Steven L. Weinberg

Bio: Steven L. Weinberg is an academic researcher from Massachusetts Institute of Technology. The author has contributed to research in topics: Reynolds number & Two-dimensional flow. The author has an hindex of 4, co-authored 4 publications receiving 2338 citations.

Peristaltic pumping with long wavelengths at low Reynolds number

Abstract: Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which the relevant Reynolds number is small enough for inertial effects to be negligible and the wavelength to diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axisymmetric 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.

Peristaltic pumping with long wave lengths at low reynolds number.

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)

An experimental study of peristaltic pumping

Abstract: An apparatus that approximates a two-dimensional, infinite train of peristaltic waves yields measurements of mean flow, of mean pressure rise, and of pressure-time pulses at fixed locations. In addition, visual observations of ‘reflux’ and ‘trapping’, using dyed fluid, are shown. The inertia-free range extends up to a Reynolds number of about 1. In this range, the theory of Shapiro, Jaffrin & Weinberg (1969) is confirmed with respect to mean pressure vs. mean flow, pressure vs. time, reflux, and trapping. The controversy regarding the criterion of material reflux is settled in favour of the Lagrangian time-mean velocity rather than the Eulerian time-mean velocity. Experiments at higher Reynolds numbers show that the second-order expansion theory of Jaffrin (1971) is valid up to a Reynolds number of about 10.

Hydrodynamic Model of Ureteral Function

Abstract: Publisher Summary This chapter discusses the hydrodynamic modeling of the transport of urine by the ureters from the kidneys to the bladder. Peristaltic waves, generated by neuromuscular action, are the main mechanism of urine transport in the ureter. The first attempt to describe the fluid mechanics of the urinary tract seems to have been made by Lykoudis. There is no flow in the inactive sections of the ureter ahead of or behind the peristaltic wave. The pressure in the ureter rises with time wherever the lumen radius exceeds the resting radius and decreases with time wherever it is below the resting radius. The entrance of a wave into the ureter and its exit seem to have no effect on the pressure recordings. The volume carried by the wave is nearly equal to the volume of the bolus and independent of the structure of the contraction. If the pressure measured is the actual pressure in the ureter and not an artifact resulting from obstruction by the catheter, the transverse dimensions of the contracted and inactive lumen must be extremely small.