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Ok this is my first$^*$ question on overflow, my apologies if this is not the right place to ask what follows!

I observed the following phenomenon: I put a (vitamin) tablet into water, then after a while a thin film forms (I have attached a picture of it). That made me wonder - is there a particular pde that models such a process (or particular stages of it)? I realize that this phenomenon is quite complex, but perhaps there are particular stages that can be modelled and studied generically (for example I think soap bubbles are studied mathematically). What interests me in particular is the transition from the stage where there is only the surface of the water to the stage where a second film has formed.

Here is the picture: enter image description here

Thanks very much for pointers to sources where I can learn more.

$^*$(Edit: I just realised it is in fact my second question here)

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    $\begingroup$ I don't know anything about this kind of math, but I know that a number of people in the mathematical modelling group in my department: lboro.ac.uk/departments/maths/research/groups/… study exactly these kinds of problems. Looking at that page might get you started while we wait for a more educated answer! $\endgroup$
    – user5117
    Commented Apr 3, 2015 at 11:29
  • $\begingroup$ en.wikipedia.org/wiki/Thin_film $\endgroup$
    – user5402
    Commented Apr 3, 2015 at 13:57

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The phenomenon you are seeing when you dissolve a tablet in water is called effervescence: the escape of gas, carbon dioxide in this case, from an aqueous solution, when it becomes supersaturated.

The expansion of bubbles in the liquid and the collapse when they reach the surface has been extensively studied, for an intro (with some equations...) see this story in Europhysics News.

The film which is produced in your glass happens by the same process that children use to make soap bubbles by blowing soap through a metal ring. The escaping gas plays the role of the blowing child and the rim of the glass plays the role of the ring. For this to work, the liquid in your glass should have sufficient surface tension, like soap. I would imagine that if you take care to use a clean glass with pure water, the film will not develop.

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