We investigate the stability of radial viscous fingering (VF) in miscible fluids. We show that the instability is decided by an interplay between advection and diffusion during initial stages of flow. Using linear stability analysis and nonlinear simulations, we demonstrate that this competition is a function of the radius r0 of the circular region initially occupied by the less viscous fluid in the porous medium. For each r0, we further determine the stability in terms of Péclet number (P e) and log-mobility ratio (M ). The P e − M parameter space is divided into stable and unstable zones-the boundary between the two zones is well approximated by M = α(r0)P e −0.55 . In the unstable zone, the instability is reduced (enhanced) with an increase (decrease) in r0. Thus, a natural control measure for miscible radial VF in terms of r0 is established. Finally, the results are validated by performing experiments which provide a good qualitative agreement with our numerical study. Implications for observations in oil recovery and other fingering instabilities are discussed.

Superparamagnetic micro-bead chains and microswimmers under the influence of an oscillating magnetic field are studied experimentally and numerically. The numerical scheme composed of the lattice Boltzmann method, immersed boundary method, and discrete particle method based on the simplified Stokesian dynamics is applied to thoroughly understand the interaction between the micro-bead chain (or swimmer), the oscillating magnetic field, and the hydrodynamics drag. The systematic experiments and simulations demonstrated the behaviors of the microchains and microswimmers as well as the propulsive efficiencies of the swimmers. The effects of key parameters, such as field strengths, frequency, and the lengths of swimmer, are thoroughly analyzed. The numerical results are compared with the experiments and show good qualitative agreements. Our results proposed an efficient method to predict the motions of the reversible magnetic microdevices which may have extremely valuable applications in biotechnology.

Miscible and immiscible injection flows in heterogeneous porous media, for which the permeability is characterized by a log Gaussian distribution, are simulated by a robust diffuse-interface formulation. The robust numerical method enables direct qualitative and quantitative comparisons regarding pattern formations in various fluid miscibility conditions. For miscible injections, the typical size of fingering structures depends strongly on the correlation length and forms tapered fingers with sharper tips. On the other hand, the typical size of immiscible fingers is affected less significantly by the permeability heterogeneity, and wide spreading tips are retained in the fingering patterns. Prominence of fingering instability is quantitatively evaluated by the channeling width and the interfacial length. The channeling width shows strong and monotonic dependences on the heterogeneous variance. On the contrary, maximum channeling width occurs at intermediate correlation length due to local resonant effect between the faster penetrating fingers and permeability heterogeneity. On the other hand, effects of the correlation length and the permeability variance on the interfacial lengths are generally consistent. Longer interfacial length is perturbed by smaller correlation length or higher variance. Interesting invariant evolutions of interfacial lengths are revealed regardless of the permeability variance in sufficiently large correlation length under all miscibility conditions. In addition, the regime of slower growth of interfacial length at later times experimentally observed in homogeneous miscible injection is verified in heterogeneous porous media as well.

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In the present study, we use direct numerical simulation to investigate the density-driven convection in a two-dimensional anisotropic heterogeneous porous media associated with significant laminated formation. At first, the heterogeneous porous media are randomly generated to represent laminated structure, in which the horizontal correlation length of permeability field is much longer than the vertical counterpart. Then, a highly accurate pseudo-spectral method and compact finite difference scheme with higher order of accuracy are employed to numerically reproduce the convection flow in the laminated porous media. The results show that the laminated structures restrict interactions among the downward plumes of heavier fluid. The plumes tend to descend more straightly in a laminated porous medium associated with a slower growth rate. As a result, the laminated distribution of permeability is considered having an inhibiting effect on the convection flow.