Dynamics of a Janus Droplet in An External Flow

Janus droplets are of crucial importance in the design of multifunctional materials. In particular, creation, control, and polymerization of Janus droplets are frequently used in construction of Janus particles needed for many technological applications. In this study, the dynamics of the simplest compound droplet—a Janus droplet that consists of two fluids occupying equal hemispherical domains, such that the internal interface (inside the droplet) remains flat—is considered at low Reynolds number. The droplet is placed into a space-uniform external flow. Thus, analytical solution in Lamb’s series can be constructed. It is shown that fluid flow can be represented as a superposition of that for two limiting cases: (i) the external flow perpendicular to the internal interface and (ii) the flow parallel to the interface. In case (i) there is no torque applied to the droplet, therefore, it materializes a stable orientation of the Janus droplet (the fluid of smaller viscosity has to be at the upper stream for the stable configuration). It is important to note that even for equal viscosities of internal fluids the problem is not reduced to the Hadamard-Rybczynski problem, because the internal interface prohibits the motion inherent to the simple droplet. In contrast, for case (ii) there is the above-mentioned reduction; for small difference in viscosities of internal fluids the overall torque is proportional to this difference. The motion of the droplet under shear flow is also studied. This shear leads to additional torque, which changes a stable configuration of a torque-free Janus droplet in such a way that the drop's axis of symmetry is tilted to the external fluid. This, in turn, generates a component of the force (and, hence, a drop velocity) normal to the external flow. These analytical results are in a good agreement with numerical computations by Fluent. The latter method becomes especially efficient for more realistic Janus droplets with curved interfaces.