Kinetic Theory of Moderately Dense Rigid Sphere Fluids. III. The Formulation and Solution of the Transport Equation for Binary Mixtures

1960 ◽  
Vol 32 (2) ◽  
pp. 538-547 ◽  
Author(s):  
Robert A. Harris ◽  
Stuart A. Rice
Keyword(s):  
Kinetic Theory ◽  
Transport Equation ◽  
Binary Mixtures ◽  
Rigid Sphere

A simple kinetic theory for granular flow of binary mixtures of smooth, inelastic, spherical particles

1986 ◽  
Vol 63 (1-4) ◽  
pp. 45-60 ◽  
Author(s):  
M. Farrell ◽  
C. K. K. Lun ◽  
S. B. Savage
Keyword(s):  
Kinetic Theory ◽  
Binary Mixtures ◽  
Granular Flow ◽  
Spherical Particles

ASYMPTOTIC ANALYSIS FOR A PARTICLE TRANSPORT EQUATION WITH INELASTIC SCATTERING IN EXTENDED KINETIC THEORY

1998 ◽  
Vol 08 (05) ◽  
pp. 851-874 ◽  
Author(s):  
JACEK BANASIAK ◽  
GIOVANNI FROSALI ◽  
GIAMPIERO SPIGA
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Transport Equation ◽  
Free Path ◽  
Null Space ◽  
Collision Operator ◽  
Mean Free Path ◽  
Molecular Flow ◽  
Asymptotic Equation ◽  
Linear Transport

In this paper we perform the asymptotic analysis for a linear transport equation for test particles in an absorbing and inelastically scattering background, when the excited species can be considered as non-participating. This model is derived in the frame of extended kinetic theory and rescaled with the Knudsen number ∊. After examining the main properties of the collision model and of the scattering operator in the case with an infinite interval of energy as well as the case with a finite interval, the modified (compressed) Chapman–Enskog expansion procedure is applied to find the asymptotic equation for small mean free path. A specific feature of this model is that the collision operator has an infinite-dimensional null-space. The main result is that in the small mean free path approximation on [Formula: see text] level we obtain a free molecular flow for a suitable hydrodynamic quantity, rather than the diffusion which is typical for linear transport problems.

The evolution of segregation in dense inclined flows of binary mixtures of spheres

2015 ◽  
Vol 782 ◽  
pp. 405-429 ◽  
Author(s):  
Michele Larcher ◽  
James T. Jenkins
Keyword(s):  
Numerical Simulation ◽  
Binary Mixture ◽  
Kinetic Theory ◽  
Binary Mixtures ◽  
Granular Temperature ◽  
Particle Segregation ◽  
Physical Experiments ◽  
Dense Flows ◽  
Mixture Velocity

We consider the evolution of particle segregation in collisional flows of two types of spheres down rigid bumpy inclines in the absence of sidewalls. We restrict our analysis to dense flows and use an extension of kinetic theory to predict the concentration of the mixture and the profiles of mixture velocity and granular temperature. A kinetic theory for a binary mixture of nearly elastic spheres that do not differ by much in their size or mass is employed to predict the evolution of the concentration fractions of the two types of spheres. We treat situations in which the flow of the mixture is steady and uniform, but the segregation evolves, either in space or in time. Comparisons of the predictions with the results of discrete numerical simulation and with physical experiments are, in general, good.

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