Constitutive modeling of an electro-magneto-rheological fluid

The present article deals with a continuum mechanics-based method to model an electro-magneto-rheological (EMR) fluid deformation subjected to an electromagnetic field. The proposed method follows the fundamental laws of physics, including the principles of thermodynamics. We start with the general balance laws for mass, linear momentum, angular momentum, energy, and the second law of thermodynamics in the form of Clausius-Duhem inequality with Maxwell's equations. Then, we formulated a generalized constitutive model for EMR fluids following the representation theorem. Later, we validate the model with the results of an EMR rheometer and ER fluid valve system-based configurations. At last, the possible simulation-based velocity profiles are also discussed for parallel plate configuration. As a result, we succeed in providing more physics-based analytical findings than the existing studies in the literature.