Lift generation in soft porous media: From red cells to skiing to a new concept for a train track

In a recent paper, Feng and Weinbaum (2000) showed that there is a remarkable dynamic similarity between a red cell gliding on the endothelial surface layer (ESL) that lines our microvessels and a human snowboarding on fresh powder although they differ in mass by 1015. One is able to produce lift forces in each case that are several orders of magnitude greater than classical lubrication theory. In the case of the red cell, Weinbaum et al. (2003) also predicted that the normal force required to compress the core proteins in the ESL is much less than the lift force due to the fluid draining pressure. Frictional drag which is proportional to this force is dramatically reduced.; Herein we shall first present non-linear exact and asymptotic solutions to a Navier-Stokes equation of Brinkman type for a stagnation point flow in a porous medium. The solutions for the two dimensional case are applied to describe the flow in the transverse plane of a ski or snowboard. We then report the first experimental and theoretical study of the pore pressures generated in snow on the time scale of skiing or snowboarding. Using a novel porous cylinder-piston apparatus, we have measured the excess pore pressure that would build up beneath the piston surface and have also measured its subsequent decay due to the venting of the air from the snow at the porous walls of the cylinder. A theoretical model for this pressure relaxation process is then developed using a consolidation theory, which shows good agreement with the experimental data. Based on these studies, we further extend Feng and Weinbaum theory to a more realistic theoretical model to describe the lift mechanics of downhill skiing or snowboarding. And finally, we employ the concepts deduced from the motion of red cells in capillaries and human skiing or snowboarding to the design of a prototype high speed train track which can support gliding vehicles weighing 50 or more metric tons with extremely low sliding friction. The permeability and elastic properties of this train track are similar to goose down.