Non-expert summaryThe displacement of one liquid by another in a channel of constant height occurs in flushing and cleaning operations. The authors study the effect of buoyancy (arising from different fluid densities) on a pressure-driven flow of two miscible fluids in inclined channels using direct numerical simulations DNS). The flow dynamics are governed by the continuity and Navier–Stokes equations, without the Boussinesq approximation for buoyancy, coupled to a convective-diffusion equation for mass transfer between the two liquids. The effect of concentration on viscosity and density is modelled. The effect of varying the density ratio, Froude number, and channel inclination on the flow dynamics is examined, for moderate Reynolds numbers. These detailed simulations give insights into mixing and cleaning behaviour.
Non-expert summaryWhen one liquid is pumped into a channel containing a second liquid, the behaviour depends on the properties of the two fluids and pressure driving force. This paper considers the stability of a flow of two miscible fluids in a horizontal channel. The flow dynamics are governed by the continuity and Navier–Stokes equations, with mass transfer between the two. An analysis of the flow in the linear regime delineates the presence of convective and absolute instabilities, and shows that vertical gradients of viscosity perturbations (caused by mixing) are the main destabilizing influence of the interface (in agreement with previous work). Previous work in the area is reviewed as well. Transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing.