Transient dynamics of eccentric double emulsion droplets in a simple shear flow

We numerically examine the time-dependent behavior of double emulsions in a simple shear flow using finite volume and front-tracking methods. A single inner drop is initially located eccentrically to the outer drop. When the eccentricity is contained within the plane of shear, the inner drop experiences a "revolving" motion within the plane of shear, orbiting about the center of the compound drop while slowly moving outward. The inner drop eventually experiences a limit cycle, where no more outward movement occurs because the distance between the two interfaces is reduced to a thin liquid film for portions of the revolving cycle. In addition, eccentricity in the direction normal to the plane of shear is tested. In this case, the inner droplet undergoes a "drifting" motion, slowly moving perpendicularly to the plane of shear until only a thin layer remains between the two interfaces. Finally, the revolving and drifting motions are simultaneously observedwhen the in-plane-of-shear eccentricity is included in addition to the off-plane-of-shear eccentricity. The observed behaviors are not qualitatively affected by the inner to outer droplet radii ratio, and are preserved when Re <= 5, Ca-o <= 0.1, and Ca-i < 0.2.