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Diffusion Equation for Concentration Spikes of Salt

## Solution to the Diffusion Equation

Consider two simultaneously deposited concentration spikes of salt (i.e. D=10-9m2s-1), each of mass M located at x = 3m and x = 7m along a narrow conduit.=(note: questions b, e, and f are optional. If you have nothing better to do, and/oryou want to challenge yourself, try them)

a. What is the solution to the diffusion equation for this scenario, i.e. what isC(x,t)?

b. Show that the expression C(x,t) you wrote for part a) satisfies the diffusionequation.

c. Write an expression for the concentration at x = 5 m.

d. Plot the concentration (either by hand or using a computer) as a functionof time at x = 5 m.

e. Determine analytically when the maximum concentration occurs at x = 5

m. Indicate this point on your plot.

f. What is C/x at x = 5 m for all time? What are the implications of this interms of Fick’s law?