The problem of electrohydrodynamic drop deformation is well understood in the case where the external electric field is weak. In one of his many celebrated papers (Proc. R. Soc. A, 291 1425 159-166, 1966), G. I. Taylor worked out a complete theory in this limit, including analytical expressions for the electrohydrodynamic flow engendered within and outside of the drop by the electric field acting on its own induced interfacial charge, and a simple function of the permittivity, conductivity and viscosity drop-to-background ratios discriminating between prolate or oblate deformation.

 

In this talk, we will employ numerical and asymptotic tools to explore the effects of interfacial-charge convection, which were neglected by Taylor but become important at strong electric fields. In particular, we will analyze (in 2D, for simplicity) how Taylor’s fore-aft symmetric solution evolves as the electrical Reynolds number is increased from zero to arbitrarily large values. What we shall find is hinted by the title of the talk. We will discuss connections between our results, numerical evidence in the literature for the formation of equatorial interfacial-charge “shocks” (a term which we shall challenge), and strong-field experiments exhibiting equatorial streaming, pattern formation and transition to spontaneous drop rotation.

 

This is joint work with Gunnar G. Peng, Rodolfo Brandão and Ory Schnitzer.