A theory of transversely isotropic fluids

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Abstract
The present paper proposes a theory for the mechanical behaviour of a fluid with a rigid microstructure. The microstructure is described by a director frame of three vectors and a second-order tensor W and its gradient are proposed as measures of the kinematics of this frame. When the frame is spinning without deforming, W reduces to the director spin velocity. Postulating the existence of a couple stress in addition to the classical Cauchy stress, the linear constitutive equations for such a structured fluid are derived and then specialized to the case of transverse isotropy.These equations are used to study rectilinear shearing flow. When [dtri ]W = 0, the condition for a non-interacting substructure, the results of the theory are shown to be in agreement with the work of Jeffery and of Ericksen. For mutually interacting substructure particles, [dtri ]W ≠ 0, a geometric analysis of the non-linear differential equations is performed in order to exhibit the effects of particle concentration on the flow kinematics.

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