An Application Of Contact Melting Theory To Skates Sliding On Ice
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P. J. Montgomery
An application of contact melting theory to skates sliding on ice P. J. Montgomery Mathematics Program, University of Northern British Columbia, 3333 University Way, Prince George, B.C., Canada Abstract The problem of a skate blade sliding over ice is a complex and classic problem, with an early form considered by Reynolds over a century ago. The problem is revisited herein: a thin layer of water in between the skate blade and the ice surface is assumed to exist, and acts as a lubricant for the sliding motion of the skate blade. The existence of the melt layer is caused by viscous friction in the liquid film itself, instead of pressure melting. Governing equations are considered for a Newtonian and inviscid fluid of constant density. These equations are reduced by considering some scaling analysis to determine the negligible terms, and a simpler planar flow is considered. Through some straightforward manipulations of the governing equations, the viscous stress on the surface of the skate blade is analytically expressed as a function of the depth of the melt layer. Other results are used to posit an approximate expression for the non-constant depth of the melt layer, and this is used to calculate the frictional force. The results are compared to others in the area, and limitations on the modelling are discussed. Keywords: multiphase flow, fluid dynamics, stefan problem. 1 Introduction Contact melting is an area of research in which two solids interact in such a way that one of the solids partially melts at the surface to create a thin melted layer between the two solids which acts to lubricate the motion between the two parts. A relatively recent review of the industrial and engineering applications of this theory has been completed by Bejan , although the area of focus of this manuscript is on the application of the contact melting theory to describe a skate blade sliding over ice. The classical mechanism of melting due to surface pressure has been
multiphase flow, fluid dynamics, stefan problem.