Understanding the motion of immiscible fluids in porous media is a cha
llenging problem in low-Reynolds-number hydrodynamics that is relevant
to many processes of technological and biological interest. Simple re
presentations of the flow on the scale of individual pores or channels
have proven useful in exposing effects of various parameters on fluid
motion and in identifying flow-induced changes in the spatial configu
rations of the fluids, which can affect the mobilities of the phases.
This paper examines a hierarchy of such prototype flows, paying specia
l attention to phenomena that cannot be described completely by the eq
uations of motion, such as flow-induced breakup and coalescence of flu
id phases. In these cases, connections between numerical computations
and experiments are especially significant, which is apparent in the s
tudies reviewed here.