Journal of Fluid Mechanics



Miscible displacements in capillary tubes. Part 1. Experiments


P.  Petitjeans a1 and T.  Maxworthy a2
a1 Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90090-1191, USA
a2 Laboratoire de Physique et Mecanique des Milieux Heterogenes, Ecole Superieure de Physique et Chimie Industrielles, 10, Rue Vauquelin, F-75231, Paris cedex 05, France
a3 Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA

Article author query
petitjeans p   [Google Scholar] 
maxworthy t   [Google Scholar] 
 

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.

(Published Online April 26 2006)
(Received January 11 1996)
(Revised May 6 1996)



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