A multiphase numerical model based on the volume of fluid (VOF) method is proposed to simulate the transient, electrochemically-generated Marangoni flow in a system comprising a NaOH electrolyte and a eutectic gallium–indium (EGaIn) metal droplet. The model incorporates appropriate equations to accurately represent the transport phenomena, including flow, electric potential, and electric current density, within the entire system. The model includes the transient variation in the interfacial tension as a function of electric current density at the interface, leading to the generation of Marangoni flow and enabling the tracking of droplet shape evolution. Notably, the model successfully captures the elongation of the droplet towards the cathode, which is validated through comparison with available experimental data.