Soap Bubble Deformation and Instability under Electric Fields

Soap bubbles under electric fields deform from hemispherical to elongated profiles, yet unlike droplets, their electrohydrodynamic behavior lacks quantitative understanding. Despite early observations by Wilson (1925) and Taylor (1964), no predictive models exist for bubble shape evolution in electric fields.

In this study, we conducted controlled voltage-sweep experiments with quantitative shape analysis, systematically mapping bubble deformation across electric field strengths (~7 kV/cm), up to the critical voltage at which bubbles become unstable. Correlation analysis among the variables shows consistent scaling behavior between deformation parameters and E²r₀, where E is the electric field and r₀ is the initial radius. We developed a numerical model coupling the Young-Laplace equation with Maxwell electric stress. Integrating from the bubble apex with an empirical charge distribution function, the model predicts bubble shapes across all voltages until instability. Near the critical voltage, the bubble's apex develops conical profiles with angles approaching the Taylor cone geometry, indicating the nature of EHD instabilities.

This study provides an experimentally validated multiphysics framework of bubble deformation in electric fields, filling a decades-old gap in understanding. The correlations and predictive model enable controlled manipulation for electrospray, microfluidics, and interfacial phenomena.