Electrohydrodynamic deformation of a miscible fluid stream by a transverse electric field

Electrohydrodynamic deformation of a cylindrical fluid stream is analyzed with a quasi-electroneutral model. The stream is miscible with the surrounding liquid, though of different electrical conductivity and permittivity, and is subject to an electric field that acts transverse to the axis of the cylinder. The formulation allows for natural gradients of electrical conductivity and dielectric constant in the transition region between the stream and the surrounding liquid; these property variations are fully coupled to the fluid motion and are assumed to stem from concentration gradients of charge-carrying solutes. Dielectric and Coulombic body forces attendant to the time-dependent, spatial nonuniformities are accounted for. The strength of the electrically driven flows is such that transport of solutes is dominated by advection. As a consequence, the initial conductivity and dielectric constant differences, between the interior of the stream and the surrounding liquid, persist through significant deformation of the stream and characterize the rate at which the stream (continuously) deforms. Calculations for aqueous systems dominated by conductivity effects agree with measurements of stream deformation made by Rhodes et al. [J. Colloid Interface Sci. 1989, 129, 78]. Calculations for systems controlled by dielectric effects show that relative permittivity differences must be at least O(1) if noticeable deformations are to occur in a matter of seconds, which may explain why Trau et al. [Langmuir 1995, 11, 4665] discerned no deformations controlled by dielectric effects in low permittivity, low conductivity systems. An implication of these latter predictions is that experiments to isolate the role of dielectric constant mismatch may not be practicable.