Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#26926] of Ryan P. Haskett

Papers Accepted

  1. Ryan P. Haskett, Thomas P. Witelski and Jeanman Sur, Localized Marangoni Forcing in Driven Thin Films, Physica D (2004)
    (last updated on 2004/10/28)

    We consider the use of localized Marangoni forcing to produce a thermocapillary ``microfluidic valve'' that allows us to control the downstream flow of a thin film of viscous fluid. To this end, we analyze the influence of this localized forcing on a flow driven by a combination of uniform Marangoni stresses and gravity in a one-dimensional model. Long-time solutions approach states that can be categorized in two classes, where the film thickness downstream of the forcing is: (I) determined by the upstream thickness, or (II) controlled by the forcing amplitude. The type~II solutions are stable stationary hydraulic jumps for thin films. We give careful attention to the relation between the forcing and the downstream film flow for the resulting bi-stable solutions. Comparison of the one-dimensional theory with two-dimensional computations and experimental results is given.

    thin films • fluid dynamics • thermocapillary valve • Marangoni forcing • lubrication theory
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320