Solution (source code)

= Solution

Use a \b[<single-pass flow-through leach test>]. A controlled leachant passes once over a known <glass> <surface area>, and successive effluent samples are analysed after the initial transient. <temperature> and <pH> are controlled, and fresh solution removes dissolved products so that they do not accumulate towards saturation with respect to the dissolving <glass>. This approaches the <forward glass dissolution rate> at those specified conditions.

At steady state, with $Q$ expressed as volume per time,
$$
\boxed{r_e=\frac{Q(c_{e,\rm out}-c_{e,\rm in})}{f_eS}}.
$$
Increase $Q/S$ across a series of tests until the normalised rate becomes independent of further dilution, within analytical uncertainty. A genuine plateau supports approach to the dilute-solution limit; it should not be assumed from one arbitrarily chosen flow rate. Check blanks, inlet <concentrations>, <temperature>, <pH>, actual flow, fines and exposed <surface area>. At high flow the <concentration> increment becomes small, so an uncorrected background can manufacture an apparent rate increase.

The resulting \b[maximum is the forward rate for the specified <temperature>, <pH> and <glass>], not an absolute maximum over every possible environment. It also differs from the lower residual rate that can develop in a static, product-rich leachate. Primary measurements demonstrate the method and the importance of background subtraction and flow variation.<Measurement of kinetic rate law parameters on a Na-Ca-Al borosilicate glass for low-activity waste by B. P. McGrail and others>[1997, experimental method and abstract, including the nonphysical flow-rate increase caused by inadequate background subtraction]{ref}