Theory Of Polar Fluids Research Articles

Some aspects in the thermodynamic theory of polar fluids

A thermodynamic theory for a non-simple hemitropic polar fluid based on the exploitation of the entropy principle with Lagrange multipliers is developed. It has been shown that the couple stress in equilibrium vanishes, while the entropy flux in a linearized theory is given by heat flux vector divided by the absolute temperature. The importance of some adimensional parameters is also discussed.

Statistical mechanical theory of polar fluids for all densities

We present results for the structure and thermodynamics of a polar fluid obtained from a recently developed theory which is based on the method of conditional distribution. Within the framework of the method the concept of the average force potentials is used to develop a truncation procedure for an arbitrary equation of the chain. A closed system of integral equations for the average force potential is formulated. The Helmholtz free energy, the pressure, structural properties and the static dielectric constant are calculated in terms of the binary distribution function. We compare our results with experimental data and find that the theory gives realistic results. Comparisons are also made for self-diffusion coefficients obtained from molecular dynamics simulations.

Computer simulation using a non-spherical reference potential for polar fluids

A Barker—Henderson type splitting of the intermolecular potential has been used to obtain a non-spherical reference potential for a perturbation theory of polar fluids. Monte Carlo simulations of the non-spherical reference fluid have been performed to obtain directly the reference fluid Helmholtz free energy A 0, and the first-order free-energy term A 1. Resulting first-order expansion predicts reasonably well thermodynamic properties for the case of dipolar Lennard-Jones fluids; however, serious deviations are noted for the case of quadrupolar Lennard-Jones fluids.

Conformal-solution theory of polar fluids: The statistical mechanical basis of shape factors

Abstract Massih, A.R. and Mansoori, G.A., 1983. Conformal-solution theory of polar fluids: the statistical mechanical basis of shape factors. Fluid Phase Equilibria, 10: 57–72. The formalism of conformal-solution theory (CST) has been extended to pure and mixed polar fluids with consideration of dipolar, quadrupolar and induced dipolar forces. The total potential energy is reduced to a form similar to that for neutral molecules by statistical averaging over orientations. The temperature dependences of the conformal parameters faa and haa are derived and it is found that the temperature variations are in opposite directions. These conformal parameters are related to Leland's shape factors θaa and φaa, for which similar trends in temperature variations are observed. Following the theory of Byers-Brown for neutral molecular fluid mixtures, with the random-mixing approximation, an expression is derived for the excess Gibbs free energy of a binary polar mixture, using a generalized mixing-rule approximation.

B�nard instabilities in polar fluids

This paper employs continuum theory of polar fluids to investigate the onset of roll-type instabilities in a fluid confined between horizontal rigid boundaries and subject to a vertical temperature gradient. A Fourier series method is used to obtain an exact expression for the determination of the critical temperature gradient for the particular type of instability. Results are presented for a wide range of the various parameters in the theory.

粒状体の流れ特性の研究

Continuum mechanical foundation for the flow of granular materials is established. The material is assumed to consist of cohesionless rigid spheres of uniform size and weight. Macroscopic laws are deduced from microscopic considerations of interparticle friction by means of statistical inference. The field is described by the theory of polar fluids. Various characteristics of granular materials such as the critical stress condition and the angle of repose are mathematically deduced from the theory. The effects of couple-stress in the Couette flow between two parallel plates is also studied and the ‘boundary layer’ is shown to exist.

Theory of polar fluids. III

Theory of polar fluids. III

Theory of polar fluids. II

Theory of polar fluids. II

The velocity slip of polar fluids

The theory of polar fluids, briefly reviewed and shown to be identical to the theory of micropolar fluids, is applied to five different viscometric flows and to the flow around a slowly rotating sphere. Comparing theoretical predictions with experimental results for the viscometric flows it is demonstrated that the theory may serve as a model for the flow of suspensions if a velocity slip along a solid wall is accounted for.

Theory of polar fluids. I

We examine a classical fluid composed of molecules which contain a polarizable electric dipole with finite permanent moment. The long-ranged dipolar and the short-ranged interactions are treated on a different footing by expanding relative to a reference system characterized by the absence of electrostatic interactions. Extensions of graph theoretical techniques developed in an earlier paper are used to analyse the pair distribution function and the dielectric constant. Reduction of the number of graphs and their complexity is effected by introducing renormalizations of the permanent moment and the polarizability. The analysis leads to the definition of a new function w(12), which is free of terms dependent on the shape of the sample. For polar, polarizable molecules the direct correlation function lacks translational invariance; its role as a basic quantity is ceded to w(12). The pair distribution function and the dielectric constant ε are expressed in terms of w(12) and two closely related functions. Attention is drawn to an unsolved problem in dielectric theory, and an alternative formula for ε is presented in the form of a conjecture. An approximation for ε is formulated for the case in which the short-ranged non-dipolar interactions are independent of the molecular orientations. A simplified version is solved analytically.

Theory of polar liquids

Two recent contributions to the statistical theory of polar fluids, namely the perturbation theory of Stell, Rasaiah and Narang (SRN) and the meanspherical-approximation (MSA) results of Wertheim, and of Nienhuis and Deutch, are compared and contrasted for the conceptually simple model of hard spheres, diameter R, with central point dipoles, of strength μ (dipolar hard spheres). It is shown that the MSA approach replaces correlation functions which enter correctly into the SRN theory by their low-density limits : to this extent it is unsatisfactory. On the other hand the MSA work does suggest reasons why the naive Padé approximant featuring in SRN theory may be expected to do reasonable justice to the physics of the problem. Numerical comparisons of the excess free-energy (as compared with non-polar hard spheres) as a function of reduced density, ρ* = ρR 3, are given at two temperatures, T* = 2 and T* = 0·25, where T* = kTR 3/μ2. Similar curves, for T* = 1 and T* = 0·5, are available from the authors. The gas-liquid (T*, ρ*)-phase boundary is located, near the critical point, on both theories, as are the vapour pressure curves. These are calculated using the Carnahan-Starling equation of state for hard spheres ; and critical comment is made in justification of employing this in the context of MSA results for the excess quantities. The two theories are found to have appreciably different numerical consequences.

On the frame-dependence of stress and heat flux in polar fluids

A special theory of polar fluids is developed with a view to providing some insight into the questions of the frame-dependence of stress and heat flux, arising out of a recent paper by Muller (1).

Dynamics of polar fluids

The theory of polar fluids is discussed from a physical standpoint. Field equations and constitutive equations are established from a different point of view. Using the entropy inequality, restrictions on material coefficients are obtained. Various boundary conditions are discussed and a new boundary condition is suggested. The classical slow motion concept is extended to the case of polar fluid motion. The expression of the increased rate of dissipation in an incompressible suspension is given and the viscosity of a dilute suspension is calculated. A convenient expression for the force exerted by the fluid on a body is established and the expression of the force by fluid on a rigid sphere in uniform translation is obtained.

On the steady rotational motion of polar fluids

It is shown that for all physically reasonable boundary conditions employed in the theory of polar fluids the theory predicts the traditional result that a fluid will undergo a pure rigid body rotation when subjected to a steady rotational motion in a cylindrical vessel.

Polar Fluids

It is noted that a number of theories proposed recently by various authors are actually identical with the theory of polar fluids suggested by Grad in 1952. The relatively close relationship of the recently presented theory of dipolar fluids to polar fluid theory is established. The thermodynamics of polar fluids with heat conduction is sketched. The solved boundary-value problems of polar fluid theory are summarized and the essential features of these solutions establish a pattern that gives insight into the behavior of polar fluids as well as indicating where the theory might be of practical significance.

Dielectric Constant Theory for Polar Liquids

In Debye's theory of polar fluids, the electrostatic interaction of the molecules was taken into account by introducing the Lorentz local field formula. This formula is inaccurate, especially for liquids. More recent treatments are of two types. One, developed by Onsager, treats one molecule explicitly and replaces the others with a continuum. The other, developed by Kirkwood, uses the statistical mechanical theory of strongly interacting molecules. The second method is rigorous and can be used to derive the approximate results of the first; nevertheless, the first has remained popular because of its simplicity. The treatment presented here attempts to combine the rigor of Kirkwood's method with the simplicity of Onsager's. This is done by use of several useful theorems of classical electrostatics, which are overlooked when dielectrics are treated in the traditional textbook manner. The result is shown to be equivalent to Kirkwood's; but it is in a more flexible form, and it can, therefore, be used to derive approximations of a more general class.