Duane W. Condiff

Bio: Duane W. Condiff is an academic researcher. The author has contributed to research in topics: Kinetic theory of gases & Boltzmann equation. The author has an hindex of 5, co-authored 9 publications receiving 428 citations.

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.

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

Abstract: 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 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 estab

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

Abstract: 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.

Transport Mechanics in Systems of Orientable Particles. II. Kinetic Theory of Orientation Specific Transport for Hard‐Core Models

Abstract: The role of orientation and polarization in the transport phenomena of hard‐core polyatomic gases is developed in detail from the standpoint of the Boltzmann equation. A rigorous orientation specific Chapman and Enskog scheme is used to establish linear constitutive relations and anisotropic transport coefficients for orientation‐specific translational and rotational diffusion and for the orientation‐summed fluxes of mass, momentum, and heat. Calculations are reported for the effect of polarization upon the shear viscosity and thermal conductivity tensors of loaded spheres. The anisotropic expressions for rotational and translational thermal diffusion, shear diffusion, and concentration diffusion coefficient tensors are determined for a dilute system of loaded spherocylinders in a bath of rigid spheres. With the use of time reversal invariance, a microscopic reciprocal theorem is established and employed to prove Onsager reciprocal relations among the transport coefficient tensors.

Kinetic Theory of Moderately Dense Gases

Abstract: A kinetic equation approach to the kinetic theory of moderately dense gases is developed by asymptotic expansions from a viewpoint independent of Bogoliubov chaos assumptions. The theory is applied to the rigid sphere model where the contributions which determine the Enskog dense gas theory are identified. The existence of divergences in the time integrations for triple collision events in the case of rigid discs and for quadruple collision events in the case of rigid spheres is confirmed by means of variable transformations. A scheme for renormalizing the divergences into an asymptotic density expansion containing nonanalytic logarithmic terms is proposed, illustrated for the case of rigid discs, and employed to deduce the fact that the first density corrections for rigid spheres, being convergent, remain intact as the lead term of the asymptotic density expansion. Numerical studies of the first density corrections to the thermal conductivity and shear viscosity of rigid spheres are performed in order to...

The non-linear field theories of mechanics

Abstract: Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield

Abstract: The flow of an idealized granular material consisting of uniform smooth, but nelastic, spherical particles is studied using statistical methods analogous to those used in the kinetic theory of gases. Two theories are developed: one for the Couette flow of particles having arbitrary coefficients of restitution (inelastic particles) and a second for the general flow of particles with coefficients of restitution near 1 (slightly inelastic particles). The study of inelastic particles in Couette flow follows the method of Savage & Jeffrey (1981) and uses an ad hoc distribution function to describe the collisions between particles. The results of this first analysis are compared with other theories of granular flow, with the Chapman-Enskog dense-gas theory, and with experiments. The theory agrees moderately well with experimental data and it is found that the asymptotic analysis of Jenkins & Savage (1983), which was developed for slightly inelastic particles, surprisingly gives results similar to the first theory even for highly inelastic particles. Therefore the ‘nearly elastic’ approximation is pursued as a second theory using an approach that is closer to the established methods of Chapman-Enskog gas theory. The new approach which determines the collisional distribution functions by a rational approximation scheme, is applicable to general flowfields, not just simple shear. It incorporates kinetic as well as collisional contributions to the constitutive equations for stress and energy flux and is thus appropriate for dilute as well as dense concentrations of solids. When the collisional contributions are dominant, it predicts stresses similar to the first analysis for the simple shear case.

Couple Stresses in Fluids

Abstract: The effects of couple stresses in fluids are considered. Linearized constitutive equations are proposed for force and couple stresses. A series of boundary‐value problems are solved to indicate the effects of couple stresses as well as for experiments measuring the various material constants. It is found that a size effect comes in which is not present in the nonpolar case (couple stresses absent).