Effect of Soluble Surfactant on Flow Patterns in Microfluidic Drops

Using microfluidic drops as microreactors is a rapidly developing area of science and engineering which enables reaction studies and optimization using a statistically relevant number of reactors under tightly controlled conditions and using small amounts of reagents. This approach reduces considerably the ecological impact of research, development and production of new formulations. Drop microreactors have been successfully used for activities including measurement of enzyme kinetic constants [1], synthesis of nano-particles [2], cell screening [3].

Precise control of flow fields, shear stresses and mixing inside the micro-reactors are of great importance for many applications. A considerable number of microfluidic devices are made by soft lithography and have a rectangular cross-section. Flow fields inside the drops moving in such devices are much more complicated compared to the drops moving in cylindrical tubes because of nonuniform velocity distribution within the continuous phase [4]. The continuous phase moves slower in thin films near the channel walls and much faster in the corners.

The presence of surfactant further complicates matters. Firstly, surfactant reduces interfacial tension between continuous and dispersed phase and therefore changes the drop shape and thickness of the continuous phase films. Secondly, due to characteristic time-scales in microfluidics, the acting interfacial tension can be far from equilibrium. Thirdly, shear stresses imposed by continuous phase can result in surfactant redistribution and partial or complete retardation of the interface. It was shown in [5] that the presence of surfactant in the continuous phase can considerably slow down the drop motion.

In microfluidic reactors, surfactants can be often present within a dispersed phase as a part of formulation. The behaviour of surfactant within the confinement of a drop with recirculation patterns present can be very different from surfactant in continuous phase. Examination of the effect of surfactant added to dispersed phase on the flow pattern inside this phase is the focus of this work.

The continuous phase used in this study was silicone oil, SO, (Sigma), and the dispersed phase, G/W, was 52:48 w:w mixture of ultrapure HPLC-grade glycerol (Alfa Aesar) and double distilled water from a water still Aquatron A 4000 D (Stuart). Glycerol was added to dispersed phase to match the refractive index with continuous phase and avoid optical distortions at the interface.

Surfactants, decyltrimethylammonium bromide, C₁₀TAB, (99%, Acros Organics), dodecyltrimethylammonium bromide, C₁₂TAB, (99%, Acros Organics), Triton X-100, TX-100, (laboratory grade, Sigma-Aldrich) and Tween 20 were dissolved in dispersed phase in the range of concentrations between 0.1 and 10 times of their critical micelle concentration, CMC.

A schematic of microfluidic device is shown in Fig.1a. The rectangular channels have a width W = 346±3 µm and a height H = 167±3 µm. Drops were formed in the flow-focusing cross-junction. Liquids were supplied to the junction by syringe pumps Al-4000 (World Precision Instruments) equipped with 5 mL plastic syringes (Fisher). The length of drops was varied in the range of W – 1.4W for all studied compositions. The size of drops was adjusted mostly by changing flow rate of continuous phase; the flow rate of dispersed phase was varied only to increase the distance between the drops to prevent coalescence.

Flow fields inside the drops were measured in the output channel after T-junction. To make measurements under the same flow conditions, compensating amount of continuous phase was added through an additional channel at T-junction to keep the overall flow rate in observation channel at 32 µL/min (superficial flow velocity 9.2 mm/s). Total flow rates of 64 and 96 µL/min were additionally used for surfactant-free drops to study the effect of capillary number on flow patterns. Flow fields were measured always in the same position at distance of ~ 10 W (within the window of 3.3 – 3.8 mm) from the T-junction. All flow patterns inside the studied drops were completely symmetrical, confirming that this distance was large enough to eliminate all distortions of the flow field imposed at junction.

Flow fields inside the dispersed phase were studied by Ghost Particle Velocimetry, GPV, [6, 7] using as tracers the speckle patterns of white light scattered by particles smaller than the diffraction limit, in this study polystyrene particles of 200 nm (10% solid, Sigma). The dispersion of nano-particles was diluted by dispersed phase at ratio 1:50 (v:v). The moving drops were recorded by a high-speed video camera (Photron SA-5) connected to an inverted microscope (Nikon Eclipse Ti2-U) at 10 000 fps, exposure time of 0.04 ms and magnification 40x giving image resolution 0.5 µm/pixel. The numerical aperture of condenser was adjusted to ~ 0.2 resulting in resolution along the optical axis around 12.5 µm. This resolution enabled probing the flow fields in several cross-sections over the channel height. In particular, the flow fields were recorded at the middle plane of the channel and at distances 20, 40, 60 and 80 µm from it. The last cross-section is very close to the bottom channel wall.

Figure 1b shows the flow field in the middle plane of the channel (co-ordinate system of channel) within a surfactant-free drop of length L = 431 µm (1.23W) moving with velocity V = 9.8 mm/s. The minimum velocity in the middle plane is observed near the side walls of the channel. It is noticeably lower than both drop velocity and superficial velocity of the liquid in the channel (9.2 mm/s). The velocity on the front edge of the drop is similar to the drop velocity, but the velocity in the central part of the drop is considerably higher, being a part of recirculation flow. Another source of this high velocity is the shear stress from the liquid in the channel corners confirmed by the flow fields at distance of 60 and 80 µm from the middle plane, where velocity at the side parts of the drop exceeded the drop velocity by ~ 25 %. At the same time the velocity in the central part of drop in cross-section of 80 µm from the middle plane was more than 30 % lower than the drop velocity. The flow patterns have a clear 3D structure with liquid moving up and down from the middle plane at the drop front and moving from the top and bottom to the middle plane at the rear of the drop.

Addition of surfactant, especially at concentrations above cmc, dramatically changes flow fields inside the drop as shown in Figure 1 c and d. Flow patterns and velocity values depends on both surfactant concentration and cmc value. At concentrations above cmc, the aspect ratio of drops laden with high cmc surfactants increases considerably and curvatures of front and rear caps become similar (Fig. 1c) pointing out on small pressure difference over the drop. For drops laden with small cmc surfactants, curvature difference becomes even larger than for surfactant-free drops, probably due to surface tension concentration difference between the front and rear parts of the drop. Drop velocity and velocity gradients inside the drop are considerably higher for surfactants with large cmc, C₁₀TAB and C₁₂TAB, than for surfactants with lower cmc, TX-100, and Tween 20. 3D structure becomes less pronounced for surfactants with small cmc at concentrations above cmc. Instead a considerable in-plane recirculation is observed.

Acknowledgment: This work was funded by the EPSRC Programme Grant PREMIERE EP/T000414/1.

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