Lubrication theory in highly compressible porous media: the mechanics of skiing, from red cells to humans
Lubrication theory in highly compressible porous media: the mechanics of skiing, from red cells to humans
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DOI：
10.1017/s0022112000001725
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发表时间：
2000-11-10
影响因子：
3.7
通讯作者：
Weinbaum, S
中科院分区：
文献类型：
--
作者：
Feng, J;Weinbaum, S
采用有效介质方法（Brinkman方程）建立了适用于高变形多孔层的广义润滑理论。这个理论是有效的，当结构是可压缩的，由纤维组成的固相弹性压缩产生的法向力与在多孔层内产生的压力相比可以忽略不计。我们假定固相的变形主要是由于边界压缩，而不是由于流体相的运动。推导了一个广义Reynolds方程，其中Darcy渗透率参数α = H/rootK(p)由于矩阵压缩而引起的空间变化由变形矩阵的简化周期纤维模型流动的新的局部水动力解确定。其中H为未变形层厚度，K-p为达西渗透率。该简化模型假设纤维在垂直方向上随变形间隙高度线性压缩，而在水平面上纤维间距保持不变。因此，该模型能够捕获由矩阵层的大幅变形引起的基本非线性。新的理论表明，红细胞在微血管内皮糖萼上的滑动运动与人类滑雪者或单板滑雪运动员在压缩粉末上滑雪有着惊人的相似之处。在这两种情况下，当运动被捕获时，我们观察到矩阵层的数量级压缩，并预测alpha的值为100阶。在这个大α极限下，人们发现在压缩矩阵内产生的压力和升力比经典润滑理论大四个数量级。在红细胞的例子中，这些斥力可以解释为什么红细胞不会与内皮质膜发生持续的粘附分子相互作用，而在滑雪者或滑雪板运动员的例子中，该理论解释了为什么一个70公斤的人可以在压缩的粉末中滑行而不会下沉到底部，如果运动被阻止，就会发生这种情况。紧密贴合的红细胞和滑雪板之间的主要区别是在滑雪板边缘的侧向泄漏的多余压力，这大大减少了升力。本文为红细胞提出了一个简化的轴对称模型，以解释引人注目的突出现象，在这种现象中，红细胞从静止状态开始，将迅速从表面升起，然后在糖萼边缘附近滑动，同时也解释了Pries等人（1994）在体内测量到的出乎意料的大表观粘度。
A generalized lubrication theory that is applicable to highly deformable porous layers is developed using an effective-medium approach (Brinkman equation). This theory is valid in the limit where the structure is so compressible that the normal forces generated by elastic compression of the fibres comprising the solid phase are negligible compared to the pressure forces generated within the porous layer. We assume that the deformation of the solid phase is primarily due to boundary compression as opposed to the motion of the fluid phase. A generalized Reynolds equation is derived in which the spatial variation of the Darcy permeability parameter, alpha = H/rootK(p), due to the matrix compression is determined by new local hydrodynamic solutions for the flow through a simplified periodic fibre model for the deformed matrix. Here H is the undeformed layer thickness and K-p the Darcy permeability. This simplified model assumes that the fibres compress linearly with the deformed gap height in the vertical direction, but the fibre spacing in the horizontal plane remains unchanged. The model is thus able to capture the essential nonlinearity that results from large-amplitude deformations of the matrix layer.The new theory shows that there is an unexpected striking similarity between the gliding motion of a red cell moving over the endothelial glycocalyx that lines our microvessels and a human skier or snowboarder skiing on compressed powder. In both cases one observes an order-of-magnitude compression of the matrix layer when the motion is arrested and predicts values of alpha that are of order 100. In this large-alpha limit one finds that the pressure and lift forces generated within the compressed matrix are four orders-of-magnitude greater than classical lubrication theory. In the case of the red cell these repulsive forces may explain why red cells do not experience constant adhesive molecular interactions with the endothelial plasmalemma, whereas in the case of the skier or snowboarder the theory explains why a 70 kg human can glide through compressed powder without sinking to the base as would occur if the motion is arrested. The principal difference between the tightly fitting red cell and the snowboarder is the lateral leakage of the excess pressure at the edges of the snowboard which greatly diminishes the lift force. A simplified axisymmetric model is presented for the red cell to explain the striking pop out phenomenon in which a red cell that starts from rest will quickly lift off the surface and then glide near the edge of the glycocalyx and also for the unexpectedly large apparent viscosity measured by Pries et al. (1994) in vivo.