Fluid Mechanical Aspects of Antisymmetric Stress

Abstract

Basic fluid mechanical concepts are reformulated in order to account for some structural aspects of fluid flow. A continuous spin field is assigned to the rotation or spin of molecular subunits. The interaction of internal spin with fluid flow is described by antisymmetric stress while couple stress accounts for viscous transport of internal angular momentum. With constitutive relations appropriate to a linear, isotropic fluid we obtain generalized Navier-Stokes equations for the velocity and spin fields. Physical arguments are advanced in support of several alternative boundary conditions for the spin field. From this mathematical apparatus we obtain formulas that explicitly exhibit the effects of molecular structure upon fluid flow. The interactions of polar fluids with electric fields are described by a body-torque density. The special case of a rapidly rotating electric field is examined in detail and the induction of fluid flow discussed. The effect of a rotating electric field upon an ionic solution is analyzed in terms of microscopically orbiting ions. This model demonstrates how antisymmetric stress and body torque can arise in ``structureless'' fluids.

Generalized extended Navier-Stokes theory: Correlations in molecular fluids with intrinsic angular momentum

“…In the absence of an external force field and for sufficiently small pressure gradients, the convection term can be ignored and the linearized form of the ENS equations read 13,20 …”

On the angular velocity slip in nano-flows

“…Since m (n) is to be treated as a contact torque and since on the second side of boundary surface there is designed contact boundary torque q ∂V , then still adopting Cauchy's argumentation, Truesdell and Toupin propose the following boundary conditions [eq. 203.6] An existence of internal couple stress tensor m was postulated on the fluid continuum ground and commented in the papers by Aero et al (1965), Condiff and Dahler (1964), Eringen (1964), Łukasiewicz (1999), Eringen (1996), Kucaba-Piętal (2004), Hoffmann et al (2007). This tensor is fundamentally nonsymmetric and its presence leads to the appearance of a nonsymmetric part of the Cauchy stress tensor t � = t T .…”

Exact controllability of Galerkin’s approximations of micropolar fluids

“…Spaces of For the model derivation and related physical discussion, see Condiff and Dalher [5], Eringen [9], [10], Lukaszewicz [24] and Petrosyan [26]. We observe that (1.1) includes as a particular case the classical Navier-Stokes equations, which have been widely studied (see, for instance, Ladyzhenskaya [19] or Temam [30] and the references therein).…”