Fick's Second Law and non-steady state diffusion

When the rate of flux via diffusion is changing with time then we need to rely on non-steady state diffusion solutions. One of these relies on the error function and allows us to calculate concentration as a function of position and time if we know the surface and initial concentration, and diffusion coefficient. This relies on the semi-infinite constant surface assumption.

[@sjpbrooklyn7699]

Your lucid explanation, oddly enough, stirred up some nostalgic memories. In 1966 or 1967 as a doctoral student at NYU I took a physical chemistry lab course taught by Paul Delahay, whose main research area was double-layer electrode kinetics. Computers of that era filled entire rooms and their use in bench chemistry was limited. Delahay insisted that programming would become as indispensable a skill as knowledge of thermodynamics, and gave us an assignment to solve Fick's Second Law with certain boundary conditions. We had about a month to (a) learn FORTRAN, and (b) figure out a suitable algorithm from one of Anthony Ralston's books on numerical analysis. We also had to present our results graphically as a function of x and t, which we did on 132-column fan-folded computer output paper.

[@TaylorSparks]

Oh man. People who did science / r&d before computers are like superheroes to me.

[@cliffordwilliams9597]

Thank you for this, it has helped me understand an article much better.

[@selenium.34]

You are a lifesaver. It really helped me to understand the concept. Maybe it would be better if I had listened to the professor in class.

[@TaylorSparks]

Lol. Happy to help and listening in class definitely helps ;)

[@wendyw9300]

it's so clear! Thank you so much!!!

[@rishabhmudgal5989]

Sir u r life savor ❤️

[@ofirmalka6528]

thank you it help me understend!

[@troykechely1141]

I've been struggling on how to apply this to a problem I'm working on involving the expansion of gas at a fixed rate at a point on the ground (so shape of expansion is hemisphere) and the gas radiating out from the source. What I need to calculate is how far from the source is the gas cloud at a specific concentration level. I know the molecular properties of the gas, the rate that it is emanating from the source, and the diffusion coefficient. This is all at room temp and 1 atm.

[@sjpbrooklyn7699]

I'm going to assume that you solved your problem last year and so will take this time-worn story with good humor. A retiring physical chemistry professor was setting his last exam for a graduate course in statistical thermodynamics. Being a bit bored with it all, he gave an exam with just one question: Is Hell exothermic (gives off heat) or endothermic (absorbs heat)? Most students wrote proofs based on Boyle's Law (gas cools when it expands and heats when it is compressed) or some variant. One student, however, wrote the following: First, we need to know how the mass of Hell is changing in time. So we need to know the rate at which souls are moving into Hell and the rate at which they are leaving. I think that we can safely assume that once a soul gets to Hell, it will not leave. Therefore, no souls are leaving. As for how many souls are entering Hell, let's look at the different religions that exist in the world today. Most of these religions state that if you are not a member of their religion, you will go to Hell. Since there is more than one of these religions and since people do not belong to more than one religion, we can project that all souls go to Hell. With birth and death rates as they are, we can expect the number of souls in Hell to increase exponentially. Now, we look at the rate of change of the volume in Hell because Boyle's Law states that in order for the temperature and pressure in Hell to stay the same, the volume of Hell has to expand proportionately as souls are added. This gives two possibilities: 1) If Hell is expanding at a slower rate than the rate at which souls enter Hell, then the temperature and pressure in Hell will increase until all Hell breaks loose. 2) If Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure will drop until Hell freezes over. So which is it? If we accept the postulate given to me by Teresa during my Freshman year that, "...it will be a cold day in Hell before I sleep with you," and take into account the fact that I still have not succeeded in going to bed with her, then #2 above cannot be true. I conclude that Hell will not freeze over and therefore is exothermic." This student received the only A.

[@eliassaf9192]

Is the Diffusivity coefficient D the same for steady state and non-steady state diffusion?

[@TaylorSparks]

Yes

[@eliassaf9192]

@@TaylorSparks And is the diffusion coefficient in the Einstein-Stokes relationship equal to the one here? Assuming the former is the diffusion of a material in another.