Numerical study of mixing viscous fluids in T-shaped micro-channels with compressibility effects

We study numerically the mixing processes of two miscible fluids in T-shaped micro-channels in the presence of compressibility effects. Three mixing modes are considered: ‘passive’ mixing, which relies on the molecular diffusion and chaotic advection; ‘active’ mixing relies on external disturbances, e.g. due to periodic compression; and a combination of these modes. In all cases considered, one of the fluids, fluid ‘A’, is initially present in the dead-end region of the micro-channel. In the `passive’ mixing case, the other fluid, fluid ‘B’, flows through the open part of the channel at a constant flow rate. In the ‘active’ case, this fluid is initially at rest but is then set in motion through pressure cycling. The combined case, involves the flow of fluid ‘B’ in the presence of compression-decompression cycles. Numerical simulations are carried out for three different fluids, accounting for their compressibility, and their pressure-dependent e.g. density, viscosity, and diffusivity; a simple mixing rule is used to model the properties of the mixed fluids. Our results indicate that the vortices in the dead-end zone, engendered by the relative motion of the fluids leads to their mixing; the combination of mixing modes is shown to promote mixing efficiency significantly.