Deformation and instability of sessile soap bubbles in an electric field

Interfacial deformation under electric fields is a common phenomenon in many industrial processes. Particularly, we are interested in the dynamics of sessile soap bubbles in a parallel-plate electric field which exhibits a stable deformation regime followed by conical instability. Using side-view imaging, we track the equilibrium shapes, the transition to the unstable regime, and the pre-jet apex dynamics within one experimental system. In the stable regime, the meridional profile is well described by a spheroidal fit, and the aspect ratio collapses across initial bubble sizes onto a single steady-state branch when plotted against the dimensionless field $E^\ast = \sqrt{\mathrm{Bo}_e}$ for data acquired within a fixed ambient session where the electric Bond number $\mathrm{Bo}_e$ is defined as $\varepsilon_0 E_0^2 R_0/(2\gamma)$. The endpoint of this branch marks the transition to the unstable regime. Above onset of instability, the apex sharpens into a cone with half-angle $30.0^{\circ}$ $\pm$ $0.6^{\circ}$, below the classical Taylor value. To quantify the late pre-jet stage, we define the axial distance $b(t)$ from the instantaneous apex to a fixed reference vertex determined from the terminal cone geometry and measure its evolution. The corresponding rate grows as jetting is approached, and a near-tip inertia-capillary model captures the observed logarithmic trend as an approximation. Together, these measurements establish a single-system experimental benchmark in which stable electrocapillary deformation is organized by a single steady-state branch that leads into conical instability and pre-jet dynamics.