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
The Enskog theory of transport in a dense gas is applied to the rough-sphere model. A formal analog of the Chapman-Enskog method is developed in order to construct the normal solution of the corresponding kinetic equation. Accurate estimates are given for the coefficients of shear and bulk viscosity and of thermal conductivity. A procedure is provided for computing the coefficient which characterizes the antisymmetric portion of the stress tensor and also for estimating the coefficients of proportionality between the flux of spin angular momentum and the gradient of the local spin velocity. Numerical values are given for these and other transport coefficients and characteristic relaxation times. A study is provided of the hydrodynamical significance of antisymmetric stress and of spin flux. Finally, the theory of this paper is compared with other, rather more heuristic, methods. 4
The dynamics of particle interactions in porous media are studied using a newly formulated mean field theory. Statistical correlations in the gel network are analyzed in detail and found to have a crucial influence on the results. Self-diffusion and mutual diffusion coefficients of Brownian particles moving through a gel are determined. Preaveraged hydrodynamic interaction tensors are derived for two mobile Brownian particles a mobile particle and an obstacle.
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