(469a) Mixing By Asymmetrical Drop Coalescence in Microfluidics

Mixing by
asymmetrical drop coalescence in microfluidics

Nina M. Kovalchuk, Marten Reichow, Thomas
Frommweiler, Daniele Vigolo, Mark J.H. Simmons

University of
Birmingham, Edgbaston, Birmingham, B15 2TT, UK

Key words: soluble surfactant, coalescence, mixing.

Droplet-based microfluidics is a rapidly developing area of
science and engineering enabling study and optimisation of drops and bubble
formation and coalescence inside immiscible continuous phase. Such studies are
crucial for emulsification and foaming and can be carried out by using small
amounts of materials across a broad range of parameters (1,
2). Promising microfluidic applications include also micro-reactors, where
chemical reactions or studies on interactions of living cells with various
compounds are carried out under well controlled conditions within isolated
drops on timescales from milliseconds to days. A microfluidic platform enables
monitoring hundreds of micro-reactors under similar conditions and therefore provides
statistically meaningful data.

One of the ways to perform a micro-reaction is bringing
together and coalescing two drops containing the reactants. Under such
arrangement the reaction starts after drops coalescence and its kinetics to a
large extent depends on the mixing inside the reactor. If the coalescing drops
follow each other, the vortices formed inside the coalesced drop due to
velocity gradient through the channel cross-section contribute to the mixing (3).
However, additional contribution to the mixing on the short time scale of drop
coalescence can be acquired if coalescing drops have different size or composition.
In the case of size asymmetry, coalescence is accompanied by penetration of
content of smaller drop into larger one due to difference of capillary pressure
between drops. However such penetration is rather weak (4).

Asymmetry in composition can often result in different
surface tension of the drops. In this case, the coalescence triggers two
processes: the content of the drop having larger interfacial tension penetrates
inside the other drop due to difference in the capillary pressure, while the
Marangoni flow spreads the content of the later drop over the surface the
former one (5).
Coalescence of drops with surface tension asymmetry was studied under condition
of close to zero Weber number in unconfined geometry (5-8).
Here we present the results of experimental study on coalescence of
asymmetrical drops under conditions of laminar flow in microfluidic device and
mixing of the drop content.

The microfluidic device was made of polydimethylsiloxane
(PDMS) using standard soft lithography and had channels with rectangular
cross-section of height h = 170 μm and width w = 360 μm. Dispersed
phase was water or water/glycerol mixture. Continuous phase was silicone oil. The
liquids were supplied to the microfluidic device by syringe pumps. Two
different sets of drops were produced in two flow-focusing cross-junctions. The
drops from both sets met at a T-junction and travelled together along the
output channel. Drops coalesced at the T-junction or in the output channel. One
set of drops was surfactant-free, whereas the second set contained surfactant
decyltrimethylammonium bromide (C₁₀TAB) at various concentrations up
to 5 times of critical micelle concentration (CMC). To distinguish between the
surfactant-laden and surfactant-free drops and follow their mixing, methyl
violet dye was added to surfactant-free drops.

Drop coalescence was recorded with high speed camera
connected to an inverted microscope (Nikon eclipse Ti2-U) at 20 kfps and
exposure time 0.02-0.05 ms. Spatial resolution of the images was 1-2
μm/pixel. Images were processed with ImageJ free-software. Flow fields
inside the coalescing drops were obtained using Ghost Particle Velocimetry
(GPV), a technique that employs speckle patterns of white light scattered by
nano-particles as flow tracers. GPV images were processed with ImageJ to remove
the background noise and analysed using the open-source MATLAB toolbox PIVlab.

Effect of such parameters as interfacial tension difference,
viscosities of continuous and dispersed phases and superficial flow rate in
output channel on coalescence kinetics and mixing on short (0.1-5 ms) and long
(10-50 ms) time scales was systematically studied. It was found that similar to
the case of drops coalescing in motionless continuous phase there is an
intrusion of drop having higher interfacial tension into the drop having lower
interfacial tension. However under condition of flow in microfluidic device
there is a distinctive dependence of the intrusion pattern on the drop order as
related to the flow direction: intrusion length is considerably larger if the
surfactant-laden drop is followed by the surfactant-free drop as it is shown in
Fig. 1. The intrusion rate increases with an increase of interfacial tension
difference, superficial flow rate in the channel (in the case when
surfactant-laden drop goes first) and viscosity of continuous phase. It
decreases with an increase of viscosity of dispersed phase. The mixing on along
time scale is also better when the surfactant-laden drop precedes the
surfactant-free one.

Fig. 1. Mass transfer at asymmetrical drop coalescence. The
surfactant-free drop is an aqueous solution of methyl-violet dye, the
surfactant-laden drop is 300 mM (5 CMC) solution of C₁₀TAB in water,
the continuous phase - silicone oil 48 mPa·s; superficial velocity in the
output channel – 7.4 mm/c. Top row – the surfactant-laden drop goes first,
bottom row – the surfactant-free drop goes first.

The reason for the dependence of mixing on the drop order
can be understood from the analysis of flow fields inside the coalescing drops.
Coalescence of similar drops results in formation of four vortices due to flow
from the coalescing drops into growing neck. While the coalesced drop moves
through the channel the vortices in the front part of coalesced drop are
decelerated by the channel flow and those in the rear part are accelerated. By
asymmetrical coalescence the vortices are formed only in the drop with higher
interfacial tension, transferring liquid from it to both the neck and drop with
lower interfacial tension. If the surfactant-laden drop is followed by the
surfactant-free one the vortices in surfactant-free drop are accelerated by the
channel flow resulting in considerable intrusion. If surfactant-free drop
precedes the surfactant-laden one, then vortices are retarded and intrusion is
small. 

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