6.021/Notes/2006-09-08
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Diffusion
- Most fundamental transport process and the one we understand the best
- Process by which solute is transported from regions of high concentration to low concentration
- Graham made some observations related to diffusion
- Quantity transported is proportional to the initial concentration
- Transport rate slows with time
- Transport of gas is greater than 1000x faster than liquids
Definitions
- Concentration:
- But matter isn't discrete, so limit doesn't make sense
- Practically, cells have about NaCl which is about
- Cells are greater than 1μm^{3} so there are many molecules in a typical cell
- Thus, we'll assume matter is continuous to simplify the math
- Flux:
Fick's First Law
- Adolf Fick (1855) at age 25, came up with Fick's first law by analogy to Fourier's law for heat flow
- We define flux to be positive in same direction as increasing x
- Diffusivitiy units:
- This is a macroscopic law
Microscopic basis for diffusion
- 1828: Robert Brown (Brownian motion)
- Even dead things moved
- Albert Einstein with random walk model
- Assumptions
- Number of solute much less than number of solvent
- Only collisions between solute and solvent
- Focus on 1 solute molecule and assume others are statistically identical
- Every τ seconds, molecule equally likely to move + l and − l
- l = 2pm for small molecule (really small length scale)
- From random walk model, easy to derive Fick's first law
- Assumptions
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