An Energetic Variational Approach to Mathematical Modeling of Charged Fluids: Charge Phases, Simulation and Well Posedness
Open Access
Author:
Ryham, Rolf Josef
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
August 10, 2006
Committee Members:
Chun Liu, Committee Chair/Co-Chair Ludmil Tomov Zikatanov, Committee Chair/Co-Chair Qiang Du, Committee Member Yousry Azmy, Committee Member Fanghua Lin, Committee Member
Keywords:
ER fluid electrokinetics Nernst-Plank-Poisson phase field
Abstract:
We propose a
model of a charged fluid and interface system.
The model is derived from the energetic variational formulation
of the Navier Stokes (NS) equations of an incompressible fluid,
the Nernst-Plank-Poisson (NPP) equations for diffuse,
binary charge densities and surface area driven interface motion.
Using the phase field as a topological labeling
of the interface, we introduce a ``short range'
potential which selectively blocks charge migration
across the interface.
The model is able to capture the dynamics of both charge
induced flow and selection by the interface.
This is demonstrated by a simulation of the coalesence
of two charge selective vesicles by charge induced motion.
We develope the existence theory for global
classical solutions of the NPP equations with smooth data in space
dimension $dleq 3,$
global weak solutions to the
NPP equations coupled with the NS equations for $d leq 3$
and global weak solutions for small initial data
with the additional phase field Allen Cahn equation in space dimension
$d leq 2.$ The NPP equations
are a system of second order, divergence form,
semilinear, nonlocal parabolic equations.
We elucidate many of the
special features of the NPP equations
which are nonstandard in complex fluid systems.
