Abstract
Fluid and solute transport in poroelastic media is studied. Mathematical modeling of such transport is a complicated problem because of the volume change of the specimen due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in both theoretical and experimental investigations. The one-dimensional version of the theory is less complex and may serve as an approximation in some problems, and therefore, a one-dimensional (in space) model of fluid and solute transport through a poroelastic medium with variable volume is developed and analyzed. In order to obtain analytical results, the Lie symmetry method is applied. It is shown that the governing equations of the model admit a non-trivial Lie symmetry, which is used for construction of exact solutions. Some examples of the solutions are discussed in detail.
Highlights
The mathematical description of transport processes in biological tissue and artificial permselective membranes is crucial for understanding the physiology and pathology of biological systems and the effectiveness of artificial life supporting systems [1,2]
Such problems involve transport through the biological tissue as in peritoneal dialysis, handling of transport through the pathological tissue as solid tumors, transport across polymer permselective membranes used in hemodialysis, or other membrane separation processes [1,2,3,4]
The mathematical model for the poroelastic materials (PEM) with the variable volume is developed under the following assumptions: 1
Summary
The mathematical description of transport processes in biological tissue and artificial permselective membranes is crucial for understanding the physiology and pathology of biological systems and the effectiveness of artificial life supporting systems [1,2]. The transport of fluid may result under some circumstances in the change of hydration of the material and subsequently in the change of its shape and volume Such changes in the size of the specimen are typically not taken into account, and the theory is derived for a fixed size of the transport medium, even if the change of hydration is included the model [1,3,7,8]. The obtained model of the one-dimensional changes of the specimen caused by the alteration of membrane hydration (due to its swelling or shrinking) evokes the problem known as the “moving boundary”, which together with the nonlinearity of the theory and several variables involved, makes the task of finding the analytical solution very difficult. We briefly discuss the result obtained in the last section
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