Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications

[+] Author and Article Information
J. S. Hou, W. M. Lai, V. C. Mow

Orthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032

M. H. Holmes

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180

J Biomech Eng 111(1), 78-87 (Feb 01, 1989) (10 pages) doi:10.1115/1.3168343 History: Received July 27, 1988; Revised December 05, 1988; Online June 12, 2009


The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A “pseudo-no-slip” kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.

Copyright © 1989 by ASME
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