Detachment phenomena in low Reynolds number flows through sinusoidally constricted tubes

We examine the nature of detachment experimentally and numerically in stead y axisymmetric flows through sinusoidally constricted tubes with Re varying from 10(-4) to 10(2). Various regions can be distinguished, including how detachment at the lowest Re used. Further, the transition in the pressure d rop from a linear Poiseuille-like behaviour to a nonlinear pressure-drop-ve locity relationship is not generally related to the appearance of detachmen t regions but rather to their form and to the nature of their growth. For t he geometries considered here, the relationship between the start of nonlin earity in the pressure drop and incipient detachment depends on whether det achment is symmetric (detachment point at the bottom of a trough): for flow geometries with symmetric incipient detachment kinematic changes occur at Re lower than or the same as that at which dynamic changes can be detected, whereas for those with asymmetric incipient detachment they occur at highe r Re. We look at various possible criteria for determining the transition f rom the viscous to the inertial range. Finally, we discuss the effect of el ongational terms in the energy dissipation on flow through periodically con stricted tubes and compare this flow with flow through porous media.