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.

Articles you may be interested inInertial and bias effects in the rotational Brownian motion of rodlike molecules in a uniaxial potential J. Chem. Phys. 134, 044530 (2011); 10.1063/1.3524534 Rotational Brownian motion of a pair of linear molecules or dipoles with anisotropic interaction Fokker-Planck equation and the grand molecular friction tensor for coupled rotational and translational motions of structured Brownian particles near structured surfacesThe coupling of rotational and translation Brownian motions is examined from several points of view. The first is a phenomenological theory based upon generalized Langevin equations of motion and a Markoff integral equation. Next, a more detailed statistical-mechanical theory is fashioned after the pattern of Kirkwood's theory for nonequilibrium processes in monatomic liquids. Both schemes lead to a generalized Fokker-Planck-Chandrasekhar equation for the singlet-distribution function. This equation includes terms that account for separate rotational and translational motions as well as two mutually symmetric contributions which are descriptive of their coupling. The friction tensors associated with the uncoupled components of these motions are found to be proportional to the autocorrelations of the environmental force and torque which act upon a given molecule. The frictional coupling is related to the cross correlation of force and torque. From the principle of microreversibility it is possible to establish a reciprocal relationship between the two coupling tensors. A third approach is to derive the generalized Fokker-Planck equation from the Boltzmann equation for a dilute solution of rotating molecules. This has been done for the model of perfectly rough spheres and also for "loaded spherocylinders." In both cases explicit formulas are obtained for the various friction tensors. The last section of the paper is devoted to the application of these theories to problems of diffusion.2

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A detailed account is given of the kinetic theory for a fluid composed of perfectly rough spheres. When one applies the method of Chapman and Enskog to a dilute gas of these spheres he finds that the nonequilibrium distribution function satisfies a nonself-adjoint integral equation. The solution of this equation is not an isotropic function of the molecular spin velocity. A study has been made of the bearing of this spin anisotropy upon the calculated values for the gas transport coefficients.