摘要:

This paper discusses the various attempts along the lines of statistical mechanics that have been made to explain certain phenomena occurring in flow of fluids through porous media. The latter particularly concerns processes of mixing miscible phases during their passage through a porous medium. The statistical theories that can be proposed are based on the following theoretical models: random walk of individual fluid particles, quasi‐turbulent flow analogy, analogy with thermodynamics, and finally, general statistical mechanics. In all cases, one ends up with equations that are very similar to a diffusivity equation.

ISSN:0148-6055    

DOI:10.1122/1.548990

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

Rigorous lower bounds on the relative viscosity have been obtained for a variety of suspensions by applying the principle of minimum energy dissipation. Results are given for suspensions of irregular particles, as well as for suspensions of spheres. Numerical values have been obtained in a number of special cases.

ISSN:0148-6055    

DOI:10.1122/1.549013

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

There are presently a large number of problems in continuum physics that may be treated from a statistical point of view. In this paper we shall discuss what is meant by the statistical solution to a continuum problem. We shall initially use the nature of the stress and strain fields in a heterogeneous material as an example. We shall then emphasize the essential similarity of all statistical continuum theories. The more developed statistical continuum theories like the statistical theory of turbulence and the theory of partial coherence will be compared to the statistical theory of heterogeneous materials. For the heterogeneous material problem we shall outline a method for deriving a hierarchy of statistical moment equations from the equations of elasticity for a medium with variable elastic properties. We conclude with a discussion of the use of perturbation procedures in determining bounds for the effective elastic constants.

ISSN:0148-6055    

DOI:10.1122/1.548991

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

A material property is often described by a proportionality factor between a solenoidal vector (electric or magnetic induction, electric current density) and an irrotational vector (field intensity); in an isotropic dielectric, for example,D=εE.Often one wishes to calculate the effective ε for a random mixture of two homogeneous materialsAandB, with constantsεAandεB,filling volume fractionspandq. There are exact formulas for the cases of boundaries all parallel or all perpendicular to the field, and an approximate formula for spheresAin a matrixBwithp≪1.For a statistically isotropic random mixture with arbitraryp, many approximations of unknown reliability have been proposed. Recently two rigorous results have been derived. (1) A series expansion inεA−εBrequires, besidesp, additional statistical information, dependent on the probabilitiesp12...n(n)of findingnpointsr1,r2,...,rnall simultaneously in materialA. (2) Given onlyεA,εB,andp1(1)(=p=1−q),we can state thatε*⩽ε⩽εwhereε*andε*are calculable and attainable. The present paper reviews these rigorous theories and presents closer bounds, based on additional information dependent onp12(2)andp123(3).

ISSN:0148-6055    

DOI:10.1122/1.549016

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

Existing rigorous theories of prediction of macroscopic elastic behavior of random media are discussed. Attention is focused on statistically homogeneous and isotropic multiphase materials and polycrystals and on fiber reinforced materials. Direct approaches for dilute suspension theory and variational approaches for arbitrary phase fractional volumes are surveyed. New results are given for elastic behavior of cubic polycrystalline mixtures and for a couple stress constant of a dilute spheres suspension.

ISSN:0148-6055    

DOI:10.1122/1.549014

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

An experiment is described in which a sphere is rotated in a bath of viscoelastic liquid with facilities for measuring the couple on the sphere over a range of rotational speeds. It was also possible to observe the streamline patterns. It is concluded that such an apparatus provides a simple means of determining useful normal stress and apparent viscosity data for viscoelastic liquids at low shear‐rates.

ISSN:0148-6055    

DOI:10.1122/1.548992

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

An extensive series of photographs of lines of flow induced in a viscoelastic liquid by a rotating cone has been obtained for polyisobutylene in cetane at various vertex angles. Torque and thrust were measured at various angular velocities, concentrations, and temperatures. Concentrations above 5% resulted in departures from Newtonian behavior. They exhibited multiple vortices and in addition, the thrust‐to‐angular‐velocity relationships were different from those for Newtonian liquids. The higher concentrations show well defined maxima of thrust and torque at definite angular velocities.

ISSN:0148-6055    

DOI:10.1122/1.549015

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

摘要:

As part of a general study of the mechanical behavior of materials with temperature‐dependent properties, idealized Couette flow is considered here. The model fluid is Newtonian and incompressible. Inertial terms are neglected in the analysis. Time‐dependent temperature and velocity distributions in the fluid are computed for: (1) the constant stress case, (2) the constant rate of stress increase case, and (3) the constant boundary velocity case. In each case, a range of thermal boundary conditions is also considered. The results are compared with closed form analytical solutions that can be obtained in special cases. The temperature distributions can influence the stability of laminar flow and cavitation in liquids. The derived velocity distributions influence the drag and protective action of lubricants. Furthermore, it appears that some apparently non‐Newtonian flows can be described more simply when the deviation is attributed to heating than when it is attributed to intrinsic, non‐Newtonian behavior. A thermistor circuit analog is demonstrated as an aid to the solution of the Couette flow equations with thermal feedback.

ISSN:0148-6055    

DOI:10.1122/1.548993

出版商:The Society of Rheology    

年代:1965

数据来源: AIP

ISSN:0148-6055    

DOI:10.1122/1.549031

出版商:The Society of Rheology    

年代:1965

数据来源: AIP