Miscible displacements in capillary tubes. Part 1. Experiments

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 largePeand anAtof 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 ofAt, is very good. At values of the averagePegreater 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.

Double diffusive effects on pressure-driven miscible displacement flows in a channel

“…Their nonlinear simulations of the Stokes equations predict that increasing the unstable density stratification and decreasing diffusion increase the front velocity. The flow fields obtained by these simulations are qualitatively similar to those observed in the experiment of Petitjeans & Maxworthy (1996) in capillary tubes and in the theoretical predictions of Lajeunesse et al (1999) for Hele-Shaw cells. The study of Petitjeans & Maxworthy (1996) discussed the formation and propagation of a single finger for a miscible fluid in a capillary tube.…”

“…For a larger δ (see figure 4c for δ = 10), the flow becomes unstable, forming symmetrical wavy interfaces because of a KH-type instability. At later stages the flow dynamics is like a three-layer core-annular flow (Chen & Meiburg 1996;Petitjeans & Maxworthy 1996;Kuang et al 2003). These instabilities occur at the interface primarily because a viscosity contrast arises due to the DD effects.…”

“…The interface between the two fluids becomes unstable, forming Kelvin-Helmholtz (KH) instabilities and 'roll-up' structures (Joseph et al 1997;Sahu et al 2009a,b). Experimental studies in miscible core-annular flows (Taylor 1961;Cox 1962;Chen & Meiburg 1996;Petitjeans & Maxworthy 1996;Kuang, Maxworthy & Petitjeans 2003) have focused on analysing the thickness of the more viscous fluid layer left on the pipe walls and the speed of the propagating 'finger' tip. The development of different instability patterns, like axisymmetric 'corkscrew' patterns, in miscible flows has also been investigated (Lajeunesse et al 1997(Lajeunesse et al , 1999Scoffoni, Lajeunesse & Homsy 2001;Cao et al 2003;Gabard & Hulin 2003).…”

Investigation of concentration‐dependent diffusion on frontal instabilities and mass transfer in homogeneous porous media

“…An exponential relation between the diffusion coefficient and concentration was proposed by Hayduk and Cheng [13] and later adopted by Das and Butler [12] to determine the diffusivity of propane and butane in Peace River bitumen. At the same time, Petitjeans and Maxworthy [14] also pointed out that the diffusion coefficient of water and glycerin is strongly dependent on local concentration and varied by a factor of about 30. [15] Later, a concentrationdependent diffusion coefficient was measured experimentally by Rashidnia and Balasubramaniam [16] for a water/glycerin system.…”

“…The local Peclet number is thus concentration-dependent and varies from 195 to 4000 across the front. In addition, a one-dimensional diffusion equation was employed to fit the experimental observations of Petitjeans and Maxworthy [14] and they were able to achieve good agreement. Later, Vanaparthy and Meiburg [22] developed a nonlinear quasisteady model to examine the effect of an exponential CDDC on miscible interfaces.…”