COLLOQUIUM
3:00 p.m., Wednesday (February 4, 2009)
WMAX 110 (PIMS)
G.M. Homsy
Department of Mechanical Engineering
University of California at Santa Barbara
Chaotic Advection in Drops Driven by Electrohydrodynamics:
Enhancement of Heat and Mass Transport
Abstract:
Chaotic advection of nondiffusing Lagrangian particles is often studied
for model flows in the absence of molecular diffusion, which leaves open
the questions of (i) whether any such flows are physically realizable,
and if they are, (ii) how are transport rates affected by the mixing? To
address these issues, we consider transport of heat or mass from
circulating droplets that are both settling and subject to a
timedependent axial electric field. The oscillatory electric field
drives an electrohydrodynamic flow which augments the Hadamard
circulation caused by the steady translation, and which results in
chaotic advection within the drop. The problem is governed by four
parameters: the Peclet number, the dimensionless amplitudes of both the
steady and oscillatory parts of the electric field, and the
dimensionless frequency of the modulation. The convective diffusion
equation is solved numerically for a wide range of these parameters. The
results are characterized by the asymptotic rate of extraction of heat
and/or mass from the droplet, (which is found to be exponential in
time), and the enhancement of the transport rates is studied as a
function of parameters. Somewhat surprisingly, the enhancement is not a
monotonic function of the frequency but rather, exhibits spectral
‘resonant peaks’ at particular values of the frequency, leading to very
significant increases in the extraction rate. Scientific visualizations
are used to determine that there exist underlying timeperiodic spatial
structures of the concentration field, so called "strange eigenmodes",
and that the temporal phase relationship between lobes of these
eigenmodes is responsible for the resonant behavior. If time allows,
extension to threedimensional flows will be mentioned.
Refreshments will be served at 2:45 p.m. (PIMS Lounge).
