Physics behind mixing of two liquids at milli-scale

We see mixing every day in so many contexts and across all scales, ranging from the very large galaxies to the very small cells. But what does it mean for something to be mixed? Generally, for two liquids, we say that they are mixed when there is no non-uniformity in concentration anywhere. The two liquids start out separately with different concentrations, then start to interact and a gradient in concentration is generated. At the interface of two liquids, diffusion is the major player which homoegenises the distribution of liquid molecules. But, diffusion is infamous for being a very slow process. If we had to rely on diffusion alone for things to mix, then we would be living in a very difficult world where making a cup of coffee would take hours. That’s not a world I would want to live in. So what can help? There is a process which is very common and is used synonymously with mixing, in the real-world. That is stirring.

Stirring is a process of changing the playground where mixing takes place. In a two-liquid system, what stirring does is to stretch the liquid elements, and fold them. This leads to thinning of the fluid elements which decreases the diffusion time, leading to faster mixing. This process of stretching and folding can be seen in the macroscopic world, but does this happen in a small-scale system? Turns out, small-scale systems where the flow is always laminar is an almost perfect system to test our understanding of mixing. Since the flow is laminar, diffusion will be the only factor deciding the mixing time unless we introduce some kind of a stirring mechanism. In the world of Microfluidics, this is done by introducing obstacles in the channel. The obstacle, when placed smartly, acts as a stirrer. What kind of obstacle, where to place them, are one of the highly studied problems.

I worked on simulating two different channel configurations in 2D:

• With a circular obstacle which produces oscillatory flow downstream
• With a pair of alternate rectangular baffles protruding from the side walls which produces trapped vortex or vortices.

These are considerably different flow fields, or stirring mechanisms. The challenge is to see how mixing is actually happening, and if we can relate it to the earlier mentioned stretching and folding mechanism. Turns out, we can! More on this coming soon. Until then, you can check out the preprint.

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This is an ongoing project, done under the guidance of Prof. Aravinda Raghavan and Prof. Meenakshi Vishwanathan at BITS Pilani Hyderabad Campus.