A Becker-Doring model of competitive nucleation

We introduce a modified Becker-Doring system of equations which models the nucleation of two types of cluster from the same monomer. This competitive nucleation system is then studied in the coagulation-dominated asymptotic r egime where a succession of timescales is identified through which the syst em passes, and in which the cluster distribution profile is described. The system is then subjected to a coarse-grain rescaling leading to a low-dimen sional system of equations for macroscopically observable quantities. This system is also solved in the coagulation-dominated regime. Examples of the full system and the reduced system are solved numerically to show the simil arities in the behaviour exhibited by their respective solutions. This stud y has applications to experiments involving crystallization where various m orphologies of growing crystals are observed, and to protein crystallizatio n, where gels and/or amorphous material precipitate out of solution simulta neously with crystals. We highlight how some aspects of observed phenomena may be determined by the kinetics of the process rather than by the relativ e thermodynamical stability of the two cluster types allowed within the sys tem.