An investigation is made on streamlines and path lines in a two-dimensional channel subjected to periodic changes in cross-sectional area. High Reynolds number flows are dealt with to bring out the possibilities of engineering application of fluid mixing by peristalsis. A potential flow analysis is developed on the basis of periodic source distributions located far away from the channel. A simplified approximate solution is derived and compared in good agreement with visual observations carried out at Reynolds numbers as high as 103. A condition which makes the approximate solution irrotational is presented. Under zero time-mean flow conditions, a fluid particle near the oscillating wall undergoes a net forward displacement, while the one away from the wall retrogrades, contrary to results at low Reynolds numbers. A distinction is found between the period of wall oscillation and the time required for a particle to complete its one cycle of trajectory.
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Ayukawa et al. (1981) studied this question.