Mixing of Immiscible Liquids

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-MIX-704

Mixing of Immiscible Liquids

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Process Engineering Guide:

Mixing of Immiscible Liquids

CONTENTS

SECTION

0

INTRODUCTION/PURPOSE

2

1

SCOPE

2

2

FIELD OF APPLICATION

2

3

DEFINITIONS

2

4

EQUIPMENT

2

4.1
4.2
4.3

Agitated Tanks
Flow Mixers
'High Shear' Mixers

2
2
2

5

SYSTEM PHYSICAL PROPERTIES

3

5.1
5.2
5.3

Density
Viscosity
Interfacial Tension

3
4
4

6

STIRRED VESSELS

4

6.1
6.2
6.3
6.4
6.5

Design for Complete Dispersion
Prediction of Phase Inversion
Design for Mass Transfer
Design for Dispersed Phase Mixing
Hold-Up in Continuous Vessels

4
5
5
6
6


7

FLOW MIXERS

6

7.1
7.2

Design for Turbulent Conditions
Design for Laminar Conditions

7
12

TABLES
1

REYNOLDS NUMBER RANGES

7

FIGURES

1

STANDARD TANK CONFIGURATION

3

2

EXPERIMENTAL RELATIONSHIP BETWEEN MASS
TRANSFER COEFFICIENT AND POWER DENSITY

10

DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

14


0

INTRODUCTION/PURPOSE

This Guide is one in a series of Mixing Guides and has been prepared for GBH
Enterprises.

1

SCOPE

This Guide deals with the mixing of immiscible liquids in agitated vessels and
flow (or motionless, static) mixers. It does not cover other mixing devices such as
multi-stage extractors or 'high shear' mixers.

2

FIELD OF APPLICATION

This Guide applies to Process Engineers in GBH Enterprises worldwide.

3

DEFINITIONS

No specific definitions apply to this Guide.
With the exception of terms used as proper nouns or titles, those terms with initial
capital letters which appear in this document and are not defined above are
defined in the Glossary of Engineering Terms.

4

EQUIPMENT

4.1

Agitated Tanks

Agitated stirred tanks may be used as reactors, washing or holding tanks, etc.
Mass transfer rates are generally such that phase equilibria in liquid-liquid
systems are reached within a short residence time (ca. 1 min). Standard solvent
extraction duties are not covered by this Guide.
The bulk fluid dynamics, power requirements and flow patterns in vessels
containing well-mixed two-phase liquids are generally similar to those of single
phase liquids when stirred at similar impeller Reynolds numbers.
The recommended equipment geometry for a reactor is shown in Figure 1. The
duty favors smaller D/T ratios, with a value of 0.33 recommended for general
purpose work.

4.2

Flow Mixers

Pipe flow mixers (also known as motionless or static mixers), as made by Kenics,
Sulzer and others, can be used to disperse one liquid as droplets in another. The
pressure drop supplies the energy for drop formation.

4.3

'High Shear' Mixers

'High Shear' mixers may be used for liquid-liquid mixing duties, especially when
one of the feed liquids or the resulting emulsion exhibits a high viscosity. As
these mixers are equally suitable for solid-liquid mixing, their application is the
subject of a separate Guide, GBHE-PEG-MIX-709 – High Shear Mixers.
FIGURE 1

STANDARD TANK CONFIGURATION


5

SYSTEM PHYSICAL PROPERTIES

For well-mixed systems, the following equations to represent the mixed fluid
properties are recommended, where the suffix c refers to the continuous phase
and the suffix d to the dispersed phase.

5.1

Density

The mixed system density is given by:

The Vermeulen equation:

is recommended for liquid-liquid systems.

5.3

Interfacial Tension

The interfacial tension may be required in the approximate calculation of the
droplet size, which in turn is used to estimate the interfacial area and the
volumetric mass transfer coefficient, kLa.
For liquids of low mutual solubility which are free of surfactant additives, the
difference between the pure liquid surface tensions will be a sufficiently accurate
estimate of the interfacial tension. This procedure could, however, lead to a
serious overestimate of the interfacial tension when the liquids exhibit
appreciable mutual solubility or when surfactants or dispersants are present.
In these cases the measurement of the interfacial tension is not recommended,
scale-up from small mixer trials being the preferred method.


6

STIRRED VESSELS

6.1

Design for Complete Dispersion

The power requirement for complete dispersion is the minimum for all duties.
This has been found to be insensitive to the interfacial properties and depends
on which phase is dispersed.
The equations for the two cases use SI units throughout. They have been
derived from experimental data on a 20 liter scale using 21 liquid pairs and are
recommended for turbine and paddle type impellers. The data obtained with
Pfaudler mixers, D/T of 0.6 and 'beaver-tail' baffles checks with published work
by Van Heuven working with standard baffles and a D/T ratio of 0.3. Scale-up on
the basis of P/V, power per unit volume, will be conservative.

6.1.1 Power Requirement for Light Phase Dispersed
Light phase fraction 0.1 to 0.9:

6.1.2 Power Requirement for Heavy Phase Dispersed
Heavy phase fraction 0.1 to 0.4:


6.1.3 Range of Variables
The ranges of variables used in the experimental work were:
Density 660 to 1620 kg/m3
Phase Density Difference 37 to 682 kg/m3
Continuous Phase Viscosity 0.00031 to 0.0173 N.s/m2
Dispersed Phase Viscosity 0.00031 to 0.0173 N.s/m2
Interfacial Tension 0.019 to 0.064 N/m

6.2

Prediction of Phase Inversion

6.2.1 Hydrophilic/Lipophilic Balance (HLB)
Dispersed phase volume fractions of nearly 100% may be supported using the
appropriate dispersant the choice of which is now very refined and outside the
Scope of this Guide. As a general point low HLB dispersants are used to support
water-in-oil (HLB number 5 or less). Dispersants, with HLB 7 to 16 are preferred
for oil-in-water.

6.2.2 'Hold-Up' (Dispersed Phase Volume Fraction) and Impeller Position
In the absence of dispersants these parameters have the major effect. The
phase of less than 40% volume fraction is likely to be dispersed. Mounting the
impeller in a phase favors the dispersion of the opposite phase so that up to 60%
of the opposite phase may be dispersed in a batch operation by mounting the
impeller in a particular phase.

6.3

Design for Mass Transfer

6.3.1 Operating Speed
It is recommended that the impeller be operated at the power levels indicated by
equations 3 and 4, since mass transfer rates will generally be high compared to
rates of reaction.


6.3.2 Scale-Up
Scale-up of the recommended geometry at constant (P/V) from 20 liters
laboratory vessels is preferred as it is not possible to define the effect of
interfacial properties on droplet coalescence, hence equilibrium droplet size
distribution. In polymerization reactors, for example, it will also be easier and
more accurate to adopt this empirical approach than to attempt to predict solute
diffusivities and distribution coefficients over the whole process.

6.3.3 Prediction of Interfacial Area
The correlation:

is recommended for an estimate of the mean droplet diameter and interfacial
area per unit dispersion volume in diagnostic work, or in relatively simple
systems such as washers.
Note the constant in equation 5 is dimensionless.

6.3.4 Prediction of Mass Transfer Coefficients
Inside Drop:


Outside drop:

where Dd and Dc are the dispersed and continuous phase diffusivities.
These expressions are strictly appropriate to non coalescing systems, but will
give general order of magnitude estimates. Note that kL is generally greater than
kd and the choice of dispersed phase may be significant.

6.4 Design for Dispersed Phase Mixing
Collision frequency increases according to (P/V) to the 0.4 power. Detailed
predictions are even more limited than those on mass transfer and empirical
tests are indicated.

6.5 Hold-Up in Continuous Vessels
The vessel outflow is not usually extracted isokinetically so that the ratio of
phases inside the vessel is not necessarily the same as that in the feed. In scale
up work ensure that the ratio:

(where v is the fluid velocity in the outflow) is the same as that proposed on the
full scale design.

7

FLOW MIXERS

Flow in the flow mixers can be laminar or turbulent; the transition Reynolds
number ranges are given in Table 1. The Sulzer SMV mixer is recommended by
Sulzer for Re > 200, for Re at or below 200 the SMX mixer should be used.


TABLE 1

7.1

REYNOLDS NUMBER RANGES

Design for Turbulent Conditions

Flow mixers operate under plug-glow conditions; this contributes to the high
volumetric and power efficiencies although their ability to generate very high
levels of turbulence, which dissipate extremely high power per unit volume (up to
700 kW/m 3) is also important.
With immiscible liquid systems they are best employed in a continuous process
requiring less than 100 seconds to complete the required operation (e.g. mass
transfer, chemical reaction). Accurate metering of the two liquid streams to the
mixer may be needed, possibly calling for expensive flow control equipment.
One advantage of continuous flow mixers is that they readily couple to
hydrocylcone phase separators, via in-line coalescers if necessary.


7.1.1 Recommended Configurations
At present there is no evidence that one sort of flow mixer is more efficient than
another in using energy to promote liquid-liquid processes such as droplet breakup and mass transfer. Conventional column packings seem to perform as
effectively as the proprietary devices. The simple design of the Kenics mixer
makes for easy cleaning while the Sulzer mixers will be shorter for a given
pressure drop.

7.1.2 Pressure Drop and Power Dissipation
The frictional forces between the flowing liquid and the flow mixer lead to
turbulence, power dissipation and pressure drop and to droplet break-up and
promotion of mass transfer between the phases.
For the calculation of pressure drop and power dissipation, refer to GBHE-PEGMIX-701, Clause 7 for static mixers in miscible liquid systems. Use the mixed
density and viscosity values as calculated by equations 1 and 2.

7.1.3 Design for Mass Transfer
The design methods for mass transfer operations in immiscible liquid-liquid
systems apply to all systems where physical mass transfer is the limiting
process. It thus includes systems where a fast chemical reaction which is not rate
limiting is occurring simultaneously with mass transfer.
For systems which do not coalesce very readily, the values of KLa for a given
power per unit volume can be enhanced by interposing empty pipe between the
mixer elements or groups of elements. No specific guidelines are available;
experiments with the system being used are essential.
The coalescence and separation of the phases after mass transfer should also
be studied experimentally prior to the design of the full-scale unit. The droplet
size achieved in the flow mixer is a compromise to give the optimum combination
of mass transfer rates and settling rates in terms of equipment size and cost. The
following points relate to the phase separation:
(a)

flow mixers give a narrower range of droplet sizes than stirred tanks; the
absence of very small droplets reduces overall settling times;


(b)

settling times increase with the flow rate through the mixer due to the
decrease in droplet size with increasing flow rate;

(c)

when the organic phase is continuous, electrostatic methods of
accelerating separation can be used;

(d)

in-line coalescers using 'Knitmesh' packing of appropriate material can
improve the settling performance;

(e)

settling time is extremely sensitive to the presence of traces of impurities
at concentrations too small to affect the measured interfacial tension. It is
therefore important that, whenever possible, the liquids used in the
laboratory study should have the same contaminants and impurity levels
as the plant process liquids. Quick comparative checks of settling times
can be made by following Rushton's method (Chem.Eng. Prog., 52, 515, 1956). This involves producing a complete emulsion, then stopping the
impeller and noting the time for the dispersion to settle to the first
appearance of a clear interface.

(f)

Water-in-oil (W/O) dispersions generally settle much faster than the oil-inwater (O/W) dispersions formed by the same two liquids.

Control over which phase becomes dispersed is important because this can
affect mass transfer and settling performance. The material of construction of the
flow mixer should be chosen so that it is wet more easily by the liquid required to
be the continuous phase. Thus polypropylene might be used if an organiccontinuous system were required. (Polypropylene 'Intalox' saddles form an
effective flow mixer packing.) The liquid forming the larger proportion of the total
feed is also more likely to form the continuous phase although dispersions with
over 90% by volume of the dispersed phase can be made.


K La values are obtained from steady state experiments using the relation:

A plot of KLa vs P/V of the form

as in Figure 2 is likely to be obtained, where C is a constant for the particular
liquid-liquid system concerned, dependent on the value of f and the flow regime,
but not on the scale of the equipment. n is likely to be in the range 0.5 to 1.0.
The calculation procedure is as follows:
(1)

a possible design is selected in terms of diameter, flow rate and number of
elements;

(2)

the P/V is calculated as recommended in 7.1.2;

(3)

obtain KLa from an experimental plot of KLa vs P/V;

(4)

E is calculated from equation 8;

(5)

further designs are examined to arrive at the most suitable one, taking into
account the settling and post-contacting re-coalescence.


In order to allow for design uncertainties, including that attached to KLa, the
length of the mixer should be 30% longer than the calculated design value.
FIGURE 2 EXPERIMENTAL RELATIONSHIP BETWEEN MASS TRANSFER
COEFFICIENT AND POWER DENSITY
Figure 2 shows the relationship between Mass Transfer coefficient, KLa, and
Power Density, P/V, in flow mixers and stirred tanks for the extraction of Cu++
from aqueous solutions using chelating agents in hydrocarbons.


7.1.4 Design for Specified Droplet Size
Design to a specified droplet size may be useful, for instance, in preparing a
dispersion of a monomer in water prior to polymerization. It is recommended that
a minimum of five flow mixer elements are used to control droplet size. When
considering a flow mixer system for a process requiring a specified droplet size it
is very important to identify the variable(s) and the control method which will be
used for fine-tuning the system. Design calculations should be carried out with
this in mind.
The design equations for calculating the Sauter mean droplet diameter, dsy , with
liquids of equal viscosity under conditions of low coalescence are:

A more detailed design procedure for static mixers to produce a required drop
size has been developed by Middleton.
When coalescence is significant, which may be the case for systems where the
volume fraction of the dispersed phase is greater than 0.1, the predicted values
of dsv may be low.
The design equation for calculating dsv for two low viscosity (µ - 10-3 N s/m2)
immiscible liquids flowing in a straight empty pipe of diameter D t is:


A pipe length of 200-500 diameters is necessary to achieve droplets of this
limiting size.
For a helical coil, the equation to be used is:

As equation (13) has only been tested for Dt / DH = 0.08 and a helix angle of 6°,
the range of validity is uncertain.
Orifice plates and valves can be used as flow mixers for immiscible liquids
though their efficiencies are said to be lower than that of a properly designed flow
mixer. For a single orifice mounted centrally in a tube, receiving a jet of the
dispersing liquid, the following dimensional equation (requiring the use of SI units
) may be used with caution to calculate the Sauter mean droplet diameter in m,
provided the variables are within the range tested:


The use of equation (12) for calculating drop sizes in full scale equipment
requires extreme caution but may give useful rough equipment sizing from which
the required drop size can be obtained by tuning the system: adjusting flow rate,
orifice size or interfacial tension.

7.2

Design for Laminar Conditions

Liquid-liquid dispersion in flow mixers under laminar conditions is likely to be
used in polymer melt processing for mixing in additives, either in a solvent or as a
master batch in polymer. Occasionally two-phase mixtures of immiscible
polymers are made because of their particular properties. This clause also
covers the problem of dispersing a relatively small amount (up to 20%) of a low
viscosity into a high viscosity liquid, and vice versa, whether or not the two are
ultimately miscible.
The design procedure in the GBHE Mixing and Agitation Manual is derived from
the account given by an American Company (1982). It is so far unproven and
should therefore be used with caution. It is strongly recommended that a smallscale experimental study of the two-liquid system involved be carried out. The
American Company only provides information on the Kenics mixer, while
Middleton (1984) gives a design procedure for Sulzer and Kenics mixers.
The American Company defines a reduced shear stress as :


In simple shear fields droplet break-up will occur if SB exceeds a critical value, S
crit of about 0.6 for values of p in the range 0.1 to 1.0. At higher values of p, S crit
increases very rapidly and break-up will not take place at all if p exceeds about
3.0. At values of p below 0.1, S crit is given by:

The American Company indicates that this relationship applies down to p = 3 *
10-6 but note that other Authors have reached somewhat different conclusions,
perhaps because of the low values of oc in their work. The American Company
also provides information on the effect of subjecting a droplet to a reduced shear
much greater than the critical value. The time required for break-up decreases
rapidly and the number of fragments increases from 10 - 30 at the critical value to
over 1000 at 10 times the critical reduced shear stress.
In extensional shear fields there is again a critical value of SB which must be
exceeded for break-up to occur, again S crit depends on p, having a minimum
value of 0.2 at p = 5 and rising to 0.5 at p = 1000, according to the relation:


DOCUMENTS REFERRED TO IN THIS PROCESS ENGINEERING GUIDE
This Process Engineering Guide makes reference to the following documents:

GBHE ENGINEERING GUIDES
Glossary of Engineering Terms
GBHE-PEG-MIX-701

Mixing of Miscible Liquids (referred to in 7.1.2)

GBHE-PEG-MIX-709

High Shear Mixers (referred to in 4.3)

OTHER GBHE DOCUMENTS
GBH Enterprises

Mixing and Agitation Manual (referred to in 7.2).


Mixing of Immiscible Liquids

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