BOUNDARY-CONDITIONS AT THE CARTILAGE-SYNOVIAL FLUID INTERFACE FOR JOINT LUBRICATION AND THEORETICAL VERIFICATIONS
BOUNDARY-CONDITIONS AT THE CARTILAGE-SYNOVIAL FLUID INTERFACE FOR JOINT LUBRICATION AND THEORETICAL VERIFICATIONS
复制标题
DOI：
10.1115/1.3168343
复制
发表时间：
1989-02-01
影响因子：
1.7
通讯作者：
MOW, VC
中科院分区：
文献类型：
--
作者：
HOU, JS;HOLMES, MH;MOW, VC
这项研究的目的是建立和验证两相混合物(关节软骨)和牛顿或非牛顿流体(滑液)之间的界面上的一组边界条件，以便可以用一组适当的数学问题来研究关节润滑问题。提出了一种“伪无滑移”运动边界条件，其原理是混合物或混合物与流体交界处的条件必须简化为单相连续介质力学中的边界条件。根据提出的运动边界条件以及质量、动量和能量的平衡，从数学上推导了两相混合物与牛顿或非牛顿流体界面的边界条件。在此基础上，推导了软骨-滑液-软骨润滑问题建模所需的适当边界条件。对于两种简单的情况，即牛顿粘性流体被迫(在附加Couette或Poiseuille流动条件下)在渗透率相对较低的多孔渗透性两相材料上流动，众所周知的经验Taylor滑移条件可以通过对界面处边界层的匹配渐近分析来推导。
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.