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The motion, deformation, and stability of compound droplets in extensional flows are investigated numerically via a three-dimensional spectral boundary element method. We examine the droplet stability under the influences of the capillary number, the inner droplet size and the relative magnitude of the surface tension of the two interfaces composing the compound droplet. The influence of viscosity on the droplet deformation is also discussed. We conclude that a compound droplet with a larger inner droplet and/or smaller inner surface tension is less stable and cannot withstand strong flow. For moderate viscosity ratios, a compound droplet with a more viscous 'shell' exhibits larger deformation at steady state. In addition, for an eccentric compound droplet, both the inner and outer droplets tend to migrate away from its original location due to the asymmetry of the problem. The initial location of the inner droplet also influences the droplet stability as well as the migration velocity of the compound droplet. [ABSTRACT FROM AUTHOR]

In this study, we investigate computationally the low-Reynolds-number droplet motion in a square micro-channel, a problem frequently encountered in microfluidic devices, enhanced oil recovery and coating processes. The droplet deformation and motion are determined via a three-dimensional spectral boundary element method for wall-bounded flows. The effects of the flow rate, viscosity ratio and droplet size on the interfacial dynamics are identified for droplets smaller and larger than the channel size and for a wide range of viscosity ratio. Owing to the stronger hydrodynamic forces in the thin lubrication film between the droplet interface and the solid walls, large droplets exhibit larger deformation and smaller velocity. Under the same average velocity, a droplet in a channel shows a significantly smaller deformation and higher velocity than in a cylindrical tube with the same size, owing to the existence of the corners' area in the channel which permits flow of the surrounding fluid. A suitable periodic boundary implementation for our spectral element method is developed to study the dynamics of an array of identical droplets moving in the channel. In this case, the droplet deformation and velocity are reduced as their separation decreases; the reduction is influenced by the flow rate, viscosity ratio and more significantly the droplet size. [ABSTRACT FROM AUTHOR]

A 3D spectral boundary element method is employed to compute the dynamics of a single droplet in a microconfined shear flow. Comparisons have been made for the motion of an initially spherical droplet near a single wall and that between two parallel plates. Investigations are conducted for the influences of the capillary number, viscosity ratio, and initial location of the droplet on the droplet deformation, orientation, velocities, as well as the transition between the initial rapid deformation and the subsequent relaxation stage. Computational results for the deformation and velocities are compared with analytical predictions. It is found that the analytical predictions are limited for small deformations, large droplet-wall distances, and near equiviscous droplets. [ABSTRACT FROM AUTHOR]