Stokes slip flow in a corrugated pipe

In vitro measurements in the context of blood flows, performed in micro fab ricated microchannels are subject to the channel-walls exhibiting some degr ee of roughness. Interestingly it is realistic to note that microdomains su ch as arteries and capillaries are prone to constrictions for various patho logical reasons. Such microdomained flow problems may be studied as flows t hrough axially corrugated pipes using continuum theory, with slip boundary condition prescribed on the surface of the pipe. Considering the axial roug hness 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 Stok es 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 en hanced flow in the domain. (C) 1999 Elsevier Science Ltd. All rights reserv ed.