Tichy John, Bou-Saïd Benyebka
Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA.
J Biomech Eng. 2008 Apr;130(2):021012. doi: 10.1115/1.2899573.
The Phan-Thien and Tanner (PTT) model is one of the most widely used rheological models. It can properly describe the common characteristics of viscoelastic non-Newtonian fluids. There is evidence that synovial fluid in human joints, which also lubricates artificial joints, is viscoelastic. Modeling the geometry of the total hip replacement, the PTT model is applied in spherical coordinates for a thin confined fluid film. A modified Reynolds equation is developed for this geometry. Several simplified illustrative problems are solved. The effect of the edge boundary condition on load-carrying normal stress is discussed. Solutions are also obtained for a simple squeezing flow. The effect of both the relaxation time and the PTT shear parameter is to reduce the load relative to a Newtonian fluid with the same viscosity. This implies that the Newtonian model is not conservative and may overpredict the load capacity. The PTT theory is a good candidate model to use for joint replacement lubrication. It is well regarded and derivable from molecular considerations. The most important non-Newtonian characteristics can be described with only three primary material parameters.
范 - 田纳（PTT）模型是应用最广泛的流变模型之一。它能够恰当地描述粘弹性非牛顿流体的共同特性。有证据表明，人体关节中的滑液（它也润滑人工关节）具有粘弹性。在对全髋关节置换的几何形状进行建模时，PTT模型被应用于球坐标系中的薄受限流体膜。针对这种几何形状推导出了一个修正的雷诺方程。求解了几个简化的示例问题。讨论了边缘边界条件对承载法向应力的影响。还得到了简单挤压流的解。松弛时间和PTT剪切参数的作用都是相对于具有相同粘度的牛顿流体降低载荷。这意味着牛顿模型并不保守，可能会高估承载能力。PTT理论是用于关节置换润滑的一个很好的候选模型。它备受认可且可从分子层面推导得出。最重要的非牛顿特性仅用三个主要材料参数就能描述。
