= Solution
Let $c_e$ be the measured mass <concentration> of element $e$, $c_{e,b}$ its blank <concentration>, $V$ the leachate volume, $f_e$ the element's <mass fraction> in the original <glass>, and $S$ the exposed <glass> <surface area>. For one closed test, the <normalised elemental release> is
$$
\boxed{NL_e=\frac{(c_e-c_{e,b})V}{f_eS}}.
$$
If <concentration> is in $\mathrm{g\,L^{-1}}$, volume in litres and area in square metres, $NL_e$ is in \b[$\mathrm{g\,m^{-2}}$ of glass-equivalent release]. Dividing by $f_e$ removes the trivial difference caused by loading different amounts of the measured element; dividing by $S$ removes the first-order geometrical scale difference. Normalising only by initial element content or reporting raw solution <concentration> does not accomplish both corrections.
For repeated sampling with leachant replacement, use cumulative released mass: add the mass removed in all earlier aliquots to the mass present in the final remaining solution, with the corresponding blank correction. A flow-through experiment instead integrates $Q(t)[c_{e,\rm out}(t)-c_{e,\rm in}(t)]$ over time. State how <surface area> was determined and whether it is held at its initial value in the reported normalisation; cracks, fines and alteration can change the genuinely reactive area.
Compare $NL_e(t)$ for several constituents. In <congruent glass dissolution>, the different element-normalised curves coincide, provided the released elements remain in solution. Preferential early alkali release can indicate <ion exchange>, whereas lower dissolved <silicon> or <actinide> release can reflect an alteration layer, sorption or secondary-phase <precipitation (chemistry)>. <boron> is often useful as a relatively mobile dissolution tracer, but not if the leachant contains a large <boron> background or if it is itself retained. A low aqueous <concentration> of one constituent is therefore \b[not automatically a low glass-dissolution rate].
A near-linear $NL_e(t)$ interval gives an approximately constant <normalised elemental release> rate. A square-root time dependence can be consistent with diffusion-limited transport, and decreasing slopes can indicate saturation or a protective alteration layer; no one curve shape proves a unique mechanism. Compare solution inventories with the altered solid by <microscopy>, composition and phase analysis. Differences in <pH>, <temperature>, leachant composition, duration and surface-area-to-volume ratio remain even after this mass-and-area normalisation. Careful background subtraction and control of solution conditions are experimentally consequential, as demonstrated in primary flow-through measurements.<Measurement of kinetic rate law parameters on a Na-Ca-Al borosilicate glass for low-activity waste by B. P. McGrail and others>[Journal of Nuclear Materials 249, 175–189; abstract on duration, background subtraction and solution-condition dependence]{ref}
Back to article page
