Generalized mechanics of incompressible multiphase suspensions

A continuum theory for multiphase particulate suspensions in liquid media was formulated. The generalized fundamental balance laws for the particulate phases and the continuous fluid phase were presented. The thermodynamics of the multiphase system was studied, and the method of Lagrangian multipliers was employed to include the incompressibility of materials constraint and the criterion for fully saturated media. Constitutive equations were developed, which included micro-rotational and micro-dilatational effects. The basic equations of motion of different phases were derived and discussed. Special considerations were given to the case of incompressible constituents. Applications of this theory to nanofluids, dilute suspension flows, and multiphase sedimentations were also described.