Can anyone tell me where to begin?
How do I find the expression for steady state flux and steady state concentration for example?
What assumed knowledge is implicit in the question?
What common mathematical facts are relevant?
Question.
(4.) Consider a substance diffusing in one dimension with diffusivity $D$ from $x=0$ where the concentration is maintained at $c(0,t)=c_0$ to $x=L$ where the concentration is maintained at $c(L,t) = 0$ (i.e., the substance is removed as soon as it gets to $x = L$).
(a) Find an expression for the steady state flux and the steady state concentration.
(b) Find an expression for the total amount of substance $m$ in the region $(0,L)$ in steady state.
(c) The average transit time $\tau$ from $x=0$ to $x=L$ can be estimated as the time for the total amount $m$ to leave the region given the flux $q$ for the amount that leaves per unit time, i.e., $\tau = m/q$. Show how this estimate of $\tau$ relates to the mean square displacement.
(d) A typical neurotransmitter has a diffusivity $\approx 10^{-6} \mathrm{cm}^2 \mathrm{s}^{-1}$. How long does it take the neurotransmitter to diffuse across a synaptic junction that is about $0.02$ micron. How does this synaptic time delay compare with the typical speed of a neutron pulse ($\approx 27 \mathrm{m}\mathrm{s}^{-1}$).
(e) NEW UNANSWERED QUESTION: The concise edition of the Encyclopedia Britannica http://concise.britannica.com/ebc/article-9030421/diffusion [sic] defines diffusion as the "process resulting from random motion of molecules by which there is a net flow of matter from a region of high concentration to a region of low concentration. A familiar example is the perfume of a molecule that quickly permeates the still air of a room. A typical perfume molecule has a diffusivity of $\approx 10^{-5} m^2 s^{-1}$. How long would it take a typical perfume molecule to diffuse across the still air of a room that is $\approx 10m$ across?
To be helpful, please explain the solution thoroughly in a way that a beginner can follow.