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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 ...
The convection–diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. For information about the equation, its derivation, and its conceptual importance and consequences, see the main article convection–diffusion equation. This article ...
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]
is the Diffusion coefficient [2] and is the Source term. [3] A portion of the two dimensional grid used for Discretization is shown below: Graph of 2 dimensional plot. In addition to the east (E) and west (W) neighbors, a general grid node P, now also has north (N) and south (S) neighbors.
The self-diffusion coefficient of neat water is: 2.299·10 −9 m 2 ·s −1 at 25 °C and 1.261·10 −9 m 2 ·s −1 at 4 °C. [2] Chemical diffusion occurs in a presence of concentration (or chemical potential) gradient and it results in net transport of mass. This is the process described by the diffusion equation.
If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear. The equation above applies when the diffusion coefficient is isotropic; in the case of anisotropic diffusion, D is a symmetric positive definite matrix, and the equation is written (for three dimensional diffusion) as:
Observing the previous equation, a trivial solution is found for the case dc/dξ = 0, that is when concentration is constant over ξ.This can be interpreted as the rate of advancement of a concentration front being proportional to the square root of time (), or, equivalently, to the time necessary for a concentration front to arrive at a certain position being proportional to the square of the ...
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.