Stokes slip flow in a corrugated pipe

In vitro measurements in the context of blood flows, performed in micro fabricated microchannels are subject to the channel-walls exhibiting some degree of roughness. Interestingly it is realistic to note that microdomains such as arteries and capillaries are prone to constrictions for various pathological reasons. Such microdomained flow problems may be studied as flows through axially corrugated pipes using continuum theory, with slip boundary condition prescribed on the surface of the pipe. Considering the axial roughness of the pipe as r' = a + b sin (2 pi z'/L), where a is the mean radius of the pipe, b is the amplitude of the projections, the corresponding Stokes flow problem is studied. The key result of the paper is the development of an analytical formula for the computation of flow rate for a prescribed mean axial pressure gradient; It is found, as expected, that slip causes enhanced flow in the domain. (C) 1999 Elsevier Science Ltd. All rights reserved.