# Stability of droplets - using Unduloids

1. Jan 23, 2010

### rsr_life

Hello,

I'm an Electrical engineering student taking a class on surface chemistry. I've been given a problem where I need to analyse the stability of droplets using Unduloids.

I have some lecture notes on unduloids in the context of this subject and it's quite limited, but every other online reference talks about the diff geometry aspect of unduloids.

Could someone point me to a good online reference for this topic, or a book that deals extensively with surface chemistry concepts, that I can get at the univ library?

If you could also include an explanation for this sort of analysis, that would be quite helpful. Also, I hope this is the right sub-forum.

2. Jan 23, 2010

### Andy Resnick

I had to look up 'unduloid', but it's simply a surface of constant curvature. Interfacial energy acts to minimize the interfacial area of a multifluid system. That's the essence of the Laplace equation $\Delta P = -\sigma \kappa$ which relates the (local) pressure jump across an interface to the product of interfacial energy and (local) mean curvature.

So, drops are spherical in the absence of gravity, and a perturbed spherical section when gravity is present (the relevant dimensionless parameter is the Bond number). Jets and liquid bridges form 'amphora' shapes with gravity present, and unduloids with gravity absent.

Chandrasekhar's book "hydrodynamic and hydromagnetic stability" (dover) has an excellent chapter that solves the problem of jet stability.

As another point of reference, you may try "Plateau's problem"

http://en.wikipedia.org/wiki/Plateau_problem

But the modern treatment of the problem is all about differential geometry.

3. Jan 23, 2010

### rsr_life

Thanks for the reply, Andy. That's a different and a more coherent view describing the various shapes that a drop can take.

That would help describe the slightly elongated shape of droplets on the bristles of a stiff comb or tips of blades of grass.

The next thing to do as a follow up would be to look up the effects that regular forces have on drops and bubbles - I should hope to get a clearer idea in that direction, in terms of analyzing such problems.

Thanks again.