A Mixture Theory for Charged-Hydrated Soft Tissues Containing Multi-electrolytes: Passive Transport and Swelling Behaviors

A new mixture theory was developed to model the mechano-electrochemical behaviors of charged-hydrated soft tissues containing multi-electrolytes. The mixture is composed of n + 2 constituents (1 charged solid phase, 1 noncharged solvent phase, and n ion species). Results from this theory show that three types of force are involved in the transport of ions and solvent through such materials: (1) a mechanochemical force (including hydraulic and osmotic pressures); (2) an electrochemical force; and (3) an electrical force. Our results also show that three types of material coefficients are required to characterize the transport rates of these ions and solvent: (1) a hydraulic permeability; (2) mechano-electrochemical coupling coefficients; and (3) an ionic conductance matrix. Specifically, we derived the fundamental governing relationships between these forces and material coefficients to describe such mechano-electrochemical transduction effects as streaming potential, streaming current, diffusion (membrane) potential, electro-osmosis, and anomalous (negative) osmosis. As an example, we showed that the well-known formula for the resting cell membrane potential (Hodgkin and Huxley, 1952a, b) could be derived using our new n + 2 mixture model (a generalized triphasic theory). In general, the n + 2 mixture theory is consistent with and subsumes all previous theories pertaining to specific aspects of charged-hydrated tissues. In addition, our results provided the stress, strain, and fluid velocity fields within a tissue of finite thickness during a one-dimensional steady diffusion process. Numerical results were provided for the exchange of Na⁺ and Ca⁺⁺ through the tissue. These numerical results support our hypothesis that tissue fixed charge density (c^F) plays a significant role in modulating kinetics of ions and solvent transport through charged-hydrated soft tissues.