Interfacial instabilities of miscible fluids in a rotating Hele–Shaw cell

Numerical simulations of interfacial stability for miscible droplet in a rotating Hele–Shaw cell by means of high-accurate numerical schemes are presented. The interfacial instability is dominated by four control parameters, such as rotating speed, viscosity contrast, diffusion between the species and injecting strength. More vigorous interfacial fingerings are found at higher rotating speed and lower viscosity contrast. The effect of stronger diffusion is not significant to the fingering patterns, but leads only to milder instability. Injection in general reinforces viscous stabilization. For the case of annulus, different mechanisms of instability are observed on the inner and outer fronts. The injecting strength tends to stabilize the outer interface, and perturbs the inner.