Knudsen Diffusivity

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Sep 26, 2022, 1:51:04 PM

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Aug 15, 2016, 12:05:16 PM

D_{K A} = \frac{d_{pore}}{3} \sqrt{\frac{8 \cdot R_{g} \cdot T}{π \cdot M_{A}}}

$D_(KA) = d_"pore" /3sqrt((8*R_g* T )/(pi* M_A ))$

(d_{pore}) pore diameter

$(d_"pore")"pore diameter"$

(T) temperature

$(T)"temperature"$

(M_{A}) molecular mass

$(M_A)"molecular mass"$

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The Knudsen Diffusivity is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved. An example of this is in a long pore with a narrow diameter (2-50nm) because molecules frequently collide with the pore wall.
Consider the diffusion of gas molecules through very small capillary pores. If the pore diameter is smaller than the mean free path of the diffusing gas molecules and the density of the gas is low, the gas molecules collide with the pore walls more frequently than with each other.
The following equation is used: $D_{K A} = \frac{d_{pore}}{3} \sqrt{\frac{8 R_{g} T}{π M_{A}}}$ $D_(KA)=d_"pore"/3sqrt((8R_gT)/(piM_A))$ , where:

$d_{pore}$ $d_"pore"$ = pore diameter
$R_{g}$ $R_g$ = gas constant
$T$ $T$ = temperature
$M_{A}$ $M_A$ = molecular mass

References

Wikipedia (https://en.wikipedia.org/wiki/Knudsen_diffusion)

This equation, Knudsen Diffusivity, references 1 page

Equations and Data Items

• R - Gas Constant (SI units) by MichaelBartmess

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