Wall Slip: Measurement and Modeling Issues

The no-slip hydrodynamic condition states, without proof, that the tangential velocity component of a liquid in contact with a solid substrate is the velocity of the substrate. This hypothesis is important because it provides a vital link between continuum equations that govern flow of bulk liquids and the complex molecular processes responsible for momentum transport across fluid-solid interfaces. A good summary of the early history surrounding the no-slip condition can be found in Ref. (1). Pioneering experiments by Coulomb, for example, are believed to have provided critical early support for the no-slip condition. Coulomb measured the drag force exerted by liquid water on oscillating metal disks smeared with grease and with grease covered by powdered sandstone and found no difference. This finding is significant because it indicates that the friction coefficient of the solid substrate has no influence on the fluid velocity at the fluid-solid interface, a requirement for the no-slip condition to be universally valid. Early analyses by Stokes and others of pressure-driven flow of simple liquids through tubes with no-slip at the walls also yielded results consistent with experimental observations for flow of water through glass tubes (1).