Orbit dynamics of Janus drop in shear flow

In this paper, we numerically investigate the orbit dynamics of three-dimensional symmetric Janus drops in shear flow using an improved ternary-fluids phase field method, focusing on how drop deformation and initial orientation affect the orbit drift of two configurations of Janus drops: dumbbell-shaped and near-spherical. We find that the motion of dumbbell-shaped drops eventually evolves into tumbling, while near-spherical drops attain stable spinning. We attribute this bifurcation in orbit drift to contrasting deformation dynamics and shape-dependent hydrodynamics of the two configurations. Specifically, the drift bifurcation is closely related to the aspect ratio of Janus drops at equilibrium, giving rise to two distinct mechanisms: (1) coupling between outer interface deformation and the surrounding flow field; and (2) interplay between inner interface deformation and vortices enclosed within the drop. In addition, we observe that for the dumbbell-shaped Janus drops with different aspect ratios, their tumbling dynamics resembles ellipsoids in shear flow. Moreover, the trajectories of the dumbbell-shaped Janus drops during orbit drift collapse onto a universal curve, independent of their initial orientations, and significant deformation and inertia accelerate the orbit transition. To quantitatively evaluate the effect of drop deformation on the orbit drift of the dumbbell-shaped Janus drops, we propose an effective aspect ratio model based on the drop shapes at equilibrium and at the maximum elongation. By incorporating the effective aspect ratio into Jeffery’s theory for solid particles, we accurately predict the rotation period and angular velocity of Janus drops in the tumbling regime and during the orbit drift, especially for drops with linear deformation. Moreover, the orbit parameter $C$ is found to vary exponentially with time for drops with linear deformation, while the time variation of $C$ transits from one exponential function to another for drops with nonlinear deformation.