UVA PHYS 3040 - Diffusive processes and Brownian motion (8 pages)

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Diffusive processes and Brownian motion



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Diffusive processes and Brownian motion

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Pages:
8
School:
University Of Virginia
Course:
Phys 3040 - Physics of the Human Body

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Physics of the Human Body Chapter 7 Diffusive processes and Brownian motion 65 Diffusive processes and Brownian motion A liquid or gas consists of particles atoms or molecules that are free to move We shall consider a subset of particles such as a dissolved solute or a suspension characterized by a number density N n x y z t V 1 that in general depends on position and time The flux of particles across a plane perpendicular to the x axis1 is the number density times the mean velocity in that direction df jx n vx 2 If the particles are moving randomly then it is clear that the number that cross the plane moving in the negative x direction must be proportional to the density immediately to the right of the plane say at position x x 2 conversely those moving to the right must be proportional to the density just to the left of the plane say at x x 2 so the flux will be jx x D n x x 2 n x x 2 D n x x That is the equation jx D n x defines the diffusion constant D 1 2 3 4 Since there is nothing special about the x direction2 we can express the flux of particles resulting from diffusion as3 j D n However if the particles are neither created nor destroyed they must obey a conservation law4 n j 0 t 4 hence by substituting the flux resulting from diffusion into the conservation equation we obtain the diffusion equation n D 2n t 5 Many physical phenomena are described by equations of this form including heat conduction in a solid transport of radiation through a dense atmosphere and movement of neutrons through fissionable material or shielding for that matter Since the underlying physical behavior that the diffusion equation models is the same in these examples it is not surprising they can be described by the same equation 1 3 3 Random walk model of diffusion To get a feeling for the physical meaning of diffusion we shall now examine several different ways to describe this phenomenon A diffusing particle is subjected to a variety of collisions that we can consider random in



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