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The momentum transfer plays an important role in the evaluation of neutron, X-ray, and electron diffraction for the investigation of condensed matter. Laue-Bragg diffraction occurs on the atomic crystal lattice, conserves the wave energy and thus is called elastic scattering, where the wave numbers final and incident particles, and , respectively, are equal and just the direction changes by a ...
The various aspects of such equilibrium are directly connected to a specific transport: heat transfer is the system's attempt to achieve thermal equilibrium with its environment, just as mass and momentum transport move the system towards chemical and mechanical equilibrium.
heat transfer (advection–diffusion problems; total momentum transfer to molecular heat transfer) Péclet number: Pe = = mass transfer (advection–diffusion problems; total momentum transfer to diffusive mass transfer) Prandtl number: Pr
The transfer of momentum between molecules is explicitly accounted for in Revised Enskog theory, which relaxes the requirement of a gas being dilute. The viscosity equation further presupposes that there is only one type of gas molecules, and that the gas molecules are perfect elastic and hard core particles of spherical shape.
The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather by considering a probability distribution for the position and momentum of a typical particle—that is, the probability that the particle occupies a given very small region of space (mathematically the volume element) centered at ...
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity , but it can be generalized to apply to any extensive quantity .
The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies (like Reynolds analogy, Prandtl–Taylor analogy) developed to directly relate heat transfer coefficients, mass transfer coefficients and friction factors, Chilton and Colburn J-factor analogy proved to be the most accurate.
The phrase "momentum diffusion" can also refer to the diffusion of the probability for a single particle to have a particular momentum. [2] In this case, it is the probability distribution function that diffuses in momentum space, rather than the (conserved) quantity of momentum that diffuses among many particles.