Viscoelasticity-contrast driven electrohydrodynamic behaviour of a droplet-suspended-in-a-confined-liquid configuration

We present an approximate analytical model (without compromise on the physics) of the electrohydrodynamics (EHD) of a confined leaky dielectric, non-Newtonian viscoelastic droplet suspended in a surrounding medium of similar characteristics. The analysis considers the Stokes flow regime through a small deformation formulation. The viscoelastic behaviour is realized by coupling the Cauchy momentum equation with the upper convected Maxwell (UCM) model. Since the study is limited to low electric field intensities, the governing Weissenberg number (Wi) $\le$ 1. We consider various combinations of the droplet and the surrounding, viz. NN-N, N-NN, and NN-NN cases. A thorough comparison with the N-N case is conducted. Here, ‘N’ represents Newtonian and ‘NN’ represents non-Newtonian. The solution put forward is validated with experimental observations in literature and works successfully in the regime of low electric field strength. We show that, for an unconfined domain, the deformation is maximum for the N-N case and least for the N-NN case, thus establishing the role of viscoelasticity-contrast. For the confined domain, we have also observed shape reversal in N-NN and NN-NN cases at higher confinement ($\alpha$) and lower electro-rheological parameter ($\delta$). For NN-N, the deformation is greater compared to the N-N case beyond a critical $\alpha$. We also report the streamline patterns within the droplet and in the surrounding medium for various cases and for different confinement. The findings reveal shape reversal phenomena in confined viscoelastic cases, and provide insights into the EHD with fluidic confinement, offering potential avenues for the design and functionality of microfluidic devices.