Asian Research Thesis Index

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.

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