Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework

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 $Q=\{n_1,n_2,\dots ,n_g\dots \}$, 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.

10 pages, 3 figures. Original work. Figures changed from png to eps in this update

References in corpus (5)

• Statistical Thermodynamics of Irreversible Aggregation and Gelation
• Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases
• Statistical Thermodynamics of Clustered Populations
• The microscopic meaning of grand potential resulting from combinatorial approach to a general system of particles
• Exact combinatorial approach to finite coagulating systems

Cited by in corpus (3)

• Rate equation limit for a combinatorial solution of a stochastic aggregation model
• Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: A study within combinatorial framework
• Combinatorial solutions to generalized electrorheological kernel aggregation