Methods: The theoretical model was built upon four approximations. 1/ After a short time, the acid concentration at the solid-liquid interface was constant and equal to the reservoir concentration. 2/ The process of dissolution was localised at the plane that formed this interface (with Ci the dissolved product concentration at that plane). 3/ The ionisation of HAP was ignored so that there was only one species diffusing (dissolved HAP) with diffusion coefficient Dp. 4/ The concentration of dissolved HAP inside the reservoir was zero at all times. In a previous experimental model system, rates of dissolution of HAP pellets were measured by photon-counting scanning microradiography.
Results: For steady state conditions, the rate of dissolution R=K(Cs-Ci), where K is the dissolution rate constant and Cs the solubility of HAP, was equated to the flux of dissolved HAP diffusing out of the aqueous column to the reservoir, F=CiDp/l. The derived equation, R=CsDp/(l+ Dp/K), was consistent with experimental results. Values for Dp and K, obtained by curve fitting of the experimental data, with l varying from 0 to 9 mm, were Dp=2.8 10-6 cm2 s-1 and K=7.5 10-6 cm s-1.
Conclusion: We have formulated a quantitative general model that explains the variation in rate of demineralisation of an HAP aggregate as a function of parameters linked to the transport of dissolved HAP in the external liquid.
Research supported by the Medical Research Council Grant: G9824467.
Web address: http://www.mds.qmw.ac.uk/dental/bip/