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.
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February 1989
Research Papers
Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications
J. S. Hou,
J. S. Hou
Orthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032
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M. H. Holmes,
M. H. Holmes
Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180
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W. M. Lai,
W. M. Lai
Orthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032
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V. C. Mow
V. C. Mow
Orthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032
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J. S. Hou
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
W. M. Lai
Orthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032
V. C. Mow
Orthopaedic Research Laboratory, Departments of Mechanical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10032
J Biomech Eng. Feb 1989, 111(1): 78-87 (10 pages)
Published Online: February 1, 1989
Article history
Received:
July 27, 1988
Revised:
December 5, 1988
Online:
June 12, 2009
Citation
Hou, J. S., Holmes, M. H., Lai, W. M., and Mow, V. C. (February 1, 1989). "Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications." ASME. J Biomech Eng. February 1989; 111(1): 78–87. https://doi.org/10.1115/1.3168343
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