Applicability of continuum mechanics to pressure drop in small orifices

Abstract

Pressure drop in small orifices (8–109 μm) is examined by comparing the experimental data of Hasegawa, Suganuma, and Watanabe [Phys. Fluids 9, 1 (1997)] with theoretical and numerical solutions of the Navier–Stokes equations in order to test the claim by Hasegawa, Suganuma, and Watanabe that the data could not be explained by traditional continuum mechanics. The Reynolds number varies from zero (for the theoretical solution to Stokes flow) to 1000. The ratio of the orifice thickness to its diameter varies from 0.092 to 1.14. The primary increase in pressure drop is shown to be due to the effect of a finite thickness of the orifice, and this effect is predicted for Stokes flow by the theory of Dagan, Weinbaum, and Pfeffer [J. Fluid Mech. 115, 505 (1982)]. Numerical results presented here agree with Dagan, Weinbaum, and Pfeffer at Reynolds numbers below 10 and with the experimental data of Hasegawa, Suganuma, and Watanabe for low and intermediate Reynolds numbers. Most of the data can be predicted using traditional continuum mechanics.