Problems in interfacial electro-hydrodynamics

Demetrius Papageorgiou

(NJIT, Mathematics)

It has been known since the pioneering work of Melcher, Taylor and others,
that electric fields can affect the stability of multi-fluid
systems due to electrical Maxwell stresses at interfaces. Stable flows
can become unstable and vice versa. More spectacularly, electric fields
can cause singular events such as the steepening of interfacial profiles accompanied
by drop ejection through a topological transition of the interface (e.g. the
Taylor cone paradigm).

This talk will begin with an overview of electrohydrodynamics encountered in
microfluidic applications and experiments such as lithographically induced self-assembly
processes and emulsification in microchannels. On the micro-scale, the electric
field provides the crucial driving mechanism that generates long-time nonlinear
dynamics and features. I will also present some long-wave asymptotic solutions that
provide novel nonlinear integro-differential evolution equations for the spatio-temporal
evolution of the interface for electrified film flows over flat and topographically
structured substrates. Rigorous analysis (existence, uniqueness and questions of
finite-time singularity formation) and numerical results will be presented. Comparisons
will also be made with direct numerical simulations based on boundary integral methods
in order to assess the validity of the long wave models. It is established that the
latter do extremely well in capturing the main mechanisms of the phenomena.