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A theoretical exploration and an analytical model for theelectro-magneto-hydrodynamics (EMHD) of leaky dielectric liquid droplets,suspended in an immiscible confined fluid domain has been presented. Theanalytical solution for the system, under small deformation approximation, increeping flow regime, has been put forward. Study of the droplet deformationsuggests that its temporal evolution is exponential, and dependents on theelectric and magnetic field interaction. Further, the direction of the appliedmagnetic field with respect to the electric field decides whether thecontribution of magnetic forces opposes or aids the interfacial net electricalforce due to the electric field. Validation of the proposed model at theasymptotic limits of vanishing magnetic field show that the model accuratelyreduces to the case of transient electrohydrodynamic model. We also propose amagnetic discriminating function to quantify the steady-state dropletdeformation in the presence of interacting electric and magnetic fields. Thechange of droplets from spherical shape to prolate, and oblate spheroids,correspond to magnetic discriminating function >0 and <0 regimes, respectively.It is shown that with the aid of low magnitude magnetic field, a substantialaugmentation in the deformation parameter, and the associated EMHD circulationwithin and around the droplet is achieved. The analysis also reveals thedeformation lag and specific critical parameters that aid or suppressed thislag behaviour; discussed in terms of relevant non-dimensional parameters.

Deformation transients of confined droplets within interacting electric and magnetic field environment