The Capillary Team Page

Overview

Group members

• Lucero Carmona (lcarmona@udel.edu)
• Anson Carter (carter@math.udel.edu)
• Van T. Lam  (vlam@udel.edu)
• Regan Beckham (beckham@math.udel.edu)
• Derek Moulton (moulton@math.udel.edu)
• John A. Pelesko (pelesko@math.udel.edu)

Key References

Please list any and all references that you find useful here.

• Books
• The Mathematics of Soap Films: Explorations with Maple by John Oprea, AMS (2000).  A good mathematical introduction.
• The Science of Soap Films and Soap Bubbles by C. Isenberg, Dover (1992).  A good physics introduction.
• Capillarity and Wetting Phenomena by P. de Gennes et. al., Springer (2004).  A nice book on capillarity.
• Calculus of Variations by R. Weinstock, Dover (1974).  Van's recommendation for variational techniques.
• Applied Mathematics by J. D. Logan, Wiley (2006).  Anson's recommendation for variational techniques. 
• Equilibrium Capillary Surfaces by R Finn, Springer-Verlag (1986).  Anson recommends (but a little heavy).
• Papers
• Liquid Rise in a Capillary Tube by W. Britten (1945).  Dynamics of liquid in a circular capillary.
• Websites
• http://fluids.snu.ac.kr/research.htm
• http://www.damtp.cam.ac.uk/user/dv211/rods.html

Background and Projects

    Image Processing

    For image processing you have several choices. MATLAB has a built in image processing toolbox.

    MATLAB is available on the computers in the lab. You might also try the program ImageJ. This is

    free program developed by the NIH. The link is to a Windows version. It is fairly sophisticated in

    its abilities, yet easy to use.

    The Rayleigh-Plateau Instability

    A long cylindrical column of fluid is unstable to spatial perturbations. You can observe this easily

    in your kitchen by turning on your faucet so that only a small stream of water comes out. Notice

    that the column breaks up into droplets by the time it reaches the bottom of your sink. Mathematical

    approaches to understanding this instability are essential to master for all of the capillary projects we are

    undertaking. We'll discuss this instability in more detail in group meetings. The following picture

    will be the focus of our discussion. Click Rayleigh-Plateau for a more detailed page on this instability.

    Static Rise of Fluid in a Capillary Tube

    If you insert a capillary tube into a fluid, the fluid will rise in the tube to a height higher than the surrounding

    liquid. This is a classic, long studied problem, but we need to understand this in order to do the dynamic problem.

    Anson Carter has worked through this problem and presented his results in group meetings. The results can

    be found Here.

    Capillary Motion of Flexible Bodies

    In this project we study the motion of flexible bodies driven by the capillary force. The classic example of capillary

    driven motion is the so-called "Cheerio's Effect." We want to understand this effect and then extend the analysis to

    the case of bodies that can deform. The information can be obtained on this page.

    The Rise of Liquid in a Tube and in a Wedge

    In this project we study the dynamic motion of fluid surfaces driven by capillary forces. We look at the rise of fluid in

    a capillary tube and the rise of fluid in a wedge. The detailed page on this is here.