The kinetic theory of fluids

The rate of a chemical reaction from the kinetic theory of fluids... 

The factors yBM and xBM cannot be justified on the basis of the kinetic theory of fluids since they are based on overall resistances. 

Volume 6 begins with two chapters on the computer simulation of molecular dynamics in fluids. The first of these chapters is concerned with fluids consisting of hard elastic particles, whereas the second of these chapters is concerned with particles that interact via a continuous pair potential. These techniques have led to a renaissance in the theory of fluids by providing an accurate picture of fluids with known force laws. The chapters on molecular dynamics are followed by two chapters on the kinetic theory of fluids. The first of the chapters covers many new topics in the kinetic theory of gases including the role of correlated collisions in producing long time-persistent effects and... 

The static properties of an isolated chain constitute a good starting point to study polymer dynamics many of the features of the chain in a quiescent fluid could be extrapolated to the kinetics theories of molecular coil deformation. As a matter of fact, it has been pointed out that the equations of chain statistics and chain dynamics are intimately related through the simplest notions of graph theory [16]. 

In the previous section, the molecular basis for the processes of momentum transfer, heat transfer and mass transfer has been discussed. It has been shown that, in a fluid in which there is a momentum gradient, a temperature gradient or a concentration gradient, the consequential momentum, heat and mass transfer processes arise as a result of the random motion of the molecules. For an ideal gas, the kinetic theory of gases is applicable and the physical properties p,/p, k/Cpp and D, which determine the transfer rates, are all seen to be proportional to the product of a molecular velocity and the mean free path of the molecules. 

In bulk diffusion, the predominant interaction of molecules is with other molecules in the fluid phase. This is the ordinary kind of diffusion, and the corresponding diffusivity is denoted as a- At low gas densities in small-diameter pores, the mean free path of molecules may become comparable to the pore diameter. Then, the predominant interaction is with the walls of the pore, and diffusion within a pore is governed by the Knudsen diffusivity, K-This diffusivity is predicted by the kinetic theory of gases to be... 

Andersen, H. C. Diagrammatic Formulation of the Kinetic Theory of Fluctuations in Equilibrium Classical Fluids. III. Cluster Analysis of the Renormalized Interactions and a Second Diagrammatic Representation of the Correlation Functions. J. Phys. Chem. B 2003, 107, 10234-10242. 

Two reasons are responsible, for the greater complexity of chemical reactions 1) atomic particles change their chemical identity during reaction and 2) rate laws are nonlinear in most cases. Can the kinetic concepts of fluids be used for the kinetics of chemical processes in solids Instead of dealing with the kinetic gas theory, we have to deal with point, defect thermodynamics and point defect motion. Transport theory has to be introduced in an analogous way as in fluid systems, but adapted to the restrictions of the crystalline state. The same is true for (homogeneous) chemical reactions in the solid state. Processes across interfaces are of great... 

The rate at which the momentum transfer takes place is dependent on the rate at which the molecules move across the fluid layers. In a gas, the molecules would move about with some average speed proportional to the square root of the absolute temperature since, in the kinetic theory of gases, we identify temperature with the mean kinetic energy of a molecule. The faster the molecules move, the more momentum they will transport. Hence we should expect the viscosity of a gas to be approximately proportional to the square root of temperature, and this expectation is corroborated fairly well by experiment. The viscosities of some typical fluids are given in Appendix A. 

The calculated vapor pressure of vanadic acid is a factor of 30 lower than the equilibrium vapor pressure of vanadic acid over pure V2O5. At this vapor pressure of vanadic acid, the transfer of V to trap is rapid while the removal of V by transpiration is negligible. Approximately 64% would be transferred from catalyst to trap, and about 0.05% removed by transpiration. This is rationalized by noting that the velocity of the vanadic acid vapor (calculated from the kinetic theory of gasesX 4.4 x 10" cm s, is four orders of magnitude higher than the superficial velocity of the fluidizing gas. Equation 3a From these calculations it is clear that mass transfer of vapor phase vanadic acid in a fluid bed is sufficient to account for the transport of vanadium from catalyst to trap. 

In micro parallel plate channel the interactions between the fluid and the wall become significant, because the molecular mean free path is comparable to 2 y 1. The gas slip along the wall with a finite velocity in the axial direction as described by Maxwell in 1890 [13]. The kinetic theory of gases gives the following boundary condition at the surface of the channel [28] ... 

For flows in conventional channels, the flow dimensions are much larger than the molecular mean free path. Therefore, fluid properties are determined primarily by intermolecular colUsions. As the channel size is reduced, the molecular mean free path becomes comparable to channel size. Intermolecular colhsions lose their importance and the interactions between the fluid and the wall become significant. The derivations of the shp flow boundary conditions using the kinetic theory of gases will be shown based on the derivations of [2] and [3] and are explained in the following manuscript in this book [4]. Briefly, the first order velocity shp is given by ... 

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