The Simplest Classical Solution for Diffusion in a Plate

Consider an initially dry plane sheet (which represents a thin flat coupon), occupying the region —/f x /, subjected to a uniform ambient fluid concentration mi at time f = 0. 

The expression (3.11) converges rapidly for large values of f, (in fact, accounting for data scatter, one term would definitely suffice for t 0.5), while (3.12) converges rapidly for small values of t (one term would definitely suffice for t 0.5). More specific details are given elsewhere (Weitsman 1981). 

Note that the non-dimensional time t varies like the square of the thickness 2/, thus so does the time-to-saturation. 

The above observation enables the early experimental evaluation of the diffusion coefficient D, as follows  

Take intermittent weight gain measurements on a flat sample of thickness 2/, at approximately equal /time intervals, up to such times when data depart from a straight line. The point of departure corresponds toD 0.557 (2/) It. 

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