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

Area of Science:

• Physics, Fluid Dynamics, Electromagnetohydrodynamics

Background:

• Understanding the behavior of viscous, poorly conducting fluids under electrical fields is crucial for various applications.
• Previous studies have explored electrokinetic phenomena, but detailed analysis of viscous drop displacement with Maxwell stress contributions is less common.

Purpose of the Study:

• To theoretically and experimentally investigate the electrically driven displacement of a Newtonian fluid drop.
• To develop a mathematical model for average-steady velocity incorporating Darcy flow and Maxwell stresses.
• To analyze interfacial instabilities, specifically fingering phenomena, in confined geometries.

Main Methods:

• Developed a mathematical expression for average-steady velocity using Darcy flow analysis and interface pressure including Maxwell stresses.
• Conducted experiments with silicone oil between conducting parallel plates at voltages ranging from 250-750 V.
• Analyzed fluid displacement, velocity changes, and interfacial disturbances using interfacial linear stability analysis.

Main Results:

• Observed a velocity change of approximately one order of magnitude, proportional to the square of the applied voltage.
• Identified a fingering instability at the trailing interface for large fluid displacements.
• Predicted and observed transitions from linear to exponential growth of single and multiple fingers within the studied voltage range.

Conclusions:

• The study provides a validated theoretical model for electrically driven viscous fluid displacement.
• Experimental results confirm the theoretical predictions and demonstrate the influence of electrical forces on fluid motion and interfacial stability.
• The findings offer insights into complex fluid behaviors relevant to microfluidics and electrohydrodynamics.