Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework.
basic_science · Level V
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- Record sourced from PubMed, PMID 30780314.
- Also identified by DOI 10.1103/PhysRevE.99.012104.
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Abstract
The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability W(Q,t) to find the system in a given mass spectrum Q={n_{1},n_{2},⋯,n_{g}⋯}, with n_{g} being the number of particles of size g. The exact expression for the average number of particles 〈n_{g}(t)〉 at arbitrary time t is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.