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Fluid dynamical instabilities are present in many different everyday things. The famous tears in wine for example are a classical example of a Marangoni effect, where surface tension gradients due to evaporation cause an instability.

I recently came across an instability that occurs when you have just emptied a glass with yoghurt drink and have only a film of the drink left on the walls of the glass. A tear-like pattern emerges over the time of about a minute that looks like shown below:

enter image description here

I have been thinking what can cause this effect. It seems somewhat similar to a Marangoni effect, but given the ingredients of the yoghurt drink I think we can safely rule out evaporation on this timescale. Another potential effect explaining this would be viscous fingering, but for that to happen I believe the gas phase has to be driven, which it isn't here. Or perhaps it is a 'surface-version' of a Rayleigh-Taylor instability? Or maybe it is related to the non-newtonian nature of the yoghurt drink?

To summarize: I don't know which instability I am looking at and I would love to know what causes this pattern on the glass with yoghurt drink! Does anyone know what is causing it?

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Yoghurt is a flocculated suspension of casein micelles. The acid secreted by the bacteria growing in the milk destabilises the casein particles and they aggregate together. Because the volume fraction of the casein particles is high in milk the aggregated particles form a gel. This image shamelessly stolen from Wikipedia gives a schematic illustration of how this happens:

Flocculated gel

However yoghurt drink is diluted yoghurt, so the volume fraction of the casein particles is lower and there aren't enough of them to form the space filling networks required by a gel. Instead they tend to form denser aggregates separated by liquid containing no particles, and this is what is happening in your glass. The casein micelles are tending to clump together leaving tracts of clear liquid between the clumps.

The exact structures formed will depend on the flow conditions and I'm not sure I'd care to try and predict in advance what shapes they will form. On the walls of your glass they are obviously influenced by the liquid draining downwards. You might want to try spreading a thin film of the drink on a flat glass surface, and you'll probably see more circular aggregates form.

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  • $\begingroup$ Very understandable, well done. I was wondering, are you familiar with the Marangoni effects in general? Looking for some literature on it, not much success. For one, I still cannot see how on earth the induced flow is from the lower surface tension part to higher surface tension regions, very counter intuitive (the gradient never vanishes then!). $\endgroup$
    – Ellie
    Mar 31, 2015 at 10:31

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