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

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.

Double-diffusive instability in core–annular pipe flow

“…It is found (not shown) that although at t = 0 the less (high) viscous fluid occupies the annular (core) region of the pipe, the double-diffusive phenomenon alters the viscosity variation at the later times by creating a highly viscous region near the wall, which is the main cause of instability observed in this case. A similar mechanism was previously observed by Mishra et al (2012) and Bhagat et al (2016) in the numerical simulations of displacement flows in planar channel and axisymmetric pipe in the presence of DD effect. On the other hand the dynamics for δ = 1 is dominated only by diffusive mixing.…”

“…The instabilities due to the influence of DD effect were also observed in other flow systems, e.g. displacement of a highly viscous fluid by a less viscous one in porous media (Mishra et al 2010;Swernath & Pushpavanam 2007), Hele-Shaw cell (Pritchard 2009), and in pressure-driven flow in a channel (Mishra et al 2012). A review of instabilities associated with DD effect in various flow configurations can be found in Govindarajan & Sahu (2014).…”

Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

“…Sahu et al 37 showed that the above system becomes absolutely unstable for a certain range of parameters and have indicated the region of absolute and convective instabilities in the Reynolds number and viscosity ratio space. There are also several investigations 29,30,[38][39][40][41][42][43][44][45][46][47][48] not relevant to the present study (but worth mentioning in the present context) that deals with stability characteristics of viscosity stratified flows in rigid channels/pipes, involving the displacement of one fluid by another. The interesting features and the type of instabilities displayed by these flow systems with boundaries as either rigid walls or rigid circular pipes suggest that it is worth analyzing the analogous flow systems in configurations with velocity slip at the boundaries.…”

Instability of a free-shear layer in the vicinity of a viscosity-stratified layer

“…Again the values of concentration are set to one and zero above and below this line respectively. The reader is referred to Mishra et al (2012) for details of the numerical method used. The dotted lines with filled triangles in panel (a) and (b) represent the profiles obtained from these direct numerical simulations for R s = −1 Sc = 100, Re = 100 and t = 80.…”