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The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation: = where D is the diffusion coefficient (in m 2 /s), D 0 is the maximal diffusion coefficient (at infinite temperature; in m 2 /s),
In dilute aqueous solutions the diffusion coefficients of most ions are similar and have values that at room temperature are in the range of (0.6–2) × 10 −9 m 2 /s. For biological molecules the diffusion coefficients normally range from 10 −10 to 10 −11 m 2 /s.
The self-diffusion coefficient of water has been experimentally determined with high accuracy and thus serves often as a reference value for measurements on other liquids. 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]
D is the diffusion coefficient; μ is the "mobility", or the ratio of the particle's terminal drift velocity to an applied force, μ = v d /F; k B is the Boltzmann constant; T is the absolute temperature. This equation is an early example of a fluctuation-dissipation relation. [7]
Thermal diffusion coefficients vs. temperature, for air at normal pressure The Maxwell–Stefan diffusion (or Stefan–Maxwell diffusion ) is a model for describing diffusion in multicomponent systems.
The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a nonzero second spatial derivative, the time derivative is nonzero as well. The heat equation implies that peaks ( local maxima ) of u {\displaystyle u} will be gradually eroded down, while depressions ( local minima ...
The diffusion coefficient is the coefficient in the Fick's first law = /, where J is the diffusion flux (amount of substance) per unit area per unit time, n (for ideal mixtures) is the concentration, x is the position [length].
c is the variable of interest (species concentration for mass transfer, temperature for heat transfer), D is the diffusivity (also called diffusion coefficient), such as mass diffusivity for particle motion or thermal diffusivity for heat transport, v is the velocity field that the quantity is moving with. It is a function of time and space.