We perform direct numerical simulations of a non-magnetic drop immersed in immiscible ferrofluids in a confined Hele-Shaw cell under an azimuthal field by a diffuse-interface method. The interface is unstable in such a condition because of the inward attraction of the ferrofluids induced by the magnetic field gradient. We focus on the fingering onset and pattern influenced by the coupling visco...

We consider a model of gas-solid combustion with free interface proposed by L. Kagan and G.I. Sivashinsky. Our approach is twofold: (I) we eliminate the front and get to a fully nonlinear system with boundary conditions; (II) we use a fourth-order pseudo-differential equation for the front to achieve asymptotic regimes in rescaled variables. In both cases, we implement a numerical algorithm bas...

We investigate the displacement of one fluid by another in a deformable medium with pore-scale disorder. We develop a model that captures the dynamic pressure redistribution at the invasion front and the feedback between fluid invasion and microstructure rearrangement. Our results suggest how to collapse the transition between invasion percolation and viscous fingering in the presence of quench...

We study mixing of two fluids of different viscosity in a microfluidic channel or porous medium. We show that the synergetic action of alternating injection and viscous fingering leads to a dramatic increase in mixing efficiency at high Péclet numbers. Based on observations from high-resolution simulations, we develop a theoretical model of mixing efficiency that combines a hyperbolic mixing mo...

The viscous fingering or Saffman-Taylor instability occurs when a less fluid penetrates more in porous medium. Fingering patterns refer to the deformation of interface between invading and displaced fluids. For mixtures composed three miscible species, dynamic each component varies greatly. In that case, multicomponent diffusion effects are primary importance, reverse could trigger from configu...