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I am creating a basic simulation of 2-D diffusion and was wondering how diffusion velocity of a particle can be calculated if the diffusion coefficient is known (using no other information). Is this possible?

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  • $\begingroup$ The units of the diffusion coefficient are m$^2$/s, so from that alone I don't believe you can determine a characteristic velocity. You'd need a characteristic length scale or characteristic time scale in addition. $\endgroup$ – Kyle Kanos Jan 3 '15 at 20:53
  • $\begingroup$ @KyleKanos What sort of length or time scale do you mean? I am planning to use a timestep of 1 second, but multiplying the timestep by the diffusion coefficient simply gives me units of m^2. $\endgroup$ – NewDogOldTricks Jan 3 '15 at 21:12
  • $\begingroup$ See, for example, this Wiki entry or this Math.SE Q&A on the length scale. The timescale is similar in concept. $\endgroup$ – Kyle Kanos Jan 3 '15 at 21:21
  • $\begingroup$ @KyleKanos That makes sense, thank you! So is it correct to say that since $$<x^2> = Dqt$$ I can say that velocity is essentially $$\frac{D*q}{characteristic length}$$ where $$q=4$$ because I am examining two-dimensional diffusion? It seems to me that a characteristic length/time scale is basically a length or time that, if it had units, would allow the final answer to have physically correct units. $\endgroup$ – NewDogOldTricks Jan 3 '15 at 21:28
  • $\begingroup$ Yes, $u_0=D_0/\ell_0$. The factor of $q$ could be absorbed into $D_0$. The characteristic scales are just useful values to non-dimensionalize your problem. $\endgroup$ – Kyle Kanos Jan 3 '15 at 21:32

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