Electrocapillary drop actuation and fingering instability in a planar Hele-Shaw cell.

The electrically driven displacement of a viscous poorly conducting Newtonian fluid drop positioned between conducting parallel plates is studied both theoretically and experimentally. A mathematical expression for the average-steady velocity is developed by using Darcy flow analysis with an interface pressure that includes a contribution from Maxwell stresses at the advancing gas-liquid boundary. Experiments were performed using silicone oil at plate separation distances less than the capillary length for voltages ranging 250-750 V resulting in a change in velocity of approximately one order of magnitude. This suggested that the driving force was proportional to the square of the applied voltage, a feature that is common among fluid motion driven by electrical phenomena. The trailing interface revealed a disturbance for large fluid displacements that is analogous to a fingering instability. The channel widths were small such that we could predict the transition from a single finger that grows linearly to a single finger that grows exponentially and to multiple fingers that grow exponentially, all occurring within the range of voltages studied. The theory and experiments show good agreement with classic interfacial linear stability analysis.