ABSTRACT
Implications to Soft Porous Lubrication ............................................................................... 161 6.5.1 Endothelial Glycocalyx Layer .................................................................................. 161
6.5.1.1 Molecular Sieve for Plasma Proteins ......................................................... 161 6.5.1.2 Mechanotransducer for Fluid Shear Stress ................................................ 162 6.5.1.3 Highly Compressible Porous Hydrodynamic Interface in the Motion
of Red and White Cells in Capillaries ....................................................... 162 6.5.2 Lubrication Theory for Highly Compressible Porous Media ................................... 164
6.5.2.1 New Reynolds Equation ............................................................................. 164 6.5.2.2 Darcy Permeability .................................................................................... 166 6.5.2.3 Results and Discussion............................................................................... 166
6.6 Lift Generation in Highly Compressible Porous Media under Rapid Compression: A Systematic, Experimental, and Theoretical Study ............................................................... 170 6.6.1 Dynamic Compression of Highly Compressible Porous Media with Application
to Snow Compaction and Skiing .............................................................................. 170 6.6.1.1 Experiments ............................................................................................... 171 6.6.1.2 Theory ........................................................................................................ 176 6.6.1.3 Remarks on the Dynamic Compression of Snow ...................................... 188 6.6.1.4 On the Characterization of Lifting Forces during the Rapid
Compaction of Deformable Porous Media ................................................ 190 6.6.1.5 Dynamic Compression of Soft Porous Media: From Finite to Inœnite
Domain ......................................................................................................206 6.7 Lift Mechanics of Downhill Skiing or Snowboarding ......................................................... 217
6.7.1 Theoretical Formulation ........................................................................................... 218 6.7.1.1 Darcy Permeability of Snow ...................................................................... 218 6.7.1.2 Pore Pressure .............................................................................................. 219
In a recent study, Feng and Weinbaum (2000), hereafter referred to as F&W, laid the foundation for a new type of lubrication theory that is applicable for porous medium whose structure is so compressible that the normal forces generated by the elastic compression of the matrix are negligible compared to the pressure forces generated within the porous layer. This new theory shows that there is an unexpected and remarkable dynamic similarity between the motion of a red cell gliding at <20 µm/s on a compressed endothelial glycocalyx layer (EGL) of sulfated proteoglycans and glycoproteins that lines the endothelial cells (ECs) of our capillaries (Figures 6.1 and 6.2a) and a human skier or snowboarder skiing on soft snow powder (Figures 6.3 and 6.46), even though their difference in mass is of the order 1015. F&W predicted that the excess pore pressure generated by a planing surface moving on any compressible porous medium scales as α2 = h2/K, where h is the layer thickness and K is the Darcy permeability and α is of an order 102 or larger for both red blood cells gliding on the EGL as shown in Figure 6.2a and human skiing as shown in Figure 6.3. Thus, the lift forces generated can be four or more orders of magnitude greater than the classical lubrication theory. The huge enhancement in the lift arises from the fact that as the matrix compresses, there is a dramatic increase in the lubrication pressure because of the marked increase in the hydraulic resistance that the “uid encounters as it tries to escape from the conœning boundaries through the thin compressed porous layer.
