A Potential Elastohydrodynamic Origin of Load-Support and Coulomb-Like Friction in Lung∕Chest Wall Lubrication

Abstract

During normal breathing, the mesothelial surfaces of the lung and chest wall slide relative to one another. Experimentally, the shear stresses induced by such reciprocal sliding motion are very small, consistent with hydrodynamic lubrication, and relatively insensitive to sliding velocity, similar to Coulomb-type dry friction. Here we explore the possibility that shear-induced deformation of surface roughness in such tissues could result in bidirectional load-supporting behavior, in the absence of solid-solid contact, with shear stresses relatively insensitive to sliding velocity. We consider a lubrication problem with elastic blocks (including the rigid limit) over a planar surface sliding with velocity U, where the normal force is fixed (hence the channel thickness is a dependent variable). One block shape is continuous piecewise linear (V block) and the other continuous piecewise smoothly quadratic (Q block). The undeformed elastic blocks are spatially symmetric; their elastic deformation is simplified by taking it to be affine, with the degree of shape asymmetry linearly increasing with shear stress. We find that the V block exhibits nonzero Coulomb-type starting friction in both the rigid and the elastic case, and that the smooth Q block exhibits approximate Coulomb friction in the sense that the rate of change of shear force with U is unbounded as U→0, shear force ∝U1∕2 in the rigid asymmetric case and ∝U1∕3 in the (symmetric when undeformed) elastic case. Shear-induced deformation of the elastic blocks results in load-supporting behavior for both directions of sliding. This mechanism could explain load-supporting behavior of deformable surfaces that are symmetrical when undeformed and may be the source of the weak velocity dependence of friction seen in the sliding of lubricated, but rough, surfaces of elastic media such as the visceral and parietal pleural surfaces of the lung and chest wall.