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

Area of Science:

• Physical Chemistry
• Colloid Science
• Statistical Mechanics

Background:

• Coagulation processes are fundamental in various physical and chemical systems.
• Understanding particle size evolution is crucial for predicting system behavior.
• Existing models often require simplifying assumptions for arbitrary initial conditions.

Purpose of the Study:

• To investigate the time evolution of coagulating particle systems with a product kernel.
• To derive an exact analytical solution for the system's mass spectrum probability.
• To obtain a general expression for the average number of particles of a given size over time.

Main Methods:

• Utilized the improved Marcus-Lushnikov approach.
• Solved the master equation for the probability distribution W(Q,t).
• Derived an exact expression for the average particle number .

Main Results:

• An exact expression for the probability W(Q,t) of a given mass spectrum Q was obtained.
• The average number of particles of size g at time t was derived.
• The derived formula was validated through numerical simulations.

Conclusions:

• The improved Marcus-Lushnikov approach provides an accurate method for studying coagulating systems.
• The derived analytical solution offers a powerful tool for predicting particle size distributions.
• The findings are applicable to systems with diverse initial particle configurations.