Thursday, January 26, 9:30 am in room MTH 3206, University of Maryland,
College Park
Thermocapillary migration of a liquid droplet on a non-uniformly heated
surface
Dr. Douglas Huntley
Institute for Mathematics and Its Applications
University of Minnesota
huntley@ima.umn.edu
In this analysis we are interested in determining if an imposed temperature
gradient in the solid can be used to translate a volatile droplet on a
horizontal plate. Lubrication theory is applied to the problem, resulting
in a nonlinear parabolic pde for the shape of the droplet (fourth order in
space), which is coupled to nonlinear ode's that describe the position of
the contact lines. This system of equations determines the behavior of the
viscous droplet. We ignore the initial transient behavior of the droplet
and investigate the limit of small-spreading rates (small capillary
number). A delta formulation of
the Newton-Kantorovich method is applied to this problem iteratively, where
the difference function delta is expanded in a set of basis functions
based on Chebyshev polynomials. The linearized equation is then solved
using standard pseudospectral methods. Results are checked against the
asymptotic limit of zero capillary number.
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