The effect of interfacial tension gradients on the flow structure of single drops or bubbles translating in an electric field

Abstract

for spherical drops or bubbles supporting interfacial tension gradients and translating in creeping flow in an electric field imposed in the direction of translation. In particular, the case in which a trace of surfactant is present is considered, and it is found that such material may produce quasistagnant zones along the interface either near the poles or the equator. Terminal velocities may be either increased or decreased relative to the value obtained in the absence of the electric field, SCOPEEarlier work has shown the ability of electric fields to generate circulatory flows in drops or bubbles that are either stationary or translating by gravity, and experimental results suggest the importance of such flows in enhancing the rate of mass or heat exchange between a drop and its surroundings. On the other hand, the effect of interfacial tension gradients, particularly as caused by the presence of traces of surfactant, has been thoroughly investigated and shown (in the usual case) to retard significantly interfacial velocity in the rear stagnation region and to reduce terminal velocity. The present work examines theoretically the combined effects of an interfacial tension gradient, drop translation, and an electric field on the flow structure of a drop or bubble and its surroundings. The simultaneous consideration of all three of these effects is necessary to the assessment of the promise of electric fields for enhancing mass or heat exchange rates in, for example, liquid extraction or directcontact heat transfer operations.

The effect of electric field on droplet formation and motion in a viscous liquid

“…(24) Although drops can circulate in the presence of an electrical field (Taylor, 1966;Chang and Berg, 1985), the Stokes Law drag expression is retained here. Hence an equation analogous to Equation ( …”

Low-Gravity Fluid Dynamics and Transport Phenomena

“…171 From this fact one might conclude that any thermodynamic variable that can generate an interfacial tension gradient could drive phase separation and the partitioning of particles, even in low gravity.…”

The transition in settling velocity of surfactant-covered droplets from the Stokes to the Hadamard–Rybczynski solution

“…In this paper, we will extend the derivation by Chang and Berg (1985) of the analytical solution for the terminal velocity of a low Re circular drop with an arbitrary surfactant (hence interfacial tension) distribution, taking here also the normal interfacial stresses into account. We show that this leads to a plethora of solutions, some of which are clearly unphysical (in the absence of an external energy input), such as a hovering drop.…”

“…We will follow in the steps of the analysis of Chang and Berg (1985), but we will also include the interfacial conditions for normal stresses. The appropriate boundary conditions are then given by Equations (4)-(6).…”