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-electrochemica l behaviors of charged hydrated soft tissues containing multi-electrol ytes. The mixture is composed of n + 2 constituents (1 charged solid p hase, 1 noncharged solvent phase, and n ion species). Results from thi s theory show that three types of force are involved in the transport of ions and solvent through slrch materials: (1) a mechanochemical for ce (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 transp ort rates of these ions and solvent: (1) a hydraulic permeability; (2) mechano-electrochemical coupling coefficients; and (3) an ionic condu ctance matrix. Specifically, we derived the fundamental governing rela tionships between these forces and material coefficients to describe s uch mech ano-electrochemical transduction effects as streaming potenti al, 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 an d Huxley, 1952a, b) could be derived using our new n + 2 mixture model (a generalized triphasic theory). In general, the n + 2 mixture theor y 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 tissu e of finite thickness during a one-dimensional steady diffusion proces s. Numerical results were provided for the exchange of Na+ and Ca++ th rough the tissue. These numerical results support our hypothesis that tissue fixed charge density (c(F)) plays a significant role in modulat ing kinetics of ions and solvent transport through charged-hydrated so ft tissues.