Two-dimensional Janus drops in shear: deformation, rotation and their coupling

In this work, the dynamics of two-dimensional rotating Janus drops in shear flow is studied numerically using a ternary-fluid diffuse interface method. The rotation of Janus drops is found to be closely related to their deformation. A new deformation parameter $D$ is proposed to assess the significance of the drop deformation. According to the maximum value of $D$ ($D_{max}$), the deformation of rotating Janus drops can be classified into linear deformation ($D_{max}\le 0.2$) and nonlinear deformation ($D_{max}> 0.2$). In particular, $D_{max}$ in the former depends linearly on the Reynolds and capillary numbers, which can be interpreted by a mass–spring model. Furthermore, the rotation period $t_R$ of a Janus drop is found to be more sensitive to the drop deformation than to the aspect ratio of the drop at equilibrium. By introducing a corrected shear rate and an aspect ratio of drop deformation, a rotation model for Janus drops is established based on Jeffery's theory for rigid particles, and it agrees well with our numerical results.