Date of Award

Spring 2013

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Michael Siegel

Second Advisor

Michael R. Booty

Third Advisor

Linda Jane Cummings

Fourth Advisor

Pushpendra Singh

Fifth Advisor

Jeffrey Franklin Morris

Abstract

We consider two-phase flow of ionic fluids whose motion is driven by an imposed electric field. At a fluid-fluid interface, a screening cloud of ions develops and forms an electro-chemical double layer or ‘Debye layer’. The applied electric field acts on the ionic cloud it induces, resulting in a strong slip flow near the interface. This is known as ‘induced-charge electro-kinetic flow’, and is an important phenomenon in microfluidic applications and in the manipulation of biological cells. The models with two different cases including the fast or slow charging time scales are studied both analytically and numerically. We address a significant challenge in the numerical computation of such flows in the thin-double-layer limit, by using the slenderness of the layer to develop a fast and accurate ‘hybrid’ or multiscale numerical method. The method incorporates an asymptotic analysis of the electric potential and fluid dynamics in the Debye layer into a boundary integral numerical solution of the full moving boundary problem.

We present solutions for the quasi-steady state problem with ψ = O(1) and solutions for the time dependent problem with ψ « 1, where ψ is the dimensionless surface potential. Leading order problems for both electric fields and fluid fields are solved with boundary conditions and matching methods. The small deformation theories when Ca is small (Ca is the electric capillary number) for both quasi-steady state and time dependent problems are developed to check numerical simulations.

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Mathematics Commons

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