Rheology and electro-magnetism stimulated non-trivial deformation dynamics of viscoelastic compound droplets

In this research, we present an analytical model describing the deformation dynamics of viscoelastic, leaky dielectric droplets confined within a surrounding liquid under the influence of direct electric field and uniform magnetic field. We have considered various combinations of droplets and surrounding fluid, which can be either Newtonian (N) or non-Newtonian (N-N), and may mimic a compound droplet scenario too. The governing equations for conservation of charge, mass, momentum and electromagnetic phenomena are solved for the leaky dielectric theory within the Stokes flow regime and the small deformation approximation. The electrical, magnetic and viscoelastic behaviour is realized using the Cauchy momentum equation in conjunction with the Maxwell stress tensor, Lorentz force and the upper convected Maxwell model, respectively. The changes in deformation and flow characteristics are comprehensively analysed through the variation of key non-dimensional parameters, namely the Capillary number (Ca), Weissenberg number (Wi) and electromagnetic interaction number (Em). The present work is restricted to Wi ≤ 1 and semi-analytical solutions to the complicated multi-physics phenomena are obtained. Our study reveals that in the presence of only an electric field, a flow field in the non-Newtonian fluid fails to develop if the droplet has relatively lower conductivity compared with the surrounding medium, owing to the insufficient intensity of the electric field. However, when the droplet is relatively more conductive than the surrounding medium, a flow field does arise. The analysis shows that an augmentation in the flow and deformation behaviour of the non-Newtonian fluid can be observed when the magnetic field is applied, but only in a specific direction relative to the electric field. Flow is induced in the + B direction when the droplet is relatively less conductive, and the electromagnetic force dominates over the hydrodynamic force. Conversely, in the − B direction, flow is induced when the droplet is relatively more conductive, as both the electric and electromagnetic forces act together. Such findings provide intricate insights into understanding electro-magneto-hydrodynamics with non-Newtonian confined droplets, and may enable avenues towards realizing precision industrial and scientific microfluidic technologies via manipulation of the movement, deformation and coalescence of droplets.