Vortices in oscillating droplets

Understanding the dynamics of liquid-liquid systems is important in the chemical industry where drops of one liquid suspended in another are involved in extractions and emulsion formation. One way to control mass transfer in droplets is through the action of an external shear flow on the droplet’s shape.

Kozlov et al.’s experiments study the steady flow of a fluid in a spherical cavity located inside a flexible silicon cylinder. The silicon provides an elastic boundary that can be rotated and flattened, deforming the initially spherical shape of the “droplet” inside. Here, the cavity is filled with a water-glycerol solution containing small plastic light scattering particles used to visualize the flow. A laser acts as a “light knife” to detect the motion of these tiny particles and the results are recorded with a high-speed video camera.

Rotational oscillation of the spherical cavity produced a steady flow consisting of two axisymmetric toroidal vortices. This pattern changed to a complex three-dimensional flow when the spherical cavity was deformed by pressing on the elastic cylinder. The authors determined the dependence of flow structure on certain dimensionless parameters while varying the amplitude and frequency of rotation.

At moderate to high dimensionless frequencies, the dimensionless velocity of the fluid in the vortices is nearly independent of frequency. At low frequencies, the qualitative nature of steady flow changes. Here, the velocity of the flow increases linearly with frequency.

Significantly, the intensity of the steady flow for deformed cavities at low dimensionless frequencies is an order of magnitude higher than for nondeformed spheres, a finding that could help improve mass transfer in droplets.

Source: “Steady flows in deformed elastic sphere subject to rotational oscillations,” by V. G. Kozlov, S. V. Subbotin, and R. R. Sabirov, Physics of Fluids (2018). The article can be accessed at https://doi.org/10.1063/1.5048789 .