• Accepted Paper

Equilibrium of a surfactant-laden liquid column in a uniform transverse electric field: A small-deformation theory

Fang Li, Xieyuan Yin, and Xiezhen Yin

Phys. Rev. Fluids - Accepted 14 September, 2026

DOI: https://doi.org/10.1103/wdpj-398s

Abstract

We theoretically investigate the equilibrium state of a surfactant-laden liquid column subjected to a weak uniform transverse electric field, within the framework of the Taylor-Melcher leaky dielectric theory in the Stokes-flow regime. Our second-order perturbation analysis yields an analytical expression for the deformation parameter D. The solution reveals that the uniform surfactant coverage $\varGamma^*_0$ (normalized by the maximum packing concentration) and the elasticity number E—which quantifies the sensitivity of interfacial tension to surfactant coverage—modulate the steady-state deformation indirectly through the electric capillary number CãE, defined as the ratio of electric forces to the surfactant-modified interfacial tension. In contrast, the surface P'eclet number Pes (the relative importance of convection to diffusion in surfactant transport) and the effective Boussinesq number B (the ratio of surface to bulk viscous stresses) do not influence the steady-state deformation up to O(CãE2). Owing to the cylindrical geometry, surface dilatational and shear viscosities yield identical dynamic responses, and their combined rheological effects can be lumped into an effective interfacial tension. Our parametric analysis shows that all surfactant-related dimensionless parameters ($\varGamma^*_0$, E, Pes, and B) significantly modulate interfacial properties and bulk flow circulation. Specifically, increasing $\varGamma^*_0$ or E enhances deformation; decreasing Pes homogenizes the surfactant distribution, thereby suppressing Marangoni stress and strengthening flow circulation; and increasing B attenuates circulatory motion. This work provides insights into the distinct roles of surfactant-mediated mechanisms in the steady electrodeformation of transversely electrified liquid columns, laying a solid theoretical foundation for understanding the behavior of surfactant-laden columns and jets in electric-field-based engineering processes.

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