The Characteristic Length of a Polar Fluid

Abstract

The constitutive equations for a linear polar fluid were introduced in 1952 by Grad [1] and were motivated by statistical mechanics considerations. Recently polar fluids have been considered from a statistical mechanics viewpoint by Dahler [2, 3] and from a continuum approach by Cowin [4], Jatjnzemis and Cowin [5], and Eringen [6]. The constitutive equations for a polar fluid relate the stress tensor T and the couple stress tensor Λ to the rate of deformation tensor D, to the angular velocity of the rigid Cosserat triad Ḡ, to the gradient of Ḡ denoted by ψ̄, and to the difference H̄ between Ḡ and the usual or regional angular velocity W̄ (W̄is one half the vorticity ∇ × v),

$$\hat H = \hat G - \hat W = \hat G - \frac{1}{2}\nabla \times v.$$

((1))