Here is a rough outline for an NSF postdoc proposal.  Comment or add anything as you see fit. 

Basic theme: 

An exploration of capillary surfaces manipulated through the application of a field.  (Just electric field here? or leave in more general terms?)

Some ideas:

Stabilization of surfaces – we have seen that an electric field may be used to stabilize soap-film bridges at greater lengths than without the field.  There are many places where this could potentially be extended to.  The area most directly related would be to study liquid bridges and/or liquid columns.  One of the questions we would seek to answer would be: Can we have stable bridges beyond the Rayleigh-Plateau limit?  Preliminary work suggests that the answer is yes, but it certainly raises design questions – what is the choice of parameters that optimizes the length?  What is the greatest length at which a stable bridge exists?  In terms of liquid columns, i.e. cylinders, these questions have been explored at least in some extent, but for general liquid bridges I think it is fairly open.

The question could similarly be turned the other way – suppose you want liquid bridges to break up – how best to apply a field in order to have this occur?  How can you alter the parameters to see breakup when and where you want it?  Could also ask questions of “how” the breakup is occurring – this type of question would fall into the realm of shape change dynamics.  From what we have seen, the analysis could be very difficult, but I think it is kind of an interesting thing to explore.

Just a thought: What other effects should be/could be included?  For instance, in the analysis we have done, the two driving forces are surface tension and the electrostatic force.   Can we achieve meaningful results in the liquid bridge/column arena with just these forces present?  Must we include fluid dynamical terms? And if so, how might we propose to deal with them?

Capillary action -  consider the rise of fluid in a capillary tube/wedge.  How can this be altered/manipulated/controlled by the application of a field?  A main area of interest could be problems with micro channels.  Seems like there are a lot of different problems/approaches we could take here.  I would think there are probably some good design/optimization questions.  Would it be best to take a dynamical approach?  For instance, can we increase the velocity of the rise?  What are some other relevant questions ? 

Another area of interest here would be with self-assembly.  Possible questions might include: Can we “guide” a self-assembly process with an applied field?  Speed up a self-assembly process?  Or, if we allow the assembling particle(s) to be deformed by the field are there structures that are achievable with a field that are unachievable otherwise?  What are the most relevant questions, and what is the best way to approach them?  

Different geometries, arbitrary geometries – we have done considerable work with a soap film between two rings and an axially symmetric applied field.  What other geometries might we be able to work with?  What about different ways of applying the field?  Or, what might we be able to prove about the problem in general?  What sort of general analysis might be possible for the equation Hu=f(u), where an arbitrary minimal surface is placed in an (arbitrary?) electric field?  In other words, with this idea we would propose a general mathematical study of the mean curvature operator and a “forcing function”. 

Experiment – it would seem that with any of the above ideas except perhaps the last one, experimental work should be feasible.  It might be worth proposing an experimental accompaniment and requesting some funding for particular experiments.  According to Dr. Pelesko, a high voltage source should be no problem to fund and would probably be necessary.  A high speed camera, on the other hand, would be impractical to request, but then, I will probably be making quite a few trips to Delaware anyway since my wife will still be attending UPenn.

Type of analysis

Obviously this would depend on which questions we were attempting to answer.  In general, though, I will say that I have a great appreciation for a qualitative type analysis.  I have enjoyed the methods employed thus far in my thesis, and I would hope/suspect that similar type methods might be applicable in answering some of the above questions.  At the same time, of course I would hope to learn new methods, and am always open to new areas of study.

Let me know what you think.  I would like to hear your thoughts as to which of these ideas/areas interests you the most, which seems the most feasible, which has the best chance of getting funded, etc..

Thanks,

Derek