A Model for Steady Laminar Flow through a Deformable Gel-Coated Channel.
A model for the steady laminar flow of an incompressible fluid through a deformable gel-coated channel with slowly varying tapered shape is presented. Previous work has shown that the flow rate through such a channel is less than that which would be expected from the Hagen-Poiseuille equation (1973, J. Lahav, N. Eliezer, and A. Silberberg, Biorheology 10, 595; 1979, P. Krindel and A. Silberberg, J. Colloid Interface Sci. 71, 39). Krindel and Silberberg also observed the onset of turbulent flow at lower rates than would normally be expected; they attributed these phenomena to a turbulent boundary layer near the channel walls. Our analysis shows that the rate reduction is in fact due to kinetic energy effects related to the converging flowlines. A model to describe this rate reduction is presented and is shown to agree well with experimental results, successfully predicting the observed flow rate reduction over Reynolds numbers ranging from 1 to 1000. Copyright 2000 Academic Press.
Yang
Canghu
C
Earth Sciences and Engineering, Imperial College of Science, Technology and Medicine, T. H. Huxley School of Environment, London, SW7 2BP, United Kingdom
Grattoni
Carlos A.
CA
Muggeridge
Ann H.
AH
Zimmerman
Robert W.
RW