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

Published online by Cambridge University Press:  09 October 2012

Manoranjan Mishra
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
A. De Wit
Affiliation:
Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
Kirti Chandra Sahu*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Yeddumailaram 502 205, Andhra Pradesh, India
*
Email address for correspondence: kirtisahu1@gmail.com

Abstract

The pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

Type
Papers
Copyright
©2012 Cambridge University Press

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