Couette flow for a gas with a discrete velocity distribution

1976 ◽  
Vol 76 (2) ◽  
pp. 273-287 ◽  
Author(s):  
Henri Cabannes
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Couette Flow ◽  
Flow Problem ◽  
Kinetic Equations ◽  
Velocity Slip ◽  
Theory Model ◽  
Slip Coefficient ◽  
Slip Coefficients

We consider a kinetic theory model of a gas, whose molecular velocities are restricted to a set of fourteen given vectors. For this model we study the Couette flow problem, the boundary conditions on the walls being the conditions of pure diffuse reflexion. The kinetic equations can be integrated by quadrature under the assumption that the walls have opposite velocities and equal temperatures. The presence on the walls of tangential velocities leads to the consequence that the velocity slip coefficient does not in general vanish when the Knudsen number goes to zero.Considering the same problem again after the suppression of tangential velocities, we obtain formulae for the velocity and temperature slip coefficients which generalize results of Broadwell (1964b), and which agree qualitatively with experiments.

On Boundary Conditions Method in the Kinetic Theory of Gases

1971 ◽  
Vol 26 (10) ◽  
pp. 1708-1712 ◽  
Author(s):  
S. K. Loyalka
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Couette Flow ◽  
Flow Problem ◽  
Kinetic Theory Of Gases ◽  
Plane Couette Flow ◽  
Proposed Modification ◽  
Maxwell’S Boundary Conditions

Abstract It is shown that the work of Cercignani and Tironi on Maxwell's boundary conditions method can be improved in a simple and logical way. The technique for improvement is illustrated by a study of the linearized plane Couette flow problem and it is found that the proposed modification yields results that are identical with some highly accurate variational results.

Boundary Conditions for Multi-Component Slip-Flows Based on the Kinetic Theory of Gases

2008 ◽  
Author(s):  
Azad Qazi Zade ◽  
Metin Renksizbulut ◽  
Jacob Friedman
Keyword(s):  
Kinetic Theory ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Gas Flows ◽  
Kinetic Theory Of Gases ◽  
Concentration Jump ◽  
Physical Importance ◽  
Jump Velocity ◽  
Slip Flows

General temperature-jump, velocity-slip, and concentration-jump conditions on solid surfaces in rarefied multi-component gas flows are developed using the kinetic theory of gases. The presented model provides general boundary conditions which can be simplified according to the problem under consideration. In some limiting cases, the results of the current work are compared to the previously available and widely used boundary conditions reported in the literature. The details of the mathematical procedure are also provided to give a better insight about the physical importance of each term in the slip/jump boundary conditions. Also the disagreements between previously reported results are investigated to arrive at the most proper expressions for the slip/jump boundary conditions. The temperature-jump boundary condition is also modified to handle polyatomic gas flows unlike previously reported studies which were mostly concerned with monatomic gases.

A multiscale view of nonlinear diffusion in biology: From cells to tissues

2019 ◽  
Vol 29 (04) ◽  
pp. 791-823 ◽  
Author(s):  
D. Burini ◽  
N. Chouhad
Keyword(s):  
Kinetic Theory ◽  
Nonlinear Diffusion ◽  
Stochastic Game ◽  
Broad Class ◽  
Kinetic Equations ◽  
Classical Mechanics ◽  
Theory Model ◽  
Macroscopic Models ◽  
Research Perspectives ◽  
Stochastic Game Theory

This paper presents a review on the mathematical tools for the derivation of macroscopic models in biology from the underlying description at the scale of cells as it is delivered by a kinetic theory model. The survey is followed by an overview of research perspectives. The derivation is inspired by the Hilbert’s method, known in classic kinetic theory, which is here applied to a broad class of kinetic equations modeling multicellular dynamics. The main difference between this class of equations with respect to the classical kinetic theory consists in the modeling of cell interactions which is developed by theoretical tools of stochastic game theory rather than by laws of classical mechanics. The survey is focused on the study of nonlinear diffusion and source terms.

Peristaltic flow of a Jeffery fluid over a porous conduit in the presence of variable liquid properties and convective boundary conditions

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
G. Manjunatha ◽  
C. Rajashekhar ◽  
K. V. Prasad ◽  
Hanumesh Vaidya ◽  
Saraswati
Keyword(s):  
Boundary Conditions ◽  
Frictional Force ◽  
Variable Viscosity ◽  
Pressure Rise ◽  
Velocity Slip ◽  
Peristaltic Flow ◽  
Physical Parameters ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Closed Form Solutions

The present article addresses the peristaltic flow of a Jeffery fluid over an inclined axisymmetric porous tube with varying viscosity and thermal conductivity. Velocity slip and convective boundary conditions are considered. Resulting governing equations are solved using long wavelength and small Reynolds number approximations. The closed-form solutions are obtained for velocity, streamline, pressure gradient, temperature, pressure rise, and frictional force. The MATLAB numerical simulations are utilized to compute pressure rise and frictional force. The impacts of various physical parameters in the interims for time-averaged flow rate with pressure rise and is examined. The consequences of sinusoidal, multi-sinusoidal, triangular, trapezoidal, and square waveforms on physiological parameters are analyzed and discussed through graphs. The analysis reveals that the presence of variable viscosity helps in controlling the pumping performance of the fluid.

Stochastic Particle Dynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Brownian Motion ◽  
Kinetic Theory ◽  
Stochastic Dynamics ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Central Place ◽  
Conclusive Evidence ◽  
Dense Fluids ◽  
Complementary Role ◽  
Collisional Interactions

Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical development of kinetic theory. Among others, it provided conclusive evidence in favor of the atomistic theory of matter. This chapter introduces the basic notions of stochastic dynamics and its connection with other important kinetic equations, primarily the Fokker–Planck equation, which bear a complementary role to the Boltzmann equation in the kinetic theory of dense fluids.

scholarly journals A Kinetic Theory Model of the Dynamics of Liquidity Profiles on Interbank Networks

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 363
Author(s):  
Marina Dolfin ◽  
Leone Leonida ◽  
Eleonora Muzzupappa
Keyword(s):  
Kinetic Theory ◽  
Network Formation ◽  
Transition Probabilities ◽  
Stochastic Game ◽  
Theory Model ◽  
Point Of View ◽  
Network Efficiency ◽  
Modelling Framework ◽  
Wide Range ◽  
Complex Adaptive

This paper adopts the Kinetic Theory for Active Particles (KTAP) approach to model the dynamics of liquidity profiles on a complex adaptive network system that mimic a stylized financial market. Individual incentives of investors to form or delete a link is driven, in our modelling framework, by stochastic game-type interactions modelling the phenomenology related to policy rules implemented under Basel III, and it is exogeneously and dynamically influenced by a measure of overnight interest rate. The strategic network formation dynamics that emerges from the introduced transition probabilities modelling individual incentives of investors to form or delete links, provides a wide range of measures using which networks might be considered “best” from the point of view of the overall welfare of the system. We use the time evolution of the aggregate degree of connectivity to measure the time evolving network efficiency in two different scenarios, suggesting a first analysis of the stability of the arising and evolving network structures.

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