Inverse problems of agglomeration kinetics: II. Binary clustering coefficients from self-preserving spectra

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An inverse problem is formulated to estimate bivariate kinetic coefficients for irreversible aggregation processes from measurements of transient size spectra. The approach is applicable in situations where the transient spectra exhibit similarity behavior. No assumptions regarding the physical nature of the agglomeration process or any properties of the coagulation kernel are made. The formulation is a generalization of our earlier one for homogeneous agglomeration frequencies. In view of the fact that the inverse problem is ill-posed, regularization techniques are employed to facilitate inversion. Numerical examples for homogeneous as well as nonhomogeneous agglomeration kernels are presented to illustrate the methodology. The results indicate that accurate data can yield good estimates of the frequency. It is thus shown that self-preserving spectra can be used effectively to estimate the binary clustering coefficients in situations where they are unknown.