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A continuum theory of dense suspensions. (English) Zbl 1065.76190
Summary: A continuum theory is introduced for viscous fluids carrying dense suspensions (such as blood) or emulsions of arbitrary shape and inertia. Suspended particles possess microinertia that makes the mixture an anisotropic fluid whose viscosity changes with motion and orientation of suspensions. The microinertia balance law coupled with the equations of motion of an anisotropic fluid govern the ultimate outcome. By means of the second law of thermodynamics, constitutive equations are obtained in terms of frame-independent tensors. In a special case, a theory of bar-like suspensions is obtained. The field equations, boundary and initial conditions are given for both the arbitrarily-shaped suspensions and for bar-like suspensions. The theory is demonstrated with the solution of channel flow problem. The mean viscosity of the fluid with suspensions is determined, and the motions of suspensions down the flow are demonstrated.
MSC:
76T20Suspensions
76A99Foundations, constitutive equations, rheology