On modelling the formation of micelles in the presence of a slow influx of monomer

Experiments by Bachmann, Luisi and Lang (Nature 357 (1992) 57-59) have shown how sodium caprylate monomers can combine to form cell-like structures known as micelles. The kinetics of this process lead to a long induction period before significant numbers of micelles are formed-a clock reaction. We study a mathematical model for the kinetics of this process during the induction period. For a sufficiently slow influx of monomer, we can construct a quasi-equilibrium asymptotic solution, which is appropriate for the experimental parameter values. This predicts a long induction period, and allows us to provide a simple explanation for its existence. However, we find that there is a severe restriction on the size of the small dimensionless parameter mu that characterizes the rate of influx of monomer, which requires that mu much less than 10(-10) for the asymptotic solution to be valid. For influxes of monomer faster than this critical rate, no straightforward asymptotic solution is available. Numerical solutions show that in this case the model predicts the formation of unusually large micelles.