According to Fick's law for short time,
M_t/M_∞ =4/h √(Dt/π)
Mt vs. square root of t is plotted and the slope is substituted in the above equation along with saturation water uptake (the other M), h is sample thickness and D is diffusion coefficient. Now the water uptake which is ratio of percentage change in weight at particular time to initial weight does not depend on size or thickness but depends on material structure, free volume, etc. But in the equation when thickness increases , diffusion coefficient increases. How does that make sense ?
Dear Muralishwara Kakunje, h is at the denominator, when it increases diffusion decreases. My Regards
why do you say that the diffusion coefficient, D, changes with the thickness (or diffusion depth) h?
The equation is not saying that... it says that the material concentration M_t changes with h, which is right
Yes, thickness and boundaries are important factors to determine diffusion coefficient.
Abdelkader BOUAZIZ No sir. h is in denominator but D is in numerator. I know by common sense that diffusion coefficient and diffusivity doesn't depend on the size but on the material morphology. But I don't understand how the equation makes sense.
Mustafa Abu Ghalia So, when thickness increases, diffusion coefficient increases ?
Giuseppe Curro Suppose two samples have same material structure with different thickness. Then Mt/square root of time is is the slope of the graph which remains same irrespective of thickness. Only saturation mass uptake will be higher for the one with larger thickness. So I substitute slope and saturation weight and thickness I get D. In that case when thickness is larger D will be larger !!! Doesn't give the right meaning.
Guys, My bad for getting the basic concept wrong. Actually Diffusion coefficient is a constant. If thickness increases, the fraction of mass of particles per saturation weight reaching the other end of the wall at any particular instant of time reduces in order to keep the diffusion coefficient constant. I was all confused because, ASTM standard to conduct water barrier testing of platics ASTM D570 says to keep the thickness constant at 3.2. I was wondering why because I have some of my samples way beyond tolerance (3.2+/- 0.3 mm). I wonder why exactly 3.2 mm !!!
Dear Muralishwara Kakunje,
It is good that you yourself adequately answered your own question.
Surprisingly, attempts have been made to give an affirmative answer to this question.
Indeed, in a purely mathematical (abstract) sense, stupidly straightforward, so one could still say about this formula. But at the same time, the physical essence of the phenomenon is emasculated.
For example, by rewriting the formula as h = 4 / (M_t/M_∞) √(Dt/π), one can come to the absurd conclusion that the thickness of the sample depends on the diffusion coefficient or time. And you can also express the number π and agree to the fact that it depends on time.
Mathematical tricks should not replace the essence of the phenomenon.
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