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This study investigates a novel microfluidic mixing technique that uses the resonant oscillation of coalescent droplets. During the vertical contact-separation process, solutes are initially separated as a result of the combined effects of diffusion and gravity. We show that the application of alternating current (AC) voltage to microelectrodes below the droplets causes a resonant oscillation, which enhances the even distribution of the solute. The difference in concentration between the top and bottom droplets exhibits frequency dependence and indicates the existence of a particular AC frequency that results in a homogeneous concentration. This frequency corresponds to the resonance frequency of the droplet oscillation that is determined using particle tracking velocimetry. To understand the mixing process, a phenomenological model based on the equilibrium between surface tension, viscosity, and electrostatic force was developed. This model accurately predicted the resonance frequency of droplet flow and was consistent with the experimental results. These results suggest that the resonant oscillation of droplets driven by AC voltage significantly enhances the diffusion of solutes, which is an effective approach to microfluid mixing. [ABSTRACT FROM AUTHOR]

Abstract This study investigates a novel microfluidic mixing technique that uses the resonant oscillation of coalescent droplets. During the vertical contact-separation process, solutes are initially separated as a result of the combined effects of diffusion and gravity. We show that the application of alternating current (AC) voltage to microelectrodes below the droplets causes a resonant oscillation, which enhances the even distribution of the solute. The difference in concentration between the top and bottom droplets exhibits frequency dependence and indicates the existence of a particular AC frequency that results in a homogeneous concentration. This frequency corresponds to the resonance frequency of the droplet oscillation that is determined using particle tracking velocimetry. To understand the mixing process, a phenomenological model based on the equilibrium between surface tension, viscosity, and electrostatic force was developed. This model accurately predicted the resonance frequency of droplet flow and was consistent with the experimental results. These results suggest that the resonant oscillation of droplets driven by AC voltage significantly enhances the diffusion of solutes, which is an effective approach to microfluid mixing.

We consider a conductive droplet sitting on a dielectric substrate which is connected to an electrical power. A systematic approach is developed to study the static profile of the interface near the contact line. We first derive the governing equations using the principle of minimum energy. The boundary condition at the contact line shows that the local contact angle, which satisfies the Young--Dupré equation, is independent of the electrical field. Next, we study the distinguished limit of the model as the dimensionless parameters β and d go to zero with d/β = O(1), where β measures the relative strength of the electricity and d is the thickness of the insulator. Analysis of the inner problem, which governs the interface profile near the contact line, shows the existence of a welldefined apparent contact angle. Thereafter, we propose a numerical method for the inner problem. The method is based on a conventional fixed-point algorithm and the Schwarz--Christoffel mapping in complex variables. Numerical results are presented for the interface and the apparent contact angle. Significant bending of the interface is observed near the contact line. The numerical results also show that the well-defined apparent contact angle depends on the applied electrical potential and the thickness of the insulator, and the relation agrees well with the Young--Lippmann equation. [ABSTRACT FROM AUTHOR]