
Surfaces with Acrylic Paint Coating (Inverted) . . . . . . . . . . . . . . . . 47
44 Droplet Formation at Distinct Time Steps on Black Insulation Tape . . . . 48
45 Power Drawn by TEC During Condensation Formation . . . . . . . . . . . 49
46 Droplet Formation at Distinct Time Steps on 1200 Grit Finished Aluminium
Sample Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
47 Droplet Formation at Distinct Time Steps on 2500 Grit Finished Aluminium
Sample Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
48 Unprocessed Images at Distinct Time Steps Represented In Binary . . . . 51
49 Morphologically Closed Images at Distinct Time Steps . . . . . . . . . . . 52
50 Images with Uniform Circular Specular Reﬂections at Distinct Time Steps 53
51 Graph of Average Droplet Radius (in Pixels) Vs Time Step . . . . . . . . . 54
52 Graph of Number of Droplets Vs Time Step . . . . . . . . . . . . . . . . . 55
53 Box Plot Spread of Droplet Radius Vs Time Step for 1200 Grit Finished
Sample Plate Processed and Unprocessed Images . . . . . . . . . . . . . . 56
54 Box Plot Spread of Droplet Radius Vs Time Step for 2500 Grit Finished
Sample Plate Processed and Unprocessed Images . . . . . . . . . . . . . . 57
55 Illustration of Contact Angle for (a) 1200-Grit Finished Surface, and (b)
2500-Grit Finished Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
V

56 Droplet Detection Code Output for (a) 1200 Grit Unprocessed Image, and
(b)1200 Grit Processed Image . . . . . . . . . . . . . . . . . . . . . . . . . 59
57 Droplet Detection Code Output for (a) 2500 Grit Unprocessed Image, and
(b)2500 Grit Processed Image . . . . . . . . . . . . . . . . . . . . . . . . . 60
58 Droplet Detection Code Output for First Time Step of 2500 Grit Finished
Unprocessed Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
59 Isometric Drawing of Completed Thermoelectric Rig . . . . . . . . . . . . . 66
60 Isometric Drawing of Base Plate . . . . . . . . . . . . . . . . . . . . . . . . 67
61 Isometric Drawing of Initial Heat Sink Modiﬁcations . . . . . . . . . . . . 68
62 Isometric Drawing of Actual Heat Sink Modiﬁcations . . . . . . . . . . . . 69
63 Isometric Drawing of Initial Sample Plate . . . . . . . . . . . . . . . . . . 70
64 Isometric Drawing of Actual Sample Plates Manufactured . . . . . . . . . . 71
65 Condensation Growth (Left to Right) on 1200-Grit Finished Sample Plate 85
66 Condensation Growth (Left to Right) on 2500-Grit Finished Sample Plate 86
67 Supplied TEC Performance Curves[25] . . . . . . . . . . . . . . . . . . . . 87
VI

List of Tables
1 Prevalence of Symptoms (%) in Relation to Method of Air Supply [10] . . 4
2 List of Parts Required For Thermoelectric Rig . . . . . . . . . . . . . . . . 32
3 Performance of TEC with Fan Constant at 10 V . . . . . . . . . . . . . . . 40
VII

1 Introduction
1.1 Motivation
The motivation behind this project is the lack of understanding of the mechanics of conden-
sation coalescence. This project aims to accurately depict a 3-D image of droplet growth
and merging over a series of time steps. The models that currently exist for this purpose
are limited by simplified image processing techniques. Once an accurate model has been
developed, it will enable characterisation of surfaces in terms of condensation formation.
As condensation formation is an extremely common phenomenon, this research will be
invaluable in applications such as HVAC design and for condensation collection purposes.
1.2 Research Hypothesis
Condensation formation is an extremely common phenomenon that involves the principles
of both thermodynamics and fluid mechanics. It usually occurs when there is relatively
high air humidity, and the temperature of a surface is below the dew point temperature.
The rationale behind this project is that condensation droplets form and coalesce in
a different manner on surfaces based on their characteristics. Although there is extensive
literature available on this topic which will be discussed in Chapter 2, this project aims
to complement the existing literature by adding to an available droplet tracking MATLAB
code from industry (which will be discussed in depth in Chapter 2).
1.3 Project Objectives
This project can be broken down into four distinct objectives:
1.3.1 Model droplet growth to test the existing code
In order to ensure that the condensation droplet tracking code provided from industry is
accurate, synthetic images of droplets will be created with known centroids and areas to
verify the returns of the tracking code. This modelling will be done in MATLAB and will
be discussed in detail in Chapter 3.
1.3.2 Further develop the existing droplet detection code
The droplet tracking code supplied from industry currently tracks the droplets on each
image discretely with no comparison to the prior image. This project aims to enhance the
code by adding a historical storage structure, i.e. create a ”family tree” of each large final
droplet from the merging and coalescence of smaller droplets during previous time steps.
1

1.3.3 Build a thermoelectric rig
In order to test the additions to the droplet tracking code discussed above, real data must
be generated. Therefore, a thermoelectric rig model must be designed and built to generate
condensation on metallic surfaces that can be photographed for analysis.
This objective involves researching existing thermoelectric devices, creating a CAD
model, purchasing and machining the necessary parts, and finally building the rig and
using it to generate data.
1.3.4 Characterise growth of condensation and coalescence behaviour
This objective arises from collecting data from the thermoelectric rig. Different sample
plates will be machined in the engineering workshop, the pattern of condensation formation
will be imaged, and read into the droplet tracking code. This objective will both test the
limitations of the droplet tracking code while also enabling a qualitative characterisation of
condensation growth and coalescence behaviour based on aspects of the different surfaces.
This project does not have the scope for deeper analysis of surface finishes.
1.4 Methodology
This report will follow a traditional methodology, which commences with a statement of
objectives. This is closely followed by a literature review of the topics involved in the
objectives, in this case mechanisms of condensation formation and coalescence and their
applications, as well as a thorough analysis of the existing droplet tracking code.
Once the literature review is complete, the experimental procedure section is to be
commenced. This involves bringing the first three objectives listed above to completion.
The final step in the methodology is analysis, which in this case is represented by the final
objective. Once the experimental section is complete, the results will have to be analysed
and conclusions should be drawn.
As this is an experimental project, the methodology is rather circular as it is expected
that unforeseen issues may arise. This will result in a return to reviewing the literature
and adapting the experimental methods before re-analysing the results.
1.5 Report Layout
The report layout is discussed in the table of contents. As this is an final report, all tasks
have brought to completion or if this proved too challenging to complete within the given
condensed time frame, a detailed discussion of the necessary potential for further work will
be included.
The layout is based on the project methodology discussed above, commencing with a
literature review section in Chapter 2 on all topics that are currently deemed relevant to
the project. This chapter is followed by an extensive chapter entitled ”Experimental Design
and Methodology” which aims to discuss the experimental methods that were followed in
the attempt to achieve the objectives listed in Section 1.3.
2

The experimental results are concisely contained in a separate chapter, in which the
limitations of this experimental analysis are also discussed. The chapter entitled ”Discus-
sion and Conclusions” will lay out an effective evaluation of both the experimental and
analytical objectives and results.
Given the analytical nature of this project, there will also be scope for improvement.
The final chapter on ”Further Work” will discuss the necessary tasks in detail that are to be
finished to improve and conclude the project. The appendices include relevant material such
as CAD drawings submitted to the workshop for the manufacture of parts, the MATLAB
code scripts that were designed and used during the execution of the project, and samples
of experimentally generated image sequences. The final bibliography section gives details
on the sources that were consulted during the literature review, and has been updated as
more research and review was deemed necessary to complete the project.
3

2 Literature Review
2.1 Sick Building Syndrome
Sick Building Syndrome (SBS) has been defined by the World Health Organisation as
an excessive volume of complaints of work-related skin and mucous membrane irritation,
headaches, fatigue and difficulty concentrating [7]. The affected buildings are typically
office buildings that are fully air conditioned. As in excess of 90% of the air in an air-
conditioned building is recirculated in order to ensure energy efficiency, a lack of ”fresh”
air is often blamed for these symptoms [10]. A generally accepted hypothesis is that
increased ventilation rates result in a decrease of air quality pollutants contained in an
indoor environment which therefore reduce the recorded occurrences of SBS [11].
Air conditioning was initially introduced to office environments to ensure the comfort
and well-being of employees. Many studies have been conducted and it has been determined
that the ideal working environment is one in which there are no large swings in temperature,
no fluctuation in relative humidity and a sufficient air flow rate to remove odours [10].
However, given the significant health impacts due to SBS (which may cause the presence
of mould cells and spores), serious health issues can be caused by inadequate ventilation
systems which increases the need for healthcare services and the level of work absenteeism
[3].
Table 1: Prevalence of Symptoms (%) in Relation to Method of Air Supply [10]
4

Table 1 indicates the results of a study into the occurrence of SBS symptoms in 9
buildings [10]. There is a clear correlation between work related SBS symptoms and air
conditioned buildings in comparison with naturally ventilated ones [10].
2.2 Air Conditioner Mechanics
A typical indoor ceiling-cassette air conditioning unit is illustrated in Figure 1. Typical
units contain a turbo fan, heat exchanger, guide vanes, discharging outlet, air inlet and a
plastic case [13]. Air enters the unit through the rotating turbo fan, completes a cooling
process in the heat exchanger, and is then discharged to the indoor environment [13]. Figure
1 clearly illustrates this process.
Figure 1: Indoor Cassette Air Conditioning Unit [12]
The selection of an air conditioning system depends on numerous parameters, such as
the required cooling area and the total heating load [4]. Both ceiling cassette and window
units are generally used for single-room applications, whereas central air conditioning is
generally preferred if the cooling load is signiﬁcantly higher, i.e. an entire building [4].
Heating, ventilation and air conditioning (HVAC) systems are becoming increasingly
popular, especially in hot-humid climates where thermal comfort is a signiﬁcant issue. As
global energy use is soaring and predicted to climb rapidly, concerns with regard energy
supply and consumption have been raised. The growth in energy use for HVAC systems has
5

caused them to become the single largest energy end use in both the residential and non-
residential buildings sector [8]. Currently, it accounts for approximately 50% of building
energy consumption, and 20% of the overall energy consumption of the United States [8].
2.3 Causes of Condensation Formation on Air Conditioning Units
One major drawback of many air conditioning units is the tendency to form dew-type
condensation on the casing of indoor units. This problem is particularly severe in highly
humid weather and in humid subtropical regions [13]. Further problems are caused by
this condensation such as mildew, mould, and other negative health impacts discussed in
Section 2.1.
Condensation formation on air conditioning units is defined by numerous parameters
such as supply air flow rate, supply air temperature. ambient air speed, and the convective
heat transfer coefficient [16]. The main cause of dew formation is thought to be humid air
being sucked into the vicinity of the air discharge outlet and coming into contact with the
cold surface of the case [12].
The airflow can generally be divided into two separate flows - discharge flow, which
has a high relative velocity in comparison with the ambient air, and suction flow which
is generated by the turbo fan [13]. A study conducted by Jin et al [12] found that the
difference in these flows creates a static pressure differential which then causes the warm,
humid ambient air to flow towards the discharge outlet. This suction flow brings the humid
air into contact with the cold surfaces of the unit, which causes dew formation as they are
cooled by the discharge flow to a temperature below the dew point temperature [13]. In
this study, a flow-blocking device was introduced to limit the suction flow, and the impact
on the stream lines is illustrated in Figure 2.
Figure 2: Comparison of Flow Fields Surrounding the Discharge Outlet [12]
Figure 3 illustrates how the formation of condensation is reduced by installing a mech-
anism which blocks the suction flow of warm air. However, it was noted that condensation
began to form on the blockage device, which reduced the effectiveness of the mechanism.
6

This case study indicates the need for further analysis on the mechanics of condensation
formation and how this can be applied to reduce the negative side effects of air conditioning
units.
Figure 3: Comparison of Condensation Formation Surrounding the Discharge Outlet [12]
2.4 Mechanics of Condensation Formation
It has been observed that condensed droplets on both hydrophilic and hydrophobic micro-
structured surfaces demonstrate different wetting characteristics from the behaviour of a
placed or injected droplet [20]. Condensation on a cooled surface is typically characterised
by one of two categories, either dropwise condensation (DWC) or filmwise condensation
(FWC) [23]. The majority of phenomena that occur naturally exhibit DWC characteristics,
where the surface is covered in droplets of varying sizes which do not completely wet the
surface [23]. Examples of this are condensation on butterfly wings and lotus leaves - as the
water cannot spread, it rolls around in small droplets and results in the removal of dirt
[19]. On the other hand, manufactured surfaces such as metals tend to exhibit a filmwise
condensation mode [23].
Wettability of a surface is characterised by the contact angle θ, with surfaces generally
classified as hydrophilic (θ < 90o
) or hydrophobic (θ > 90o
) [23]. The contact angle is also
dependent on other factors such as surface cleanliness, energy, roughness, and preparation
of the surface [14].
2.5 Micro-level Condensation Nucleation
Dropwise condensation consists of four stages of development - formation, growth, coales-
cence and departure, and originates from a molecular clustering nucleation process [23]. If
molecular clusters coalesce and form a large enough structure that can overcome the free
energy barrier of nucleation, a nucleus is formed [23]. This droplet grows by absorbing
nearby clusters and molecules.
7

In general, filmwise condensation is formed when numerous clusters form randomly on
the surface immediately once the surface is cooled [23]. There are enough discrete clusters
that the condensate covers the entire material surface, and develops into a film [23]. With
the passage of time, this films grows thicker and does not rupture, and is hence called
filmwise condensation [23]. This was viewed to occur experimentally at low values of θ,
namely θ ≈ 16o
[23].
2.6 Growth Dynamics on a Hydrophobic Rough Surface
A superhydrophobic surface is defined as having an extremely large contact angle, typically
greater than 150o
[19]. Rough or superhydrophobic surfaces can be manufactured through
various processes such as vapour deposition, micromachining or lithography [19]. When a
drop is deposited on a surface, the liquid arranges itself into a geometrical configuration
defined by one of the discrete wetting states [19]:
Cassie-Baxter: An air pocket is trapped below the droplet - i.e. when the drop is gently
put on the substrate (not typical of condensation).
Wenzel: The interpillar space below the droplet is filled with liquid. Droplets in the
Wenzel state are highly pinned [22].
Penetration: The drop is defined by the Wenzel state but also fills the region of sub-
strate that surrounds the droplet.
Figure 4: Transition from a Cassie-Baxter State to a Wenzel regime of a Droplet During
Evaporation [14]
There is little to no information on whether the same geometrical configuration models
remain valid for droplets produced by condensation on a surface.
8

2.7 Condensation Formation on Microgrooved Surfaces
Anisotropic wetting refers to a liquid characteristic in which it spreads preferentially in a
particular direction [20]. The difference in size, shape and distribution of droplets can be
observed in Figure 5. Nucleation of droplets occurred at the same rate in both cases, and
small droplets formed in the manner of dropwise condensation [20]. Individual droplets
initially are observed to have a small and equal average radius on both surfaces. Once
the point of coalescence and merging with adjacent droplets was reached, the behaviours
diverged - the density of droplets on the flat surface was much greater, but the average
volume of each droplet on the microgrooved surface was larger than the flat equivalent [20].
Figure 5: Growth, Coalescence, and Merging of Droplets on a Flat and Microgrooved
Surface with Increasing Condensation [20]
As condensation proceeded with respect to time, the droplets in the microgrooves merge
anisotropically along the grooves, forming long parallel drops [20]. It is also apparent from
Figure 5 that the drops merge at a higher rate on the flat surface than on the microgrooved
surface.
9

It can therefore be concluded that on patterned surfaces, condensation droplet growth
will occur preferentially along the pattern due to pinning, whereas on a flat surface con-
densation growth tends to proceed in a random fashion.
2.8 Condensation Collection
To achieve dropwise condensation effectively, condensate must be effectively removed from
the surface once it accumulates [6]. This is generally achieved by orienting the plate at
such an angle that the effect of the gravitational force causes the droplet to roll off the
surface [6].
Figure 6 illustrates a typical such condensate collection mechanism. Although the
surface is a cylindrical tube rather than a flat plate, the principle remains the same -
condensation forms on the large surface area of the cooling coil and falls directly into the
drain pan under the effects of gravity and is removed via the condensate drain pipe.
Figure 6: Schematic of a HVAC unit with a Condensation Collection Mechanism [4]
The volume of condensate collected during an operating period is highly dependent on
meteorological factors such as humidity, dew point temperature, ambient temperature and
the operating hours of the unit [4]. A study by Khan and Al Zubaidy [2] investigated the
HVAC condensate collection possibilities of buildings in hot and humid climates such as
Dubai and Abu Dhabi. It was concluded that in the region of 78 m3
of condensate could be
collected monthly from a 20-floor building. As this condensate is of relatively high quality
due to a low content of Total Dissolved Solids (TDS), it could potentially be used for water
sustainability purposes such as irrigation and building energy recovery [4].
10

2.9 Self-Propelled Dropwise Condensation
Another method of condensation removal that does not utilize the gravitational forces
as described in Section 2.8 is the potential for autonomous removal without any external
forces on superhydrophobic surfaces [6]. This spontaneous motion is powered by the surface
energy that is released upon the coalescence of droplets, and is unusual in that in-plane
coalescence results in an out-of-plane jump [6].
This spontaneous motion can be observed to occur naturally, as is evident from ”Buller’s
Drop” [21]. Ballistospore mushrooms excrete a droplet near their base, and once the drop
reaches a critical radius it wets the spore and acts as a surface tension catapult, which is
used to propel the spore away.
Figure 7(a) illustrates the stages of how dropwise condensation conventionally occurs on
hydrophobic surfaces. Figure 7(b) on the other hand reveals the characteristics of dropwise
condensation on a superhydrophobic roughened surface. In contrast with the hydrophobic
surface, it can be seen that large drying occurs at the 20 minute stage, which is the results
of the autonomous removal of drops from the surface [6].
Figure 7: (a) Dropwise Condensation on a Horizontal Hydrophobic Flat Surface and (b)
on a Horizontal Superhydrophobic Rough Surface [6]
2.9.1 Stages of Condensation Growth
The growth of condensation droplets on a surface typically follows a power law [5]:
2r ∼ tα
where 2r is the mean droplet diameter in µm, t is the time and α is the growth law ex-
ponent, depending on the stage of condensation. Two stages of condensation were observed
for hydrophobic surfaces, whereas rough superhydrophobic surfaces exhibited a third stage
[6]:
11

1. Initial Growth Without Coalescence: Drops nucleate and grow without signif-
icant interaction, and negligible surface coverage is noted. α has a value of 1
3
for both cases
during this phase [6].
2. Immobile Coalescence: Once the surface coverage is sufficiently large, droplets
begin to merge and coalesce. However, the centre of mass of the droplets does not change
significantly after coalescence. On the hydrophobic surface, α would typically be 1, whereas
for a textured surface α is in the region of 0.8 [6].
3. Mobile Coalescence: This stage is observed for the superhydrophobic state only.
Once the average drop diameter reaches a threshold value, rapid coalescence results in a
removal of the droplets from the surface, exhibiting an power exponent value of approxi-
mately 0.02 [6]. This is illustrated in Figure 7.
This behaviour exhibited in Stage 3 was captured by high-speed camera during a study
by Boreyko et al [6]. Both static merging of neighbouring droplets and dynamic coalescence
(where a droplet in motion impinges on a static neighbouring droplet with a velocity as
high as 1 m/s) were observed.
The self-propelled droplet is powered by the surface energy that is released upon the
coalescence of neighbouring droplets [6]. The surface energy released upon the coalescence
of two drops on a superhydrophobic surface can be as high as 20% of the initial energy,
which is ten times larger than the energy barrier for transition from the Wenzel to the
Cassie-Baxter regime discussed in Section 2.6 [6].
2.10 Droplet Tracking Code
A MATLAB code was available from industry which could track condensation droplet
location, size and shape. A modified version of the supplied code script is included in
Appendix B.1. Firstly, droplets were generated on a surface using a thermoelectric rig.
They were observed under an optical microscope, videoed using a Raspberry Pi camera and
converted to PNG images using an image processing software entitled ”Blender”. Figure 8
is a random example of one of the generated images.
This image was then read into the MATLAB code. It was converted to binary for ease
of manipulation, i.e. a 2-D array of ones and zeroes rather than the initial 3-D colour
matrix. The colours were also inverted, as is visible in Figure 9.
12

Figure 8: Droplet Formation Observed Under an Optical Microscope [17]
Figure 9: Binary Representation of Droplets [17]
Using the ”bwconncomp” function, all connected areas were labelled. A threshold
specular reflection area was set, and all connected areas greater than this threshold (i.e.
the surface not wetted by the droplets) was set to zero. In this manner, the specular
reflection of each droplet was identified and stored in a matrix, as illustrated in Figure 10.
13

Using the stored specular reflection locations, the reflections on the original image were
identified (Figure 11).
Figure 10: Specular Reflections in Binary [17]
Figure 11: Reflections on Original Image [17]
14

A Voronoi diagram breaks a plane down into regions based on a set of ”seed” points
(in this case, the specular reflections). Each region consists of the set of points that are
closer to one particular seed point than any other seed point. The blue lines in Figure 12
approximately divide each droplet into its discrete region in the image.
Figure 12: Voronoi Diagram [17]
As explained in Section 2.4, on a hydrophobic surface tension wants to make the drop
spherical. This competes with the wetting state, and therefore the drop can be approx-
imated as hemispherical. The diameter of the droplet is extracted radially by averaging
pixel values as a line rotates around the specular reflection, and the red circles in Figure
13 approximate each droplet as circular.
Realistically, the red circles are only an approximation of the size of the droplet as the
code takes the average radius, and no indication is given as to the droplet shape. The final
step of the MATLAB code uses image segmentation techniques to approximate the droplet
boundaries. Using the ”activecontour” command, a set of contours (i.e. edge boundaries of
droplets) based on pixel intensity are extracted from the image and plotted as the yellow
contour curves.
15

Figure 13: Droplets Approximated as Circles [17]
Figure 14: MATLAB Mask Approximating Size and Shape of Droplet [17]
This MATLAB code will serve as the basis for much of the experimental part of this
project.
16

3 Experimental Design and Methodology
3.1 Droplet Growth Modelling
The following code iterations were done in MATLAB to attempt to replicate real droplet
growth and coalescence. The initial target of this project was to test the current droplet
tracking code outlined in Section 2.10, essentially by creating synthetic images where the
coordinates of the droplets are known, and comparing it to the coordinate data returned
by the droplet tracking code.
3.1.1 First Iteration
The first iteration was a function where the user could in put the x- and y- resolution,
number of initial droplets, maximum initial droplet radius, droplet radius growth rate (in
pixels), and number of time steps.
The code initially generated a binary image with the input number of circular droplets
in random x- and y-coordinates. Each droplet was given a random initial radius that was
less than the maximum user input radius. The binary first timestep is shown in Figure 15,
including specular reflections.
Figure 15: Binary Representation of Droplet Growth
Figure 16 portrays the realistic representation of droplet growth. ”Salt and Pepper”
noise was applied to the image as well as a Gaussian filter to blur the image in order to
simulate the resolution of camera-captured images.
The MATLAB code that causes the droplets to increase in size is relatively simplistic,
but problems arose with simulating the coalescence of the droplets. In order to detect
17

whether droplets overlapped at any time step, a methodical check of the droplet area was
introduced. The maximum initial input radius and the droplet radius growth rate were used
to calculate the maximum possible area of a singular droplet. Using the ”bwconncomp”
MATLAB function, the areas of all connected regions were calculated.
Figure 16: First Iteration Representation of Droplet Growth
If any of the calculated connected areas were greater than the maximum possible area
of a singular droplet, those droplets were deemed to be merged, a new centroid and radius
was calculated, and a new circular droplet was plotted in place of the overlapped droplets.
This code functioned in most cases, but as can be seen at the bottom of images (c) through
(f) in Figure 16, overlapping droplets with a combined area that was smaller than the
maximum possible singular drop area were not detected.
Therefore, a second iteration of the code was necessary to improve the coalescence
mechanism.
18

3.1.2 Second Iteration
The second iteration of the MATLAB code operates much like the first iteration, where
a user can input parameters into the function, a binary image is generated, and filters
are applied to the image to imitate camera resolution. Although the images in Figure
17 appears more rudimentary than the first iteration, the thought process behind it was
significantly more advanced.
Droplet generation and growth was left unchanged, but the coalescence mechanism was
based on centroids rather than on area. Using the ”bwconncomp” function similarly, the
pixel locations occupied by each droplet were calculated and compared to a list of the
droplet centroids from the previous time step. If more than one centroid was detected in a
connected component, the droplets were deemed merged and replaced by a circular droplet.
Although the thought process behind this coalescence mechanism appears sound, the
algorithm did not function as expected, which is evident from the overlapping droplets
illustrated in Figure 17. It was thought that a bug in the code could be causing this issue,
and more work was needed to further develop the algorithm.
Figure 17: Second Iteration Binary Representation of Droplet Growth
19

The bug that eventually was discovered was an issue with the floating point numbers
stored in MATLAB. The ”bwconncomp” MATLAB function calculates properties of con-
nected components, and in this case was used for calculating the centroid of each droplet.
The issue with this function was that in many cases it returned a value that was extremely
similar to the value stored in the initial centroid array, but not exactly the same. As the
”intersect” function searched both arrays for an exact match, it didn’t return values that
were separated by a small decimal, and therefore overlapping droplets were not detected.
An attempt was made to manipulate the code by adding padding values around each
centroid calculated by the ”bwconncomp” function, but this added significantly to the
complexity and time required for each step and therefore was not deemed to be a suitable
solution. Therefore, a third iteration of the droplet modelling code was necessary in order
to accurately represent droplet coalescence.
3.1.3 Third Iteration
The third and final iteration of the modelling code began similarly to the first two iterations.
It is 115 lines long, and is based off a similar concept to the second iteration of tracking
centroids. The MATLAB script for this code is available in Appendix B.2.
Similarly to the second iteration, the ”bwlabel” function was used to detect the con-
nected components, and the area and centroid information was extracted from this structure
and sorted into arrays. This centroid array was then compared to the original stored cen-
troids. Any entries that were in the original array that were not detected in the calculated
centroid array were deleted. The binary values of these droplets were also re-initialised to
zero.
Centroids in the calculated array that were not in the initial array were added to the
initial array. The area of the droplet with the new centroid was used to calculate the new
circular droplet equivalent radius, and a new merged droplet was added to the image.
Although this code appeared to function well, there was a minor bug that caused some
random merged droplets to cease growing or shrink in further time steps in an unexplained
manner, and the cause of this bug was never discovered. However, given that in a real-
life scenario individual droplets will grow at different rates and not at the same specified
initial rate as in this code, this bug was not considered detrimental to the purpose of the
simulation.
The final sequence of images that were used to test the droplet tracking code are dis-
played in Figure 18. For the droplet tracking code to read in the images without error,
a colour inversion was necessary. A Gaussian filter was applied to the image to lower the
resolution to that of a video still image from a high speed camera. ”Salt and Pepper” noise
could not be applied to this image as the centroids of the noise pixels interfered with the
the tracking of the centroids of the droplets.
20

Figure 18: Third Iteration Final Representation of Droplet Growth
3.2 Testing the Droplet Detection Code
The initial objective of creating the synthetic images was to test the droplet detection
code, i.e. giving known inputs and checking if the outputs correlate. Figure 19 is a random
synthetic output image that was used to test droplet detection code.
21

Figure 19: Random Sample of Synthetic Image
The initial issue that was noted was that some of the synthetic droplets were not
extracted from the image, as seen in Figure 20. This was due to the fact that the size
of the generated reflection was above the allowed reflection size threshold of the droplet
detection code. This problem was easily rectified by creating a loop in the synthetic image
generation code that prevented the reflection from growing above the allowable threshold.
Figure 21 reflects this update.
However, this minor difficulty indicated that the droplet detection code could encounter
problems with large specular reflections once non-uniform real images were generated. At
this point it was realised that image preprocessing to refine specular reflection size and
shape would most likely be necessary.
Although it appears that the code is still not detecting all of the droplets, it should be
noted that the command ”imclearborder” is in the detection code, which clears all objects
that are in contact with the image boundary. Therefore, any droplets located in Voronoi
cells that are in contact with the image boundary are not processed.
The yellow contour curves based on pixel intensity were not plotted in this test as they
were simply overwriting the red circular approximation due to the circular nature of the
fabricated droplets. This test of the droplet synthetic code was perhaps too simplistic
as all of the input droplets were perfectly circular. A test with better scope would use
manufactured images with irregular shaped droplets as input but unfortunately that was
not within the range of this project.
Overall, Figure 21 illustrates the success of the code at identifying the location and
computing the size of droplets.
22

Figure 20: Droplet Detection of Synthetic Code Droplets with Over-Large Reﬂections
Figure 21: Droplet Detection of Synthetic Code Droplets
3.3 Creating a Historical Droplet Tracking Structure
One of the key objectives of this project involved modifying the droplet detection code
supplied by industry outlined in Section 2.10. The code initially supplied only analysed
23

each image singularly, and has no mechanism for tracking the ”family tree” of each large
end droplet. This objective is essentially creating a method of storing how the droplets
merge and coalesce.
Initially, the level set method was considered as a potential approach for building a
network that would extract topological information. The level set method is typically
used to model objects that vary with time, which was why it was originally selected for
analysis. Figure 22 was supplied by the project supervisor as a similar sample illustrating
a 3-D model of droplet coalescence, and the ability of the level set method to extract
topographical information at any time step.
Although every eﬀort was made to adapt this method to incorporate the real generated
images, the function proved too challenging to research and adapt given the condensed
time frame of the project.Therefore, a less mathematically based approach was taken, and
is outlined below.
Figure 22: Computing the Movement of Droplets Using the Level Set Method (Provided
By Supervisor)
This process began by reading in the images, converting them to binary and storing
them in a 3-D matrix. The droplet detection method is based on initially identifying droplet
reﬂections, however these regions created issues when identifying the connected regions, and
24

therefore the ”holes” left in the image by the reflections had to be filled. The results of
this for synthetic and real images are shown in Figures 23 (a) and (b) respectively.
Figure 23: Sample of (a) Synthetic Image, and (b) Real Image in Binary with Reflections
Filled
3.3.1 First Iteration
The initial objective of the first iteration was to graph the droplet growth and coalescence
and store which droplets merged in a data structure. The synthetic data whose generation
is discussed in Section 3.1 proved invaluable for this purpose, as it allowed the user to
generate images with small amounts of data (i.e. five drops, as shown in Figure 24).
The thought process behind this graphing technique was relatively rudimentary. Using
the binary images in Figure 23 and the ”bwconncomp” MATLAB command, the connected
components at each time step were identified, and the ”regionprops” command was used
to identify the pixel identities of each droplet. Utilizing this information, the droplet pixels
at each time stop were plotted as a layer on a 3-D graph as illustrated in Figure 24.
No progress was made on linking each discrete image to characterise droplet coalescence
behaviour.
25

Figure 24: Sample of First Iteration of Historical Graphing Structure
Figure 25: Sample of First Iteration of Historical Graphing Structure with Synthetic Data
The main issue that was discovered during this iteration was that the sheer volume of
data in the real images created signiﬁcant computational issues in MATLAB, and caused
the programme to crash. This method of tracking droplet coalescence was entirely too
26

computationally expensive to run on the 500 images obtained from the high speed camera.
Figure 25 was generated using synthetic images with a realistic number of droplets, and
it can be seen that the magnitude of the data causes the figure to become illegible and
useless.
Given these issues, it was decided not to pursue applying this historical storage structure
to real data, and therefore no progress was made on the data structure for storing the
coalescence data. Therefore, a second iteration was deemed necessary to overcome this
issue.
3.3.2 Second Iteration
The aim of the second iteration was to make the code less computationally expensive
and link each time step. The binary 3-D image stack was computed similarly to the first
iteration. Initially, the first two images were extracted from the array, and using the
MATLAB ”bwconncomp” and ”regionprops” command, the list of pixels in each connected
component and their corresponding centroids were found and stored in a cell array.
The centroid of each droplet on the first image was then plotted. Using a double nested
for-loop, each droplet in the first image was compared to every droplet in the second image
to check if they overlapped by comparing the pixel ID lists. If they overlapped, a line
was drawn connecting the two centroids across the ”slice” of the 3-D structure. In this
manner, it was easy to detect at which time step droplets merged, as a tree-like structure
was created, which is visible in Figures 26 and 27. The outline of each droplet was also
plotted in green for each droplet.
Figure 26: (a) XY and (b) XZ View of Historical Graphing Structure with Synthetic Data
27

Figure 27: 3-D View of Historical Graphing Structure with Synthetic Data
A binary 3-D matrix was also ﬁlled with which droplets overlapped for each time step,
and this is represented in Figure 28. Essentially, if Droplet 1 in time step 1 overlaps with
Droplet 1 in time step 2, entry (1,1) in the matrix is true. All entries where no overlap
is detected are false. This results in an identity matrix output, unless droplets overlap in
that time step. This droplet overlap phenomenon is visible in Figure 28 where both entries
(2,2) and (2,3) are true - i.e. Droplet 2 and Droplet 3 in time step 3 merge to form Droplet
2 in time step 4.
This simple binary structure enabled the user to extract information about overlapping
droplets, as entry (2,2) and (2,3) could be searched in the ”regionprops” cell array structure
to return information such as centroid, pixel ID list, area and other properties, which can
then be compared to the converged droplet, (4,2). The MATLAB script for this droplet
network is available in Appendix B.3.
28

Figure 28: (a) Second and (b) Fourth Time Step Representation of Overlapping Droplet
Matrix
3.4 Thermoelectric Rig Model
3.4.1 Thermoelectric Rig Design
Although synthetic images were modelled in Section 3.1, real data also was necessary to
test the droplet tracking code. Therefore, a thermoelectric rig was required to generate
condensation on metallic surfaces that could be photographed for analysis.
Figure 29 is a CAD representation of the model that was initially designed to be built.
The main principle of this rig is that the cold side of a thermoelectric cooler is used to
chill the sample plate. Compressed air from a cylinder is bubbled through the gas bubbler
in order to saturate the air with water vapour. This saturated air then condenses on the
chilled sample plate.
29

Figure 29: Front View of Initial CAD Model of Thermoelectric Rig
In order to operate in a stable manner, the hot side of the thermoelectric cooler is
connected to a finned heat sink. The heat sink is in turn cooled by a fan which circulates air
through a perforated plate. Stability is also to be maintained by controlling the temperature
of both the hot and cold sides of the thermoelectric cooler. The temperatures are measured
using type K thermocouples. Power supply to the thermoelectric cooler was designed to
be controlled by a PID circuit with a solid state switch, thermocouple amplifiers, and an
Arduino Mega (not pictured). The entire apparatus is constructed using M3 standoff pins.
30

Figure 30: Front View of CAD Model of Manufactured Thermoelectric Rig
The components were sized to fit a specific heat sink that was to be sourced from RS
components. However, a cheaper heat sink and fan combination became available in the
interim, and the updated CAD model that was actually built is shown in Figure 30. As
can be seen, the assembly of the heat sink and fan no longer requires a perforated plate,
which both enhanced the cooling mechanism and reduced the need for specialised parts.
Another notable modification to the initial design is the hole in the heat sink. The grounds
for this modification will be discussed in Section 3.4.2.
31

Table 2: List of Parts Required For Thermoelectric Rig
A bill of materials is shown in Table 2. The actual parts required to assemble the
thermoelectric rig differed very little from the parts specified in the interim report. Nylon
standoff pins were chosen due to their low thermal conductivity so as not to upset the
thermal equilibrium of the rig. The electrical parts mentioned were necessary for the
construction of a PID circuit to control the power supply to the thermoelectric cooler and
regulate the temperature set point. The evolution of this design will be further discussed in
Section 3.5.2. Thermal paste was also added to the bill of materials to improve conductivity
between the thermoelectric cooler and both the heat sink on the hot side and the sample
plate on the chilled side.
3.4.2 Construction of the Thermoelectric Rig
Construction of the thermoelectric rig commenced with the submission of drawings to
the engineering workshop for the manufacture of customised parts. Figures 60, 61, 63 in
Appendix A show the isometric drawings of the custom base plate, heat sink modifications
and sample plates that were submitted to the workshop initially.
The heat sink required 3 mm holes drilled to fit the M3 standoff pins. A decision was
made to manufacture the sample plates and the base plates from 2 mm aluminium sheets.
The reasoning for this was that aluminium is thermally conductive, which would allow the
32

sample plates to be adequately chilled by the thermoelectric cooler. It is also a ductile
metal which suited this purpose for furnishing each plate with a different surface finish.
In order to accurately measure the temperature of the surface of the thermoelectric
cooler, a 0.5 mm slot was initially designed to be machined into the centre of each sam-
ple plate, as illustrated in Figure 63 in Appendix A. The objective of this was to fit a
thermocouple into this slot in order to measure the temperature of the cold side of the
thermoelectric cooler for the PID temperature control circuit.
However, after significant consultation with workshop technicians, it was decided that
this slot was mechanically infeasible given the availability of tooling in the workshop due to
its small dimensions. Given that the aluminium sheet was also 2 mm thick, this machining
process could also cause the sample plates to warp and not have adequate surface contact
with the thermoelectric cooler.
After some deliberation it was decided that the most effective way to proceed was to
drill a small hole as close to the top of the heat sink as possible to measure the temperature
of the hot side of the thermoelectric cooler instead. The updated drawings that reflect these
changes to both the sample plates and the heat sink are shown in Figures 62 and 64. The
smallest hole possible with the workshop tooling was 1.2 mm. There were also issues with
the depth of the hole, as the deeper the hole, the less effective the evacuation of the chips.
A deeper hole could also result in the breakage of the drill bit or the deviation of the drill
bit from the horizontal, which could puncture the surface of the heat sink. Therefore,
complete freedom was given to the workshop technician, and a 1.2 mm hole was drilled
approximately 20 mm deep into the heat sink. Significant deliberation was also given to
the surface finish of the plates, which will be discussed in Section 3.4.3.
33

Figure 31: Parts for Building the Thermoelectric Rig
The actual construction of the thermoelectric rig was relatively simplistic once all of the
parts had been manufactured and purchased. Figure 31 shows all of the parts that were
necessary for the assembly. Figure 32 illustrates the constructed rig. As can be observed,
the rig is very neatly compiled with M3 standoﬀ pins for ease of changing the sample plate.
The base plate was also designed to replace the glass base plate in the optical microscope.
This was secured by a spring loaded mechanism, and was designed for optimal space usage
and constraint of the thermoelectric rig.
34

Figure 32: Front View of the Assembled Thermoelectric Rig
After the testing conducted in Section 3.5.1, the initial fan failed and a new fan had
to be sourced. A ’Corsair’ 120mm computer fan was used, and a duct was built out of
cardboard and tape to direct the air ﬂow through the heat sink, as shown in Figure 33.
This fan also had a rated voltage of 12 V. This design was also superior - by removing the
fan from the assembly, vibration was reduced and overall image quality was improved.
Figure 33: Thermoelectric Rig with Altered Duct and Fan
As the air from the fan was directed through the heat sink via a makeshift duct, the
35

air flow through the heat sink was also increased. The initial fan provided a complex flow
field with edge cooling, whereas the laminar flow through the heat sink via the duct from
the new fan provided more reliably uniform cooling of the heat sink which reduced the
variation between experiments. The evidence of this is the difference between Figures 37
and 38, where the initial fan produced much noisier results and less uniform cooling.
3.4.3 Sample Plate Surface Finishes
In total, six sample plates were manufactured to the same dimensions with different surface
finishes. The objective of this was to both test the limitations of the droplet tracking
code while also enabling a loose qualitative characterisation of condensation growth and
coalescence behaviour based on aspects of the different surface finishes. The manufactured
plates with varying surface finishes are shown in Figure 34.
Figure 34: Manufactured Sample Plates with Varying Surface Finishes
There were no definite surface finishes specified in the project briefing. Although signifi-
cant research was performed on potential surface finishes for aluminium (such as anodising,
powder coating, sublimation) the main factor that influenced surface choices was what was
available in the engineering workshop. Therefore, workshop technicians were consulted and
their advice was taken with regard to potential surface finishes.
Four of the six sample plates were finished with an emery cloth. An emery cloth is
defined as a coated abrasive fabric-based material with manufacturing range grains [24].
The woven cloth backing ensures that emery cloth has greater tensile strength than sand-
paper. This surface finish is applied by hand. A range of grades were applied to individual
36

surface plates. The grain size included 40 (most coarse grain size available), 80, 150 and
1200 (finest grain size available) respectively.
The final two sample plates were given a matt ”shop-blasted” finish. This is similar to
sand blasting, and involves bombarding the sample plate with abrasive media (in this case,
fine AlO particles). Compressed air is used to blast the particles at the work piece from a
specified distance and results in a uniform matt finish.
Care had to be taken when handling the sample plates to avoid contamination of the
surface finishes with oil, water or other contaminants from careless handling.
3.4.4 Optical Microscope Configuration
Figure 35: Labelled Schematic of the Light Path Through The Optical Microscope
Figure 35 schematically illustrates the experimental set-up for image collection. A diffuse
light source was aimed down one of the eyepieces. This light beam filtered through the
optical lens and reflected off the sample plate. This light travelled back up through the
lens until it reached the beam splitter, in which 50% of the light was directed toward the
eyepiece and 50% towards the camera.
Illumination and focus proved to be extremely challenging in this case, as light re-
flection off the condensation droplets was complex and the surface roughness of the metal
37

plates reflected light excessively along grooves. The procedure followed in overcoming these
challenges is outlined in Section 3.5.3.
3.5 Experimental Procedure
3.5.1 Determining Sample Plate Temperature
In order for condensation to form on the sample plate, it had to be chilled to as low
a temperature as possible using the thermoelectric cooler. Appendix D illustrates the
various performance curves for the TEC 1-2706 units. It was decided that the plate should
be chilled to as cold a temperature as physically possible with the given apparatus. From
the performance curves it was apparent that for a hot side temperature of 50◦
C with applied
voltage and current of 9 V and 3 A respectively result in a 50◦
C temperature differential
[25]. Consequently, the temperature of the chilled sample plate should theoretically reach
0◦
C.
Under the performance specifications on the data sheet for the TEC1-12706, the max-
imum allowable voltage and current respectively were listed as 16.4 V and 6.4 A [25].
Therefore, maximum current and voltage values were set on the power supply unit as 12
V and 4 A correspondingly. The power supply unit used was a ”TTi CPX400DP Dual 420
watt Power Supply”. As it had dual terminals it had the capability of supplying constant
voltage to the fan while enabling varying voltage supply to the TEC.
A brushless DC fan was initially used, which had a rated voltage of 12 V. However,
after the TEC performance was determined, this fan ceased to work. Another fan with a
12 V rating was obtained and the testing was repeated. It was decided for the purpose
of determining the TEC performance curves to supply a constant voltage to the fan while
increasing the voltage supply to the TEC by 0.5 V increments. After each incremental
increase, the system was allowed a 3 minute period to reach thermal equilibrium before the
temperature of the chilled plate and the heat sink were measured.
38

Figure 36: Experimental Determination of Chilled Sample Plate Temperature
As the Arduino thermometer circuit was not yet fully functional, a hand-held dual
output thermocouple reader was used. The temperature of the heat sink was measured
by inserting the probe into the custom drilled hole in the heat sink (as shown in Figure
62 in Appendix A). The temperature of the chilled plate was measured by a hand-held
probe applied to the centre of the surface of the plate. The entire experimental apparatus
is shown in Figure 36.
The thermoelectric rig was allowed to cool back down to room temperature and the
experiment was repeated with the fan voltage held constant at 11 V and 10 V respectively.
The experimental results were recorded in Tables 3, 4 and 5.
39

Table 3: Performance of TEC with Fan Constant at 10 V
40

Once the data was obtained and recorded, the temperature of the chilled plate against
incremental increase in voltage supplied to the TEC was plotted for each distinct fan speed.
The results are illustrated in Figure 38. It can be seen that each of the curves exhibit similar
trends, with the chilled plate temperature decreasing initially to a minimum before rapidly
increasing as the applied voltage advances. This behaviour is mimicked by the testing done
with the initial fan, which is shown in Figure 37. The results obtained from the initial
testing were much noisier, and it is assumed that this is because the initial fan provided
less consistent cooling.
The reason for this trend is fairly simplistic - up to a certain applied voltage, the heat
sink and fan are capable of immediately dissipating the generated thermal power. However,
once a certain voltage is reached the heat diffusion mechanism is not as effective, and heat
is radiated upwards towards the sample plate which results in a temperature increase.
Similar logic applies to why the conditions specified in the datasheet in Appendix D
were not achieved. In this experiment, the temperature of the hot and cold side of the
TEC were measured indirectly by the temperature of aluminium plates attached to both
sides of the TEC. As the thermal contact between the TEC and the plates is imperfect and
aluminium is not a perfect conductor, not all of the heat generated/dissipated by the TEC
was conducted through the plates.
The lowest surface temperature achieved during this experimental analysis was 6.5◦
C,
with applied voltage to the TEC of 5.5 V and the fan operating at the rated voltage, i.e.
12 V. Therefore, it was decided to adopt these parameters as the set point condition for
the circuit.
41

Figure 37: Chilled Sample Plate Temperature at Varying Initial Fan Voltages
42

Figure 38: Chilled Sample Plate Temperature at Varying Actual Fan Voltages
Figure 39 is an illustration of the temperature differential, i.e. the difference in tem-
perature (in ◦
C) between the heat sink and the chilled sample plate. Each experiment
exhibited similar results - a linear increase in temperature differential for increased applied
voltage to the TEC. This experimental analysis agrees with the data sheet curves supplied
in Appendix D.
However, the theoretical minimum of 0◦
was never experimentally achieved. This was
due to the fact that the temperature of the chilled sample plate was measured, rather than
the actual surface of the TEC. It is expected that some of the cooling power is lost to the
environment.
There were a number of observations made with regard to the accuracy of this experi-
mental analysis. Firstly, the dimensions of the heat sink and the sample plate are greater
than the dimensions of the TEC. This results in unbalanced cooling of the sample plate.
As the temperature measurements of the chilled plate were taken by hand, there may be
experimental error. Although the temperature was continually measured at the centre of
the plate, each measurement was not exactly uniform.
43

Figure 39: Temperature Differential of TEC at Varying Fan Voltages
The method of measurement of the chilled sample plate may also introduce experimental
error. The tip of the thermocouple was held against the chilled plate, and therefore only
one side of the thermocouple was directly in contact with the plate. As the other side
of the thermocouple was in contact with the air which was at a higher temperature than
the plate, the temperature recorded may have an offset error. However, as all experiments
were conducted in the same environment it is expected that all measurements have similar
offsets and therefore the trends are still valid.
3.5.2 PID Temperature Controller
The initial proposal was to construct a thermometer using an Arduino and a type K
thermocouple, measure the temperature of the TEC, send this information via serial port
to a Python code which would then be utilized to control the voltage supplied to the TEC.
The Arduino thermometer circuit was relatively simplistic to construct, as illustrated
in Figure 40. On a breadboard, the positive and negative wires from the thermocouple
were inserted into the terminals of the thermocouple amplifier. Using jumper wires, the
pins from the AD8495 chip were connected to the Arduino.
44

Figure 40: Calibrating the Arduino Thermometer with a Hand-Held Thermocouple Reader
A basic code was written in arduino to output the temperature on the serial monitor.
The analogue voltage signal was first converted to digital. The conversion from voltage to
temperature was defined by an equation given on the data sheet of the AD8495 chip:
V − 1.25
0.005
(1)
However, using this equation gave readings that were above what was expected. Using
the hand-held thermocouple reader shown in Figure 40, the thermometer was calibrated
and Equation 2 was found to be optimal.
V − 1.215
0.005
(2)
However, the thermometer was extremely temperamental and could not be relied upon
to produce accurate temperature readings consecutively. This was due to the fact that the
voltage differential between the thermocouple pins was so small that any perturbation due
to wire movement or environmental effects was then amplified. Given that the PID circuit
was to be automated, any extreme readings could cause the circuit to fail.
The PID circuit was then discarded. The temperature was to be measured using the
hand-held thermometer and manually recorded. A code was constructed using Python
45

which was designed to control the power supply unit. The voltage and current supplied to
the TEC were initially set at 5.5 V and 1.69 A respectively. The Python code queried the
actual voltage and current supplied every 3 seconds, and output the results to a text file
for each test.
The intention of this was to plot the voltage and current information over time to observe
whether the condensing droplets had any substantial impact on power requirements.
3.5.3 Gathering Experimental Data
Once the TEC requirements had been established to chill the plate adequately, experimental
data for each surface finish had to be collected in order to determine the effect of surface
finish on droplet condensation.
A ’Thorlabs’ scientific camera was attached to the top of the optical microscope, and a
lamp was directed down the eyepiece of the microscope for optimal lighting, as illustrated
in the schematic in Figure 35. Initially, the fan and TEC were set to their optimum voltage
settings - 12 V and 5.5 V respectively. Each sample plate was screwed on by hand as
illustrated in Figure 32. The camera was set to record, and output a ’.tif’ file for each
surface. A MATLAB code was then used to convert the files to ’.png’ format. A random
image from three of the datasets is shown in Figure 41. Figures 41, 42 and 43 have all had
their colours inverted for image coherence purposes.
Figure 41: Droplets on (a) 80, (b) 150 and (c) 1200 Emery Cloth Finished Metallic Surfaces
(Inverted)
As illustrated in this figure, the droplet formation was extremely unclear on each of the
metallic surfaces. Droplets could barely be picked out from each image by eye, and the
droplet tracking code would most certainly not be able to locate each droplet.
Figure 42 illustrates the next step taken in this process. A permanent marker was used
to coat a portion of each surface with water resistant ink. The experiment was repeated,
and data was collected for each surface. A marked improvement is illustrated, especially
46

in Figure 42(c), with the 1200 grade emery cloth finish. However, the other sample plates
did not exhibit such clear behaviour and were not suitable for the code.
with Marker Coating (Inverted)
As this project is attempting to characterise condensation growth as a function of
surface roughness, the surface chemistry of each piece was deemed of secondary importance.
Surface coatings were acceptable as they would maintain the peaks and troughs of the
surface. Black acrylic paint was then used to darken the surface, as it was thought that the
matt black finish would prevent the light from reflecting off the surface grooves and enable
a clearer image of each droplet. The same three surfaces coated in acrylic paint are shown
in Figure 43.
with Acrylic Paint Coating (Inverted)
As Figure 43 illustrates, the paint had a worsening effect on droplet coherence. It caused
each of the surfaces to become more hydrophilic, and condensation occurred in a filmwise
47

manner rather than forming discrete droplets. Therefore, this method was also deemed
unsuitable for data collection.
Although the project was based on condensation formation on metallic surfaces, black
insulation tape was employed to ascertain whether there would be any improvement on
image quality. With increased image exposure, droplet growth from Figure 44(a) to 44(b)
was recorded, and as is evident there was a marked improvement in droplet coherence.
These images were used to initially develop an image processing MATLAB code outlined
in Section 3.5.4.
Figure 44: Droplet Formation at Distinct Time Steps on Black Insulation Tape
After consultation with a partner in industry and analysis of the collected data, it was
decided that the more polished surfaces resulted in greater droplet coherence. Given the
time constraints on this project, image processing on images such as 42(a) and (b) would
prove too challenging.
The sample plates finished as outlined in Section 3.4.3 were modified to fit the purpose.
A technician in the materials science laboratory was consulted with regard to producing a
mirror finish on a sample plate. This task proved difficult, as the dimensions of the sample
plate were too large for the polishing wheel’s fittings. Grit paper with grit sizes 1200 and
2500 was obtained, and it was decided to re-finish two of the sample plates with varying
mirror finishes by hand.
Although one of the plates had been surface finished with 1200 emery paper already
(as outlined in Section 3.4.3), the surface finish applied by the technicians in the machine
shop was unidirectional. Therefore, this plate was refinished with 1200 grit paper in an
attempt to remove this directionality from the surface. Another sample plate was selected
and finished with 2500 grit paper.
As these plates were finished by hand, it proved difficult to apply uniform pressure over
the entire plate’s surface. Once the polishing had been performed, the surface was cleaned
with isopropyl alcohol and allowed to air dry. A patch on each surface was coated with
48

indelible ink, as this appeared to produce optimum lighting conditions (as visible in Figure
42 (c)). This patch was then cured with a heat gun and left overnight.
Both datasets were collected the same day to ensure as little fluctuation as possible in
environmental variables - the ambient temperature, pressure and water temperature were all
constant. Other variables such as distance to light source, compressed air pressure, distance
of humidified air pipe from sample plate, voltage and current applied to the TEC and fan
respectively were all controlled and kept constant over the course of the measurements.
Figure 45 illustrates the power drawn by the TEC during the course of each experiment.
The voltage and current were set by means of a Python code as described in Section 3.5.2.
A MATLAB code was designed to read the text files of voltage, current and time data and
output a power vs time graph for both sample plates, as shown in Figure 45.
Figure 45: Power Drawn by TEC During Condensation Formation
The initial slopes differ due to clamping pressure and thermal contact resistance. As
the sample plates were screwed on by hand, the tightness of each screw will have some
slight variation, which will result in irregular contact between the sample plate and the
TEC. The differing surfaces also have varying roughness which results in different thermal
contact with the surface of the TEC. These factors account for the initial discrepancy in
the power output curve slopes. As shown, the power remains constant over the course of
each experiment once the initial threshold time has passed. Therefore, it can be assumed
49

that the liquid mass accumulated on both surfaces must be roughly equal, as the thermal
flux is similar for both plates at all time steps. Figure 46 displays droplet formation on
the 1200 grit finished surface at varying time steps. Although every attempt was made to
remove the directionality from the sample plate, it is clearly visible from the anisotropic
droplet growth in Figure 46(a) and to a certain degree in (b) and (c) that the directionality
is still present. Droplets grew preferentially along the grooves, and were pinned, verifying
the literature discussion in Section 2.7.
Figure 46: Droplet Formation at Distinct Time Steps on 1200 Grit Finished Aluminium
Sample Plate
The higher polished 2500 grit finished sample plate can qualitatively be seen to exhibit
better dropwise condensation. Figure 47 shows the progression of condensation formation
over a series of time steps, and it can be seen that these droplets are more coherently
circular than Figure 46. More comprehensive image sequences for both data sets is attached
in Appendix C. Both sets of data were then analysed as described in Section 3.5.4.
Figure 47: Droplet Formation at Distinct Time Steps on 2500 Grit Finished Aluminium
Sample Plate
50

3.5.4 Experimental Data Image Processing
Due to the varying surface finishes, the data collected in Section 3.5.3 was a lot noisier and
less clean than the initial dataset shown in Figure 15 that was provided from industry. It
is assumed that the provided image series was collected on a superhydrophobic surface, as
the droplets exhibit a consistent degree of eccentricity and a much lower droplet density.
Therefore, some image preprocessing was deemed necessary before the experimentally ob-
tained images could be read accurately by the droplet detection code outlined in Section
2.10.
The image was initially loaded and converted from an RGB image to black and white
using the ’im2bw’ function. Figure 48 illustrates two initial random time step images from
the 1200 grit polished surface that were read into the code and converted to binary. Otsu’s
method was then employed to return a single threshold value for the image, separating the
foreground and background pixels. MATLAB’s ’imquantize’ function used this threshold
value to segment the image into two regions.
Figure 48: Unprocessed Images at Distinct Time Steps Represented In Binary
A morphological structural element was then created. A disk was selected in this case,
due to the typical droplet structure. The disk is a binary value neighbourhood in which the
’true’ pixels are included in the morphological operation and the ’false’ pixels are excluded.
Once this structural element is selected, it is used to morphologically close the image (this
is a mathematical concept in which ’closing’ is defined as the erosion of the dilation of the
binary image). It is an effective technique in image processing as it manages to eliminate
much of the noise in the image, as can be seen by comparing the images in Figure 49 to
the unprocessed images displayed in Figure 48.
Much of the noise in these images were microscopic droplets, and therefore removing
them is technically altering the dataset. However, this was deemed an acceptable action as
51

these droplets are much smaller than the average droplet size at a particular time step, and
therefore upon merging with a larger droplet their effect was almost imperceptible. A 2-D
filter was then applied to the image in an effort to further reduce noise, with each output
pixel containing the median value of the surrounding eight pixels.
Figure 49: Morphologically Closed Images at Distinct Time Steps
An issue that had arisen when attempting to read the unprocessed images into the
droplet detection code was that often the specular reflections were oversized (as suspected
when testing the droplet detection code with the synthetic images in Section 3.2) and
irregularly shaped, and the detection code classified the reflections as background, especially
in the images where the droplets were larger. Therefore, the centroids of all reflections were
identified, the reflection binary values set to zero and redrawn as uniform circles. This step
was possible as it was not affecting the actual droplet size or shape. The effect of this
process is visible in Figure 50. Finally, the binary image was stacked and output in RGB
format. The code used for this purpose is attached in Appendix B.4.
52

Figure 50: Images with Uniform Circular Specular Reﬂections at Distinct Time Steps
53

4 Experimental Results
The preprocessed images and the raw images for both the 1200 and 2500 grit finished
sample plates were read in to the droplet detection code. The droplet detection code
had undergone a few minor adjustments, including outputting a text file with the average
droplet radius and number of droplets for each time step. The same time steps were selected
for all analyses.
The droplets were initially too small to detect the specular reflections, and therefore the
55th image of each data set was selected as the first time step. Data was analysed for the
first 30 time steps, as beyond this the droplets were overly large and the droplet detection
code had difficulty with detecting specular reflections.
The yellow contour curves initially in the droplet detection code were removed as they
were proving inaccurate at estimating droplet shape for these surfaces. The calculation for
average droplet radius was based on averaging the radii of the red circular approximations
for each time step.
Figure 51: Graph of Average Droplet Radius (in Pixels) Vs Time Step
54

Figure 51 illustrates the average droplet radius per time step for each sample plate for
both the raw and preprocessed images. The manual measurements were taken for the first,
middle, and last time steps using ’ImageJ’ image processing software.
Figure 52 exhibits the data collected for number of droplets in each image for each time
step. Similarly to Figure 51, data points are plotted for raw images, preprocessed images,
and manually measured using ImageJ for both surfaces.
Figure 52: Graph of Number of Droplets Vs Time Step
The minimum and maximum droplet radius along with both the first and third quartile
data were also extracted for each time step from the droplet detection code. This data
was used to create box plots of the range of droplet radius in the unprocessed images and
the preprocessed images. Figure 53 and 54 illustrate this data for the 1200 and 2500 grit
finished sample plates respectively.
55

Figure 53: Box Plot Spread of Droplet Radius Vs Time Step for 1200 Grit Finished Sample
Plate Processed and Unprocessed Images
56

Figure 54: Box Plot Spread of Droplet Radius Vs Time Step for 2500 Grit Finished Sample
Plate Processed and Unprocessed Images
A contact angle goniometer was employed to measure the contact angle of the water
droplets on each of the surfaces. A dropper was used to place water droplets of the same
volume on each surface, and the sample plates were then photographed as illustrated in
Figure 55. Although the ’Ossila’ software offered an analysis option, ’ImageJ’ was employed
to measure the contact angles. Ten images were taken for each sample plate, and their
average contact angle was measured. The average contact angle for the 1200-grit finished
surface was 47.84025◦
, and 88.4883◦
for the 2500-grit finished surface.
57

Figure 55: Illustration of Contact Angle for (a) 1200-Grit Finished Surface, and (b) 2500-
Grit Finished Surface
4.1 Limitations
Prior to coming to a conclusion based on the graphs in Section 4, there are a number of
factors that need discussion and clarification. Firstly, the difference in the processed and
unprocessed images in the droplet detection code for the 1200 grit finished sample plate is
illustrated in Figure 56. The Voronoi diagram decently segments the image for each discrete
droplet in both images. However, there are significantly more droplets inaccurately detected
in the unprocessed image due to noise. Although the processed image misses a few droplets
with overly large reflections, it provides a much better approximation.
58

Figure 56: Droplet Detection Code Output for (a) 1200 Grit Unprocessed Image, and
(b)1200 Grit Processed Image
Similar logic should be applied to the average droplet radius. Figure 56(a) shows little
coherent detection of droplet size. Although 56(b) also contains some inaccurate approx-
imations, the overall average area approximation is significantly more precise. Therefore,
the line in Figures 51 and 52 that represents the 1200 grit finished sample plate unprocessed
image should be disregarded.
Figure 57 illustrates the droplet detection code output for the 2500 grit polished sample
plate for the unprocessed and processed images respectively. The data collected from these
image series would appear to be significantly more similar and accurate than for the 1200
images. Both datasets appear to detect both a similar number of droplets and accurately
approximate droplet area.
59

Figure 57: Droplet Detection Code Output for (a) 2500 Grit Unprocessed Image, and
(b)2500 Grit Processed Image
Another limitation imposed on the results includes the basis for the average droplet
radius calculation. The droplet radius for each droplet is calculated from the red circu-
lar approximation for that droplet. Given that the droplets are irregularly shaped, this
approximation for the radius should be treated with due caution.
As discussed in the droplet detection code breakdown outlined in Section 2.10, the
’imclearborder’ function is used to clear all data in contact with the image boundaries.
This could adversely affect image comparison, especially in the droplet nucleation stage
where there may be a high density of small droplets. As this issue affects all images, in the
course of this analysis it is assumed that its effects are equal and may be disregarded.
60

5 Discussion and Conclusions
Figures 51 and 52 illustrate trends that are significant from both a droplet detection code
accuracy and material surface finish approach.
Firstly, Figure 51 illustrates a general trend for all data - with increasing time step, the
average droplet radius per image increases. This was expected, as an increase in elapsed
time increased the probability that a given droplet would have merged and coalesced with
its neighbouring droplets. As discussed in Section 4.1, the line representing the 1200 grit
finished sample plate’s unprocessed images will be disregarded due to the significant level
of error.
However, there is also a significant discrepancy between the average radius measured
from the raw and preprocessed images for the 2500 grit finished plate. This result was
surprising, as Figure 57 would seem to indicate that both images would have a similar data
output.
In order to better discuss this discrepancy, ImageJ (an open source scientific image
processing programme) was employed to manually measure the radii of the droplets. Each
droplet was approximated by a hand drawn ellipse. The ellipse area (in pixels) was calcu-
lated using the inbuilt ’Measure’ function, and then the radius of the equivalent circular
droplet was computed by simply using the equation fo a circle, i.e. radius = Area
Π
.
Given the tedium and time required for this task, manually measured data was only
obtained for the first, middle and final time step. Figure 51 shows that for the 1200
data, the average radius measured manually agrees completely with the output from the
droplet detection code for the preprocessed image series. For the 2500 data, if the manually
measured trend is approximated as linear, the actual average droplet radius lies between the
raw and preprocessed image plots. Therefore, no conclusive evidence can be drawn from this
graph as to whether the preprocessed or raw image data provides a better approximation
of average droplet radius.
The number of droplets identified per time step is similarly plotted in Figure 52. The
1200 grit finished plate preprocessed image data agrees with the ’ImageJ’ manual mea-
surements, further validating the above claim that this data is accurate. The number of
droplets recognised for both of the 2500 data sets agree closely for all time steps. How-
ever, the manually counted number of droplets for the initial time step far exceeds either
approximation. Figure 58 shows that there are still a significant number of microdroplets
at this stage that have no specular reflection and are therefore not detected as droplets.
Although the approximation improves with time, this is a significant limiting factor on the
conclusions that can be drawn from both the raw and preprocessed image data for the 2500
grit finished surface.
61

Figure 58: Droplet Detection Code Output for First Time Step of 2500 Grit Finished
Unprocessed Images
The box plots in figures 53 and 54 illustrate the spread of droplet radius for each time
step for both data sets. In all four data sets, it is immediately clear that the data is skewed
right - i.e. the upper 50% of the data has a wider range for each image series. A theory
that could explain this asymmetry is the tendency of the droplet detection code’s circular
approximations to overestimate the droplet size, sometimes wildly, as seen in Figures 56
and 57, whereas an under-approximation is rare.
There is no significant evidence in any of the box plot series that the range of droplet
radius approximation changes with time. The general conclusion that can be drawn from
this is twofold - firstly, the droplet detection code’s estimate of radius has similar accuracy
for each time step. Secondly, the underlying trend would indicate that there are a variety
of differently sized droplets present at each time step, while the average droplet size slowly
increases as time elapses.
In terms of the effect of surface roughness on average droplet radius, it is apparent
from Figure 51 that the average droplet radius on a 1200 grit finished aluminium surface is
greater at each time step. The manual measurements would appear to indicate that droplet
radius increases at a similar rate for both surface finishes. However, the output from the
droplet detection code would indicate that the 2500 grit finished surface causes droplets to
grow at a slower pace.
62

As discussed in the literature review in Section 2, rougher surfaces tend to be more
hydrophilic (with the exception of the superhydrophobic roughened surfaces discussed in
Section 2.9). Therefore, droplets on a rougher surface will exhibit a lower contact angle,
and for a similar mass of condensate will occupy a greater surface area (i.e. have a greater
droplet radius).
This is approximately experimentally observed, but more experimental data would be
required in order to reach a definitive conclusion. This theory is strengthened by the contact
angle data presented in Figure 55, with the average contact angle measured as 47.84025◦
and
88.4883◦
for the 1200- and 2500-grit finished surfaces respectively. The contact angle for the
2500-grit finished surface was observed to be very close to the hydrophilic-to-hydrophobic
transition angle of 90◦
discussed in Section 2.4.
The effect of surface roughness on the number of droplets also appears significant. The
more accurate manually measured data for the 2500-grit polished surface indicates that the
number of droplets decreases polynomially with increasing time step, with a similar trend
to a lesser degree exhibited by the 1200-grit finished surface. This trend is explained by
droplet density - as illustrated for both surfaces in Figures 46 and 47, the droplet density
at earlier time steps is significantly greater than at later time steps. With greater droplet
density, there is greater droplet activity as it takes a smaller incremental increase in droplet
radius to impinge on another nearby droplet, causing merging and coalescence.
The number of droplets on the 2500-grit finished surface decreases more dramatically
with each time step. This is due to the fact that the droplet density is significantly greater
than the 1200-grit finished surface, and therefore there is a greater probability of droplets
merging. According to the literature reviewed in Section 2, condensation formation on more
hydrophobic surfaces tend to exhibit ’mobile coalescence’ behaviour, as merging becomes
more dynamic as a droplet in motion impinges on a static droplet, powered by the surface
energy released upon the coalescence of neighbouring droplets.
This phenomenon could be applicable to the 2500-grit finished surface, as it is clear from
Figures 47 and 55 that this surface has a high surface energy as it exhibits a low wettability,
and its contact angle approaches the hydrophobic threshold. However, a camera with a
higher resolution and a higher frame rate would be required to reach this conclusion.
In conclusion, the droplet detection code exhibits an acceptable method of collect-
ing condensation formation data. Although further work is required on both the image
processing and the droplet detection code itself (improvements are discussed in Section
6), reasonable data can be extracted from the obtained images. As discovered using the
’ImageJ’ image processing software, manually obtaining data would have significant time
requirements and is not practically feasible, especially for large data sets.
Although there is room for significant code enhancements, especially of the historical
storage structure of droplets and increasing the robustness of the image processing and
droplet detection code, the coding principles developed during the course of this exper-
imental analysis can be expanded to form a basis for a more detailed investigation of
condensation behaviour on metallic surfaces.
The conclusion that can be reached with regard to the effect of surface roughness on
63

condensation formation is that there appears to be a link between surface roughness and
both droplet radius and number of droplets on the surface. The more polished surface
forms a greater density of smaller droplets which coalesce at a faster rate, and a rougher
surface exhibits greater wettability. However, as only a single data set for each surface was
investigated, these trends are not entirely robust. The experiment should be repeated for
more significant results.
The real-life application of this would be that more polished surfaces should be selected
for applications such as the HVAC units discussed in Section 2. As more polished surfaces
tend to exhibit a lower wettability (droplets have less affinity for the surface) and droplets
are smaller and tend to coalesce at a faster rate, this would enhance the effectiveness of
condensation collection mechanisms (such as condensate removal due to gravity) discussed
in Section 2.8. This in turn would lead to less moisture in HVAC units, and a potential for
reducing sick building syndrome, as less moisture would be circulated in air conditioning
systems.
64

6 Further Work
Given the complexity of this project, there is significant potential for further work. Firstly,
the condensation growth simulation detailed in Section 3.1 could be further developed
to better imitate realistic droplet growth. The current model outputs perfectly circular
droplets which is not consistent with the data collected, although it did prove useful for
testing the droplet detection code and developing a historical storage structure.
Secondly, the historical storage structure developed during the course of this project was
rather rudimentary and has not undergone significant testing with real datasets. Although
the visual depiction in Figure 27 appears adequate, the lines connecting droplet centroids
are a feature of MATLAB’s figures and the data points are not connected in the underlying
structure. Graph theory should be investigated as a method of improving the network of
this structure. As previously discussed in Section 3.3, the level set method should also be
adapted as a method of extracting topological information from the image series.
Although sample plates with varying finishes were machined as described in Section
3.4.3, Figures 41, 42 and 43 illustrate the difficulty that was noted in collecting readable
data from these sample plate finishes. As this difficulty was not envisaged, time constraints
did not allow for developing a method for collecting usable data although every effort was
made, as described in Section 3.5.3. Collection of data from different surface finishes
would broaden the project’s scope and enhance material selection based on condensation
characteristics.
The image processing algorithm was also not sufficiently developed. As a binary image
was output for the droplet detection code to read, all of the complexities of the initial image
were lost during processing. Although this was suitable for the purpose of determining
average droplet radius and number of droplets, all of the depth of the initial image was
lost which would hinder a deeper analysis. Although some image processing is necessary,
a more subdued approach would remove less of the image characteristics.
The overall area for further work that would be most beneficial is actually in the droplet
detection code that was supplied by industry. This algorithm was developed for a particular
dataset of smooth data. It is currently not very robust to noise, and droplet detection
based on specular reflections has proved to be cumbersome. Perhaps an approach based
on identifying the centroid of each component would be more suited to this purpose. The
yellow adaptive contour lines illustrated in Figure 14 were removed from the code for the
datasets obtained during this experimental analysis, as the droplet density of the images
obtained experimentally was much greater than the provided images, and this exceeded
the capability of the adaptive contour. The level set method could also be investigated for
use in determining the exact shape of each droplet.
65

A Thermoelectric Rig Isometric Part Drawings
Figure 59: Isometric Drawing of Completed Thermoelectric Rig
66

Figure 60: Isometric Drawing of Base Plate
67

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