Liquid metal droplet-enabled electrocapillary flow in biased alternating electric fields: a theoretical analysis from the perspective of induced-charge electrokinetics

Abstract

The phenomenon of Marangoni chaotic electroconvection of electrolytes induced by liquid metal droplets has been serving as a method of choice for pumping of microfluidics in the past ten years. Although an external additional alternating voltage, usually being sufficiently small, was invariably employed in practical experiments for stabilizing the unidirectional liquid motion caused by a preexisted direct-current electric field, its subtle effect on the superimposed non-uniform surface tension and the final fluid transport state is still theoretically unclear. From the physical perspective of induced-charge electrokinetics, we present herein an analytical criteria for the conditions under which a sessile metal drop can actuate unidirectional liquid motion passing across it affected by a biased alternating voltage signal, wherein a mechanical balance between the linear pump pressure and nonlinear bipolar stress components exerted on the conducting drop surface has been taken into account. For accuracy validation, a numerical model was developed, in which multiple frequency electrochemical polarization was calculated under the Debye–Huckel limit, and coupled to the mechanical problem via inserting the resultant surface tension gradient as a source term of electrocapillary stress at the droplet–medium interface. The analytical solution accords well with the simulation results, in terms of the threshold voltage amplitude for effective liquid transport along the static potential gradient. At last, we demonstrate that the effect of continuous electrowetting can be fully exploited for simultaneous pumping and extraction of microscale impurities in closed fluid loops embedding a network of three-dimensional floating electrode plates for invoking auxiliary dielectrophoretic attraction. These results prove invaluable for achieving a high degree of freedom manipulation of particle and liquid contents in modern microfluidic systems with flexible conducting microdroplets.