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.
