Abstract:
In this thesis, the problems of flow and ion-induced deformation of soft porous bi
ological tissues have been examined by using continuum mixture theory approach.
In particular, we focus on the tissue deformation due to non-Newtonian fluid and
externally applied magnetic field. In this regard, we first analyze the problem of
non-Newtonian flow-induced deformation from pressurized cavities in absorbing
porous tissues. Specifically, a model with a spherical cavity embedded in an in
finite porous medium is used to find fluid pressure and solid displacement in the
tissue as a function of non-dimensional radial distance and time. The governing
nonlinear equations have been solved numerically to highlight effects of various
emerging parameters. Furthermore, based on the geometry of the previous prob
lem, the effect of the externally applied magnetic field on flow-induced deformation
of absorbing porous tissues is investigated. A biphasic mixture theory approach
has been used to develop a mathematical model. The governing dimensionless
equations for fluid pressure and solid displacement have been solved numerically
using the method of lines approach and the trapezoidal rule, respectively. The
effect of magnetic parameter on fluid pressure and solid displacement is illustrated
graphically. Finally, the problem of ion-induced deformation of articular cartilage
with strain-dependent nonlinear permeability and magnetohydrodynamic effects
is presented. The governing set of coupled partial differential equations are non
dimensionalized using suitable dimensionless variables. Analytical solutions are
provided for the constant permeability case whereas for the nonlinear permeabil
ity case the displacement equation is solved numerically using the method of lines
technique. The influence of magnetic and permeability parameter on solid dis
placement and fluid pressure is illustrated graphically. In some cases, a graphical
comparison to the previously reported literature is also presented.
