Article révisé par les pairs
|The pressure-driven miscible displacement of a less viscous fluid by a more viscousone in a horizontal channel is studied. This is a classically stable system if the moreviscous solution is the displacing one. However, we show by numerical simulationsbased on the finite-volume approach that, in this system, double diffusive effects canbe destabilizing. Such effects can appear if the fluid consists of a solvent containingtwo solutes both influencing the viscosity of the solution and diffusing at differentrates. The continuity and Navier–Stokes equations coupled to two convection–diffusionequations for the evolution of the solute concentrations are solved. The viscosityis assumed to depend on the concentrations of both solutes, while density contrastis neglected. The results demonstrate the development of various instability patternsof the miscible ‘interface’ separating the fluids provided the two solutes diffuse atdifferent rates. The intensity of the instability increases when increasing the diffusivityratio between the faster-diffusing and the slower-diffusing solutes. This brings aboutfluid mixing and accelerates the displacement of the fluid originally filling the channel.The effects of varying dimensionless parameters, such as the Reynolds number andSchmidt number, on the development of the ‘interfacial’ instability pattern are alsostudied. The double diffusive instability appears after the moment when the invadingfluid penetrates inside the channel. This is attributed to the presence of inertia in theproblem.