Papers Accepted
Abstract:
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.
Keywords:
thin films • fluid dynamics • thermocapillary valve • Marangoni forcing • lubrication theory