Abstract
A mechano-electrochemical theory for charged hydrated soft tissues with multi-electrolytes was developed based on the continuum mixture theory. The momentum equations for water and ions were derived in terms of a mechanochemical force (gradient of water chemical potential), electrochemical forces (gradient of Nernst potentials) and an electrical force (gradient of electrical potential). The theory was shown to be consistent with all existing specialized theories. Using this theory, some mechano-electrokinetic properties of charged isotropic tissues were studied. The well-known Hodgkin–Huxley equation for resting cell membrane potential was derived and the phenomenon of electro-osmotic flow in charged hydrated soft tissues was investigated. Analyses show that the tissue fixed charge density plays an important role in controlling the transport of water and ions in charged hydrated soft tissues.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Achanta, S., Cushman, J. H. and Okos, M. R.: 1994, On multicomponent, multiphasic thermomechanics with interfaces, Int. J. Engng. Sci. 32, 1717-1738.
Bowen, R. M.: 1980, Incompressible porous media models by use of the theory of mixtures, Int. J. Engng. Sci. 18, 1129-1148.
Coelho, D., Shapiro, M., Thovert, J. F. and Adler, P. M.: 1996, Electroosmotic phenomena in porous media, J. Colloid Interf. Sci. 181, 169-190.
Donnan, F. G.: 1924, The theory of membrane equilibria, Chem. Rev. 1, 73-90.
de Boer, R.: 1996, Highlights in the historical development of the porous media theory: toward a consistent macroscopic theory, Appl. Mech. Rev. 49, 201-262.
de Groot, S. R. and Mazur, P.: 1984, Non-Equilibrium Theormodynamics, Dover, New York.
Fair, J. C. and Osterle, J. F.: 1971, Reverse electrodialysis in charged capillary membranes, J. Chem. Phys. 54, 3307-3316.
Frank, E. H. and Grodzinsky, A. J.: 1987a, Cartilage electromechanics-I. Electrokinetic transduction and the effects of electrolyte ph and ionic strength, J. Biomech. 20, 615-627.
Frank, E. H. and Grodzinsky, A. J.: 1987b, Cartilage electromechanics-II. A continuum model of cartilage electrokinetics and correlation with experiments, J. Biomech. 20, 629-639.
Frank, E. H., Grodzinsky, A. J., Phillips, S. L. and Grimshaw, P. E.: 1990, Physicochemical and bioelectrical determinants of cartilage material properties, In: V. C. Mow, A. Ratcliffe and S. L.-Y. Woo (eds), Biomechanics of Diarthrodial Joints, Vol. 1, Springer-Verlag, New York, pp. 363-390.
Grodzinsky, A. J.: 1990, Mechanical and electrical properties and their relevance to physiological processes, In: A. Maroudas and K. Kuettner (eds), Methods in Cartilage Research, Academic Press, San Diego, pp. 275-281.
Gu, W. Y., Lai, W. M. and Mow, V. C.: 1993a, Transport of fluid and ions through a porous-permeable charged-hydrated tissue, and streaming potential data on normal bovine articular cartilage, J. Biomech. 26, 709-723.
Gu, W. Y., Lai, W. M. and Mow, V. C.: 1993b, Theoretical basis for measurements of cartilage fixed-charge density using streaming current and electro-osmosis effects, In: J. M. Tarbell (ed.), Adv. Bioeng. ASME, Vol. 26, BED, New York, pp. 55-58.
Gu, W. Y., Lai, W. M. and Mow, V. C.: 1994, A generalized triphasic theory for multi-electrolyte transport in charged hydrated soft tissues, In: M. J. Askew (ed.), Adv. Bioeng. ASME, Vol. 28, BED, New York, pp. 217-218.
Gu, W. Y., Lai, W. M. and Mow, V. C.: 1997, A triphasic analysis of negative osmotic flow through charged-hydrated soft tissues, J. Biomech. 30, 71-78.
Gu, W. Y., Lai, W. M. and Mow, V. C.: 1998, A mixture theory for charged-hydrated soft tissues containing multi-electrolytes: passive transport and swelling behaviors, J. Biomech. Engng. 120, 169-180.
Heodug, W. K. and Wong, S-W.: 1996, Hydration swelling of water-absorbing rocks: a constitutive model, Int. J. Num. Anal. Methods Geomech. 20, 403-430.
Helfferich, F.: 1962, Ion Exchange, McGraw-Hill, New York.
Hodgkin, A. L. and Huxley, A. F.: 1952a, The components of membrane conductance in the giant axon of Loligo, J. Physiol. (London) 116, 473-496.
Hodgkin, A. L. and Huxley, A. F.: 1952b, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (London) 117, 500-544.
Huyghe, J. M. and Janssen, J. D.: 1997, Quadriphasic mechanics of swelling incompressible porous media, Int. J. Engng. Sci. 35, 793-802.
Katchalsky, A. and Curran, P. F.: 1975, Nonequilibrium Thermodynamics in Biophysics, 4th edn, Harvard University Press, Cambridge, Mass.
Kedem, O. and Katchalsky, A.: 1961, A physical interpretation of the phenomenological coefficients of membrane permeability, J. Gen. Physiol. 45, 143-179.
Lai, W. M., Hou, J. S. and Mow, V. C.: 1991, A triphasic theory for the swelling and deformation behaviors of articular cartilage, J. Biomech. Engng. 113, 245-258.
Lai, W. M., Gu, W. and Mow, V. C.: 1994, Flows of electrolytes through charged hydrated biologic tissue, Appl. Mech. Rev. 47 (part 2), 277-281.
Maroudas, A.: 1968, Physicochemical properties of cartilage in the light of ion exchange theory, Biophy. J. 8, 575-595.
Mow, V. C., Kuei, S. C., Lai, W. M. and Armstrong, C. G.: 1980, Biphasic creep and stress relaxation of articular cartilage in compression: theory and experiments, J. Biomech. Engng. 102, 73-84.
Nernst, W.: 1888, Zur Kinetik der Lösung Befindlichen Körper: Theorie der Diffusion, Z. Phys. Chem. 3, 613-637.
Onsager, L.: 1931a, Reciprocal relations in irreversible processes. I, Phys. Rev. 37, 405-426.
Onsager, L.: 1931b, Reciprocal relations in irreversible processes. II, Phys. Rev. 38, 2265-2279.
Salzstein, R. A., Pollack, S. R. and Mak, A. F. T.: 1987, Electromechanical potentials in cortical bone-I. A continuum approach, J. Biomech. 20, 261-270.
Silberberg, A.: 1982, The mechanics and thermodynamics of separation flow through porous, molecularly disperse, solid media, Biorheology 19, 111-127.
Teorell, T.: 1953, Transport processes and electrical phenomena in ionic membranes, Prog. Biophys. Physicochem. 3, 305-369.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lai, W.M., Mow, V.C. Transport of Multi-Electrolytes in Charged Hydrated Biological Soft Tissues. Transport in Porous Media 34, 143–157 (1999). https://doi.org/10.1023/A:1006561408186
Issue Date:
DOI: https://doi.org/10.1023/A:1006561408186