Numerical simulations of interfacial instabilities on a rotating miscible magnetic droplet with effects of Korteweg stresses

Abstract

Interfacial instability of a miscible magnetic droplet in a rotating Hele-Shaw cell is simulated numerically. The influence of magnetic strengths, the Korteweg stresses, and their coupled effects are first discussed qualitatively by fingering patterns and streamlines. Quantitative measurements are evaluated by interfacial length L, number of fingers n, and diameter of gyration Dg. The results confirm with coupling rotational effects more vigorous fingering instability occurs on stronger magnetic strengths and less effective surface tensions (Korteweg stresses). Without the effects of Korteweg stresses, significant nonlinear fingering merges occur which lead to reduction in fingering number, early decay of interfacial length and reversed plane trajectories. Before the occurrence of fingering merges, monotonic growths of interfacial lengths, constant fingering numbers, and nearly linear pattern trajectories are observed. If the significant Korteweg stresses are taken into account, the nonlinear merge is prevented and the features of fingering patterns resemble the immiscible situations remarkably. The fingering behavior can be approximated by a master line of dL∕dDg≈0.386n+0.13 within the linear fingering region.