Chemical Front Propagation in the Hele-Shaw Flow
                        under the Buoyancy Effects

                                   by

                                 J. Zhu

               JTB120,  3:20pm Monday, November 25, 1996

                                Abstract

We consider the propagation of chemical fronts in a Hele-Shaw flow where
the front is assumed to propagate with a curvature dependent velocity.
The motivation is to model some recent experiments that employ aqueous
autocatalytic chemical reactions in such a device. The density change
across the front in such experiments is quite small so the Boussinesq
approximation can be used, and the flow field generated is exclusively
due to the buoyancy effects. We derive a free boundary formulation based
on Darcy's law and a single layer potential, and describe the evolution
in terms of the $\theta-L$ formulation, in which the tangent angle and
the perimeter of the closed front are followed in time. Numerical solutions
are obtained for this formulation with a rising and expanding bubble. As
observed in the experiments, a fingering phenomenon which is different from
the surface tension associated phenomenon appears in our calculations.
One mechanism is proposed and verified numerically for the wavelength
selection of the fingers observed.


Requests for preprints and reprints to: zhu@math.utah.edu
This source can be found at http://www.math.utah.edu/research/