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Miscible displacements in capillary tubes. Part 1. Experiments

Published online by Cambridge University Press:  26 April 2006

P. Petitjeans  and
T. Maxworthy
P. Petitjeans
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90090-1191, USA
T. Maxworthy
Affiliation:
Laboratoire de Physique et Mecanique des Milieux Heterogenes, Ecole Superieure de Physique et Chimie Industrielles, 10, Rue Vauquelin, F-75231, Paris cedex 05, France
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Abstract

Experiments have been performed, in capillary tubes, on the displacement of a viscous fluid (glycerine) by a less viscous one (a glycerine–water mixture) with which it is miscible in all proportions. A diagnostic measure of the amount of viscous fluid left behind on the tube wall has been found, for both vertical and horizontal tubes, as a function of the Péclet (Pe) and Atwood (At) numbers, as well as a parameter that is a measure of the relative importance of viscous and gravitational effects. The asymptotic value of this diagnostic quantity, for large Pe and an At of unity, has been found to agree with that found in immiscible displacements, while the agreement with the numerical results of Part 2 (Chen & Meiburg 1966), over the whole range of At, is very good. At values of the average Pe greater than 1000 a sharp interface existed so that it was possible to make direct comparisons between the present results and a prior experiment with immiscible fluids, in particular an effective surface tension at the diffusing interface could be evaluated. The effect of gravity on the amount of viscous fluid left on the tube wall has been investigated also, and compared with the results of Part 2. A subsidiary experiment has been performed to measure both the average value of the diffusion coefficient between pure glycerine and several glycerine–water mixtures, in order to be able to calculate a representative Péclet number for each experiment, and the local value as a function of the local concentration of glycerine, in the dilute limit.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 326 , 10 November 1996 , pp. 37 - 56
Copyright
© 1996 Cambridge University Press

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