My mama taught me when you find something you’ve been looking for, you put it back in the first place you looked. Hence, Google-catalyzed question necromancy.
Square centimeters per second is the compressed unit for the diffusion coefficient, convenient for transport and storage. Thrown in a vacuum and allowed to expand, the full unit for the diffusion coefficient is:
grams flux per second for each change in concentration per centimeter.
Which I don’t like, let’s talk about the inverse of D.
Change in concentration per centimeter for each gram flux per second.
Water vapor’s D in 25 C air is 0.282 cm2/s. We’re watching one square centimeter that we’re absolutely fascinated with. We’re also studying the inverse of D, so:
If the concentration here is 1 gram per milliliter and 0.282 grams of water vapor are passing through our square centimeter, then the concentration one centimeter over there is 0 grams per mL and one centimeter in the opposite direction it’s 2 grams per mL. Or rather, the instantaneous concentration on top of our square centimeter is such. Then calculus roughs up some statistical distributions, less unprofessional chemists claw their eyes out, and I don’t care.
The time unit is the temporal distance to our second reference point for measuring flux. Measuring grams per hour is a very different D from measuring grams per second.
The first length unit is the linear distance to our second reference point for measuring concentration. If the concentration here is x, then D tells us one distance unit away the concentration is y. If the distance unit is meters instead of centimeters, naturally the concentration at y will be less and D as measured to that distance unit will be different.
Take these out and the rest of the unit for the non-inverted D is g/ua per g/mL, where ua is the incredibly rare microare, as in hectare. Without the per-second to make sense of it, it’s hard to imagine what grams per microare are. So let’s be crazy and go American:
pounds per square inch for each pound per cubic inch.
PSI is an obvious unit for pressure, and as long as we’re being crazy, g/mL is a unit for density Yes, I realize that a pound of weight is not a pound of mass, especially for gases outside STP, but I don’t think it hurts at all to think of diffusion as what happens after you stop holding back the pressure a fluid of a given density exerts on a given area.
Now back to sanity. We have g/cm2 per g/cm3. Dimensional analysis cancels it out to the second length unit. What is it? A scaling factor, because cubes go up with the cube and squares go up with the square, which is an ever growing ratio.
If the concentration is 1g/cc, and I convert it to 1000000g/m3, then the polite thing to do is to convert the flux from 1g/cm2 to 10000g/m2, which changes the ratio of density to pressure 100-fold, and subsequently the value of D in these units.
If a substance with a given ratio of diffusion density to diffusion pressure is let go, what does it look like one second later, one centimeter away, given that my scaling ratio is 1 cc per cm2?