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Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
Specifically, Matano proved that the diffusion rate of A atoms into a B-atom crystal lattice is a function of the amount of A atoms already in the B lattice. The importance of the classic Boltzmann–Matano method consists in the ability to extract diffusivities from concentration–distance data.
A model of grain boundary diffusion developed by JC Fisher in 1953. This solution can then be modeled via a modified differential solution to Fick's Second Law that adds a term for sideflow out of the boundary, given by the equation + (,) = ′, where ′ is the diffusion coefficient, is the boundary width, and (,) is the rate of sideflow.
Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles.
The higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other. Typically, a compound's diffusion coefficient is ~10,000× as great in air as in water. Carbon dioxide in air has a diffusion coefficient of 16 mm 2 /s, and in water its diffusion coefficient is 0.0016 mm 2 /s. [1] [2]
Usually, convection occurs as a result of the diffusion process. The rate at which diffusion occurs depends on the state of the molecules: it occurs at a high rate in gases, a slower rate in liquids, and an even slower rate in solids. In gases, molecular diffusion is dependent on pressure and temperature. The higher the pressure, the slower the ...
The Marangoni number (Ma) is, as usually defined, the dimensionless number that compares the rate of transport due to Marangoni flows, with the rate of transport of diffusion. The Marangoni effect is flow of a liquid due to gradients in the surface tension of the liquid. Diffusion is of whatever is creating the gradient in the surface tension.
The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the total mass transfer rate (convection + diffusion) to the rate of diffusive mass transport, [1] and is named in honor of Thomas Kilgore Sherwood.