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A while ago I was wondering if the displacement of fluid described in this blog post could be modelled with mean curvature flow or some other flow, but when I asked someone in Engineering they replied that industry is generally not interested in simple mathematical models.

However, I noticed in this article that they do actually model bouncing of droplets and the associated coalescence phenomenon using mean curvature flow and get quite good agreement with experiment and numerical simulations. Are there are any other possibilities for modelling fluid flows with mean curvature flow? I am thinking along the lines of contracting bubbles and things like that.

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    $\begingroup$ I don't think the "correct" description is a simple mean curvature flow. Things like contracting bubbles you have really a two-phase fluid with a free boundary interface. The standard model for surface tension is given by the mean curvature. The motion of the free boundary then is by pressure difference between the two phases minus the mean curvature (or something like that). Mean curvature flow by itself is probably too naive. $\endgroup$ – Willie Wong Jun 23 '20 at 15:53

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