Mesoscopic models of nucleation and growth processes: a challenge to experiment

In this paper we formulate and analyse several models of generalised nuclea tion and growth processes which include primary and secondary nucleation in the presence of inhibitors, at various levels of coarse-graining from micr oscopic, through mesoscopic to macroscopic. The mesoscopic models are based on ones derived in an earlier paper (J. A. D. Wattis and P. V. Coveney, J. Chem. Phys., 1997, 106, 9122), but until now none of their physicochemical properties have been studied. Our analysis, which makes extensive use of m atched asymptotic expansions, shows the dependence of the induction time on the cluster size for which the strongest inhibition and/or secondary nucle ation occurs. One potential application of the model is to barium sulfate n ucleation and crystal growth, of relevance inter alia to scale formation in oil wells and reservoirs.