J. Adhesion Sci. Technol., Vol. 20, No. 12, pp. 1333–1343 (2006)
Also available online - www.brill.nl/jast
Spreading of liquid drops over solid substrates:
‘like wets like’
ABDULLATIF M. ALTERAIFI ∗
and BASHAR J. SASA
Department of Mechanical Engineering, UAE University, P.O. Box 17555, Al-Ain, United Arab
Received in ﬁnal form 3 July 2006
Abstract—The classic hydrodynamic wetting theory leads to a linear relationship between spreading
speed and the capillary force, being determined only by the surface tension of the liquid and its
viscosity. Both equilibrium and dynamic processes of wetting are important in adhesion phenomena.
The theory appears to be in good agreement with the results generated from experiments conducted on
the spreading of poly(dimethylsiloxane) (PDMS) on soda-lime glass substrate and fails to account for
the behavior of other liquids. In this study, the spreading kinetics of four different liquids (hexadecane,
undecane, glycerol and water) was determined on three different solids, namely, soda-lime glass,
poly(methyl methacrylate) (PMMA) and polystyrene (PS). Droplets from the same liquid allowed to
spread under identical conditions on three different substrates produce distinctly different behaviors.
The results show that the equilibrium contact angles are qualitatively ranked in accordance with the
critical surface tension of wetting (γc) of the respective solid, i.e., high-γc solids caused the low surface
tension liquids to assume the least equilibrium spreading (largest contact angle). On the other end,
low-γc solids with the lowest surface tension liquid produce the most wetting (smallest contact angle).
The results suggest that equilibrium spreading could be explained on the basis of the axiom ‘like wets
like’; in other words, polar surfaces tend to be wetted by polar liquids and vice versa.
Keywords: Droplet; spreading kinetics; surface tension; partial wetting.
Spontaneous spreading of liquids over solid surfaces (‘wetting’) is unquestionably
an important phenomenon, which is associated with several important technologies,
such as coating and adhesion. Both equilibrium and dynamic processes of wetting
are essential in these technologies. Moreover, wetting is a fundamental prerequisite
for several applications; for example, in paint ﬁlms, composites, adhesives, paper
∗To whom correspondence should be addressed. Tel.: (971-50) 631-2100. Fax: (971-3) 762-3158.
1334 A. M. Alteraiﬁ and B. J. Sasa
manufacture, printing, ﬁber manufacture, pharmaceutical tablets, cosmetics, deter-
gency, water puriﬁcation and oil recovery. In addition, it is important in a number of
biological applications, e.g., cell separation, cell adhesion and attachment, bacterial
adhesion to tooth surfaces, marine fouling and phagocytosis.
Attempts to model the spreading kinetics have been pursued through various
scientiﬁc disciplines, most prominent of which being physical chemistry and ﬂuid
dynamics. Recent reviews of the literature on spreading dynamics by Marmur ,
de Gennes  and several other contributors to a more recent book edited by Berg
 attest to the continual interest in the subject.
Several theories deal with the spreading kinetics of liquids on solid substrates,
most of which relate the rate of spreading to the surface tension, and the viscosity
of the liquid only. De Gennes’ model , Tanner’s model  and that proposed
by Seaver and Berg  expressed the rate of spreading in terms of surface
tension and viscosity. Nevertheless, surface tension and viscosity are properties
of the spreading liquid, whereas spreading of liquids on solids is an interfacial
phenomenon involving all three interfacial tensions, i.e., liquid–vapor (surface
tension), solid–vapor and solid–liquid. Indeed Young’s equation describes a system
of interfaces in terms of three interfacial tensions. The present theory, in general,
appears to be in good agreement with the results obtained from experiments
conducted on the spreading of poly(dimethylsiloxane) (PDMS) over soda-lime
glass substrate and fails to account for the behavior of other liquids or spreading
on other solids. The phenomenon essentially entails solid–liquid and solid–vapor
interactions, which suggests that their role should be explored.
The molecular kinetic theory was earlier proposed by Blake and Haynes . They
assumed that the leading contribution to the dissipation during spreading was due
to the adsorption and desorption of molecules within the three-phase zone near the
wetting line. According to Blake and Haynes , the velocity of the wetting line
is then characterized by K, the frequency of molecular displacements, and λ, the
typical length of each molecular displacement. They have established a relationship
between the equilibrium contact angle and the velocity of the wetting line.
The evidence in the literature suggests that the solid substrate plays a key role
in spreading kinetics. For example, it was noted that PDMS droplets exhibited
spreading kinetics on soda-lime glass that was very different from that on Teﬂon .
Also in Hoffman’s experiments  PDMS was found to spread readily on the glass
surface, unlike the two other liquids, ‘Admix-760’ and ‘Santicizer-405’ (Ashland
Chemical, Dublin, OH, USA). To induce these liquids ‘to give a large static
contact angle as desired’, the glass surface was altered by a vigorous chemical and
thermal treatment. These experimental evidences suggest that solids indeed play an
important role in the spreading kinetics of a liquid. This role is in fact described
in Young’s equation in term of the solid–liquid interfacial tension. This arises from
the molecular interaction between liquids and solids.
This paper examines the role played by the solid substrate in the equilibrium
spreading of liquid droplets. The set of experiments in this study used different
Spreading of liquid drops over solid substrates 1335
types of liquids with different surface tension and viscosity values on three different
solid substrates (glass, poly(methyl methacrylate) (PMMA) and polystyrene (PS)).
The experimental setup is shown in Fig. 1. To conduct the experiment, the liquid
was charged into a 5.0-µl syringe (SGE International, Australia). The syringe was
attached to a metal stand and suspended vertically by a micromanipulator on top of
the glass slide. The micromanipulator was used to adjust the position of the needle
tip of the syringe carefully above the clean glass slide. The tip of the syringe was
positioned a few micrometers from the surface of the glass to eliminate impact effect
when the droplet was released. The droplet volume was selected to be 1.5 µl so,
that gravity effect was negligible .
The solid substrate was placed on an optical stand within the focus of a half-
inch CCD digital video camera (JVC TK-c1380, Japan), with 10× eyepiece
magniﬁcation, placed underneath the glass slide. The camera was connected to a
video recorder, which, in turn, was connected to an image analysis system (Analysis
Soft Imaging System, Germany). Each data point represents an average value of at
least ten measurements. The standard deviation calculated for each data point was
found to be less than 6%. All experiments were carried out at ambient conditions,
i.e., 25 ± 1◦
C and 47 ± 3% RH.
Figure 1. Sketch of the experimental setup for contact area measurements.
1336 A. M. Alteraiﬁ and B. J. Sasa
List of liquids used and their viscosity µ, and surface tension γ
Liquid µ (cP) γ (mN/m)
Undecane 1.1 29.0
Hexadecane 3.1 32.1
Glycerol 954 67.6
Water 0.9 72.2
The viscosity data were obtained from .
Solid surfaces used and their γc values 
Solid γc (mN/m)
Soda-lime glass 70
Poly(methyl methacrylate) (PMMA) 39
Polystyrene (PS) 33
2.1.1. Liquids. Table 1 lists the liquids used in the study. All were chemical
grade liquids obtained from Fluka (Buchs, Switzerland). Deionized water with a
resistivity of 18.2 M /cm was used in the study. As seen from the table, the surface
tension values ranged from 29.0 mN/m to 72.2 mN/m. Surface tension values were
measured with the torsion balance technique using a device obtained from White
Electrical Instruments (London, UK). The measurement accuracy ranged within
0.5% error, and veriﬁed with published results in the literature . The viscosity
values ranged from 0.9 cP to 954 cP .
2.1.2. Solids. Table 2 lists the solids used in the study: soda-lime glass,
poly(methyl methacrylate) (PMMA) and polystyrene (PS). The critical surface
tension (γc) values ranged from 33 mN/m to 70 mN/m. The γc values were obtained
using the Zisman approach  using a series of non-polar and non-volatile liquids,
and were in agreement with published results in the literature .
The dry soda-lime glass slides (26 × 26 mm) (Menzel-Glaser, Geschnitten,
Germany) were cleaned by immersing in chromic acid solution for 4 h followed
by a thorough rinsing with distilled water and were further cleaned with acetone
(99.5% purity, Panreac, Barcelona, Spain). The clean slides were subsequently
dried in a vacuum oven at 70◦
C for 30 min, at the end of which the slides were
allowed to cool under vacuum. Subsequently, the slides were carefully transferred
to a desiccator, where they were stored until used. Each cleaned, dried glass slide
was used only once. The effectiveness of cleaning and drying procedures on the
cleanliness of glass surface morphology was assured by examining the slides before
and after cleaning using a Scanning Electron Microscope (Jeol JSM5600, Japan)
at 5000× magniﬁcation. The quality of surface roughness and heterogeneity was
inspected by measuring contact angle hysteresis on cleaned soda-lime glass surface.
Spreading of liquid drops over solid substrates 1337
The contact angle hysteresis was determined by taking the difference between the
advancing and the receding contact angles values. For water on soda-lime glass
surfaces, the measured contact angle hysteresis was found to be 6–7◦
slides were obtained from a commercial source. PMMA slides were immersed in
ethanol for 2 h. The slides were rubbed gently with a soft sponge to get rid of
adhesive layer. Subsequently, the slides were rinsed with DI water and immersed
in DI H2O for at least 5 min. Finally, the slides were allowed to dry in fresh air
just before the start of the experiment. The effectiveness of the cleaning procedures
on the cleanliness of the PMMA surface was assured by examining sample slides
before and after cleaning using SEM at 5000× magniﬁcation. The quality of surface
roughness and heterogeneity was determined by measuring contact angle hysteresis
on cleaned PMMA surface. The measured contact angle hysteresis for water on
PMMA surfaces was approximately 7◦
A clean lab sheet of polystyrene obtained from Barloworld Scientiﬁc (Stafford-
shire, UK) was used in this study. Sheets were examined under an SEM to make
sure that the surfaces were free from any residues and were smooth. The measured
contact angle hysteresis for water on polystyrene surfaces was approximately 6◦
should be pointed out that although the solid surfaces used in this study were very
smooth, they may still have a very small percentage of chemical heterogeneity prob-
ably due to contamination from the coating material or dust in the air. This might
be the cause for the observed contact angle hysteresis.
2.2. Measurements and analysis
The experimental measurements were based on liquid/solid contact area. The
contact area is the printout of experimental measurements for the liquid drop
over solid substrate for different time intervals. The image analysis system was
initially calibrated by measuring the distance between the lines of a recorded stage
micrometer. The images (frames) were grabbed by the image analyzer from which
the contact area was digitized and measured as a function of time.
3. RESULTS AND DISCUSSION
Before discussing the experimental results obtained, it is important to ascertain
that droplet volume was conserved and thus evaporation losses were negligible.
Additionally, gravitational forces should be considered.
For incompressible liquids, the conservation of volume for the duration of the
experiment was veriﬁed using the following equation, which is based on spherical
θ = R3
f θf, (1)
where Rf and θf are the ﬁnal equilibrium contact radius and ﬁnal equilibrium contact
angle, respectively. Figure 2 shows cosine of the contact angle which is obtained
1338 A. M. Alteraiﬁ and B. J. Sasa
Figure 2. Cosine of contact angles for the liquids used in this study plotted in terms of equation (1)
to verify that evaporation losses are negligible during the experiment.
using spherical cap approximation plotted versus cos(R3
), which is measured
experimentally. A straight line with a slope of unity demonstrates clearly that
volume of the droplet for all liquids was conserved at least for the duration of the
experiment and that evaporation losses were indeed negligible.
The importance of gravity relative to capillary forces was inspected using the
Bond number, Bo :
where g is the gravity acceleration, Ro is the radius of the spherical droplet before
spreading and ρ is the liquid density. The Bond number was found in the range
between 0.115 and 0.362 for the liquids used in this study. Since Bo < 1, capillary
forces were expected to dominate gravity. The hydrodynamic theory is valid when
the surface tension and viscous forces are dominant, as it basically considers that
the capillary driving forces are compensated by the viscous damping forces. In this
study, the inertia effects were negligible because of the low values of both Reynolds
number and Weber number.
First we examine the spreading kinetics of low surface tension liquids on the three
solid substrates. Hexadecane and undecane were selected for their relatively low
surface tension values of 32.1 and 29.0 mN/m, respectively. In addition, hexadecane
and undecane have a non-polar character and are known to exhibit incomplete
spreading on soda-lime glass . Figures 3 and 4 show the spreading kinetics
of these liquids on the three solids.
Spreading of liquid drops over solid substrates 1339
Figure 3. Typical data for hexadecane spreading on glass, PMMA and PS.
Figure 4. Typical data for undecane spreading on glass, PMMA and PS.
1340 A. M. Alteraiﬁ and B. J. Sasa
Contact areas (cm2) and contact angle values (degrees) for hexadecane and undecane (low surface
tension liquids) on glass, PMMA and PS
Liquid Solid Contact Contact Tanner’s R2
area angle constant C
(cm2) (equation (3))
Hexadecane Glass 0.081 23.9 0.131 0.992
PMMA 0.141 11.5 0.164 0.996
PS 0.205 6.5 0.187 0.997
Undecane Glass 0.272 4.3 0.210 0.996
PMMA 0.385 2.6 0.244 0.966
PS 0.407 2.4 0.263 0.976
The major attribute characterizing the spreading process is the equilibrium contact
area. Noting that a constant volume droplet (1.5 µl) was used in all experiments, the
equilibrium contact area may be taken as a measure of wettability. The macroscopic
shape of the spreading droplet may be approximated by spherical cap geometry .
This approximation has been used to relate the contact angle to the radius and the
volume of the spreading droplet, i.e., the droplet height h = 0.5Rθ and its volume
V = 0.5πhR2
. Accordingly, it is also possible to calculate the corresponding
contact angle based on the spherical cap relationship, i.e.,
θ = 4V/πR3
where V is the droplet volume and R is the radius of the contact area. Estimates
of the equilibrium contact area drawn from Fig. 3 for hexadecane and Fig. 4 for
undecane and the corresponding contact angles are summarized in Table 3.
Several theoretical models [2, 4, 5] which describe the spreading of PDMS on
soda-lime glass substrate are found to be in good agreement with the experimental
measurements. These models which are derived on basis of different theoretical
considerations give rise to closely similar results, in what appears to be the power
law relation . Considering the most commonly referenced model, Tanner’s law
described the kinetic data in terms of the power law relation. The law is based on
hydrodynamic considerations accounting for the surface tension γ and the viscosity
µ of the liquid . Tanner’s law:
D = C
where θD is the dynamic contact angle, U is the interline velocity and C is a non-
dimensional parameter that has to be determined empirically, was ﬁrst formulated
to describe the case in which equilibrium contact angle of liquids against the solid
was zero. This led to a spreading law of the form:
R = Ct0.1
Spreading of liquid drops over solid substrates 1341
Figure 5. Typical data for glycerol spreading on glass, PMMA and PS.
Later modiﬁcation, however, to account for the effect of the solid substrate under
conditions of partial wetting, led to a shifted Tanner’s law, of the form:
D − θ3
f = C
where θf is the ﬁnal equilibrium contact angle. Tanner’s constants C for the
spreading of hexadecane and undecane (Figs 3 and 4) are listed in Table 3. The
experimental values of C are in agreement with Tanner’s theory (R2
Different contributions of different solid substrates to the wetting process are
evident. Equal droplets from the same liquid allowed to spread under identical
conditions on three different substrates produce distinctly different behaviors.
Expectedly, the equilibrium contact angles (Table 3) may be qualitatively ranked
in accordance with the critical surface tension of wetting (γc) of each respective
solid. Glass caused hexadecane and undecane to assume the least equilibrium
spreading (largest contact angle). On the other end, PS, with the lowest γc, produced
the most wetting (smallest contact angle). PMMA produced an intermediate effect.
It is useful to bear in mind that hexadecane and undecane are non-polar, low
surface tension liquids as is the case with polystyrene. Therefore, it is reasonable
to introduce the axiom ‘like wets like’ to rationalize the equilibrium wetting of
hexadecane and undecane on the three solids. This axiom is coined in analogy to
the famous rule ‘like dissolves like’ in physical chemistry.
Secondly, we examine the spreading behaviors of glycerol and water on soda-
lime glass, PMMA, and PS, which are shown in Figs 5 and 6. These two liquids
1342 A. M. Alteraiﬁ and B. J. Sasa
Figure 6. Typical data for water spreading on glass, PMMA and PS.
Contact areas (cm2) and contact angle values (degrees) for glycerol and water (high surface tension
liquids) on glass, PMMA and PS
Liquid Solid Contact Contact Tanner’s R2
area angle constant C
(cm2) (equation (3))
Glycerol Glass 0.086 26.5 0.104 0.968
PMMA 0.042 70.6 0.082 0.964
PS 0.032 104.5 0.071 0.963
Water Glass 0.076 29.3 0.110 0.967
PMMA 0.049 55.8 0.093 0.977
PS 0.036 88.2 0.078 0.982
have high surface tension of 67.6 and 72.2 mN/m, respectively. Estimates of the
equilibrium contact area derived from Fig. 5 for glycerol and Fig. 6 for water and the
corresponding contact angle values are summarized in Table 4. Tanner’s constants C
for the spreading of glycerol and water (Figs 5 and 6) are listed in Table 4. Hence,
for the determined values of C, the experimental measurements are in agreement
with Tanner’s theory (R2
Noting that glycerol and water are relatively high surface tension liquids, the
axiom ‘like wets like’ appears to rationalize qualitatively the equilibrium spreading
of glycerol and water on the same set of solid substrates. The largest equilibrium
Spreading of liquid drops over solid substrates 1343
spreading (smallest contact angle) was noted on glass, the least on PS and on PMMA
it was intermediate.
Hexadecane and undecane, low surface tension liquids, were found to exhibit
equilibrium wetting that was proportional to the γc of the solid substrate. Glycerol
and water, high surface tension liquids, were found to exhibit equilibrium wetting
that was inversely proportional to the γc of the solids. These observations are related
to Young’s equation, where
cos θ = (γSV − γSL)/γLV, (7)
provided that γSV is somehow related to Zisman’s γc (the critical surface tension of
wetting). In a pragmatic sense, ‘like wets like’ seems to work.
The present investigation provides experimental evidence that the solid substrate
plays a signiﬁcant role in determining equilibrium contact angle. Results show that
hexadecane and undecane, low surface tension liquids, exhibit equilibrium wetting
that is proportional to the γc of the solid substrate. Similarly, glycerol and water,
high surface tension liquids, were found to exhibit equilibrium wetting that was
inversely proportional to the γc of the solids. Therefore, the axiom ‘like wets like’
appears to rationalize the equilibrium wetting of both types of liquids on all three
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