Flows of Electrolytes Through Charged Hydrated Biological Tissue

Abstract

In this paper, analyses of the flows of water and electrolytes through charged hydrated biologic tissues (e.g., articular cartilage) are presented. These analyses are based on the triphasic mechano-electrochemical theory developed by Lai and coworkers (1991). The problems analyzed are 1-D steady permeation flows generated by a hydraulic pressure difference and/or by an osmotic pressure difference across a finite thickness layer of the tissue. The theory allows for the complete determination of the ion concentration field, the matrix strain field as well as the ion and water velocity field inside the tissue during the steady permeation. For flows generated by a hydraulic pressure difference, the frictional drag induces a compaction of the solid matrix causing the fixed charge density (FCD) to increase and the neutral salt concentration to decrease in the downstream direction. Further, while both ions move downstream, but relative to the solvent (water), the anions (Cl−) move with the flow while the cations (Na+) move against the flow. The theory also predicts a well-known experimental finding that the apparent permeability decreases nonlinearly with FCD. For flows generated by an osmotic pressure difference, first, fluid flow varies with the FCD in a nonlinear and non-monotonic manner. Second, there exists a critical FCD below which negative osmosis takes place.