Stress due to Electric and Magnetic fields in Viscoelastic Fluids

A clear understanding of body force densities due to external electromagnetic fields is necessary to study flow and deformation of materials exposed to the fields. In this paper, we derive an expression for stress in continua with viscous and elastic properties in presence of external, static electric or magnetic fluids. Our derivation follows from fundamental thermodynamic principles. We demonstrate the soundness of our results by showing that they reduce to known expressions for Newtonian fluids and elastic solids. We point out the extra care to be taken while applying these techniques to permanently polarized or magnetized materials and derive an expression for stress in a ferro-fluid. Lastly, we derive expressions for ponderomotive forces in several situations of interest to fluid dynamics and rheology.