John S. Dahler

Fluid Mechanical Aspects of Antisymmetric Stress

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...

Brownian Motion of Polyatomic Molecules: The Coupling of Rotational and Translational Motions

The 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 Kirkwoods 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 estab...

Transport Properties of Polyatomic Fluids, a Dilute Gas of Perfectly Rough Spheres

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.

Molecular Friction in Dilute Gases. II. Thermal Relaxation of Translational and Rotational Degrees of Freedom

Expressions for the rates of equilibration of the translational energies in multicomponent gas mixtures of structureless molecules are derived in terms of characteristic relaxation times. The approach to equilibrium is found to be completely dominated by an exponential decay factor for molecules interacting with inverse power potentials; the decay should be essentially exponential for more realistic potential functions. The calculations of rotational relaxation times are presented for several rigid molecular models: rough and partially rough spheres, spherocylinders, and loaded spheres. The relaxation times obtained are in good agreement with those observed experimentally and with those predicted by previous theories. It is found that, in general, on the order of 10 collisions are required to reduce an initial temperature difference by a factor of 1/e for translational‐rotational equilibration.

Molecular Friction in Dilute Gases. III. Rotational Relaxation in Polyatomic Fluids

Formulas are derived for the rotational relaxation times of gases composed of molecules interacting with square well potentials with rough spherical and spherocylindrical cores. The temperature dependence of the relaxation times is discussed and compared with previous theoretical results.

Kinetic theory of simple reacting spheres

Dilute and dense gas Enskog theory calculations are reported for a fluid composed of simple reacting spheres. Results for the dilute gas provide qualitative confirmation of previous calculations based on the MIRS (multiple interaction, reacting sphere) model. At high densities the viscosity and ’’empirical’’ diffusion coefficients vary almost linearly with the heat of reaction. The diffusion coefficients associated with the collisional transfer or ’’surface reaction’’ contributions to the component mass fluxes depend very strongly on density. For small heats of reaction and large densities this novel mechanism can completely overshadow regular diffusion. The transport coefficients associated with this surface reaction term fall into two categories, those with numerical values which tend to zero for large heats of reaction and those which increase rapidly as the exothermicity rises. The mass fluxes of reaction products belong to the latter category.

Hydrodynamic screening and particle dynamics in porous media, semidilute polymer solutions and polymer gels

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.

Mass and momentum transport in dilute reacting gases

A formal kinetic theory and illustrative model calculations are presented for a mixture of four species coupled together by the two chemical reactions A+BC?AB+C. The cross sections for reaction are not restricted to be small and so the reactive collisions can not be treated as if they were small perturbations, but must be dealt with on an equal par with nonreactive events. To describe the dynamics of the reactive collisions we use an extension of the DIPR (direct interaction, product repulsion) model which takes into account rotational–translational exchanges of energy and, in a cruder way, vibrational excitation as well. Because the dynamics of these reactive events are not derived from a Hamiltonian, care must be exercised to insure that the condition of microreversibility is satisfied. A moment method is used to extract from the kinetic equation estimates for the nonequilibrium corrections to the reaction rates and for the changes of viscosity and diffusion coefficients due to the chemical reaction. Ca...

Equilibrium constants for the formation of van der Waals dimers: Calculations for Ar–Ar and Mg–Mg

A variety of calculations of the equilibrium constant for the formation of atom–atom van der Waals complexes have been performed. Several approximate classical and quantum methods are compared with ‘‘exact’’ numerical calculations. Included are approximations which involve uncoupling, to varying degrees, of the vibrational and rotational motions. These approximate techniques can be generalized to larger systems for which exact calculations are infeasible. Calculations are performed for both Ar2 and the somewhat more strongly bound Mg2, using realistic analytic potentials and more approximate Lennard‐Jones potentials. Our goal is to understand better the accuracy of approximate calculations of the equilibrium constants for weakly bound systems.

The Boltzmann equation for a polyatomic gas

A formulation of the kinetic theory of dilute, classical polyatomic gases is given which parallels the Waldmann development for structureless molecules. In the first section the Boltzmann equation is written in terms of the specific rates of inelastic collision processes and then the properties of these rates and those of the corresponding collision cross sections are examined. The dependence of the distribution function on the dynamical variables is discussed and the equations of change for the gas are derived. Finally, a study is made of the properties of the linearized Boltzmann collision operation. In the second section the Boltzmann equation is deduced from a rigorous statistical-mechanical point of view and discussed in terms of the basic ideas of Bogoliubov. The computationally important special case of impulsive interactions is then considered.