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# Accession Number:

## AD0679180

# Title:

## PERISTALTIC PUMPING WITH LONG WAVE LENGTHS AT LOW REYNOLDS NUMBER.

# Descriptive Note:

## Summary rept.,

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE FLUID MECHANICS LAB

# Report Date:

## 1968-09-01

# Pagination or Media Count:

##
61.0

# Abstract:

## Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which 1 the relevant Reynolds number is small enough for inertial effects to be negligible and 2 the wavelength-diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axi-symmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values. Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward reflux time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid mechanical peculiarity with physiological implications is that of trapping under certain conditions an internally-circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#