On peristaltic flow and its efficiency

The question of efficiency in performing biological functions is raised in the context of peristaltic fluid transport. To deal with this problem a complete solution for peristaltic flow in a pipe and in a channel, assuming a given time mean flow, is developed, by a double expansion in terms of the Reynolds number and the square of the wave number. This solution is valid for arbitrary waveshapes. We resolve a long-standing problem and show that quite generally the pressure rise per wave length is constant on a cross section. We also show that for a sinusoidal wave (and others) the interaction of Reynolds number and wave number is a third-order effect for this pressure rise. Plow-type waves, nipple-type waves and the sinusoidal wave are compared for maximum efficiency and for minimum energy usage. It is found that large plows are best from mechanical efficiency considerations, but large nipples use the least energy. The biological implications of these results are discussed.