Sol-gel transition in a source-enhanced coagulating system

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Disperse systems evolve through particle interactions.
• Coagulation and particle sources significantly impact particle mass spectra.
• Understanding temporal changes is crucial for characterizing these systems.

Purpose of the Study:

• To exactly solve the Smoluchowski equation for specific coagulation kernels and sources.
• To investigate the time evolution of particle mass spectra in disperse systems.
• To analyze the formation and behavior of gels in these systems.

Main Methods:

• Solving the Smoluchowski equation with a coagulation kernel proportional to the product of masses.
• Analyzing systems with a constant rate source of fresh particles.
• Investigating particle mass spectra and integral characteristics under varying source productivities.

Main Results:

• A gel forms after a critical time (tc), transitioning the sol spectrum to an algebraic function.
• The particle mass spectrum exhibits universal behavior (g^-5/2) when the third moment of the source productivity is finite (gamma>4).
• For 3

Conclusions:

• The study provides an exact solution for a specific Smoluchowski equation scenario.
• Gelation dynamics and critical phenomena in disperse systems are elucidated.
• The findings offer insights into the behavior of particle mass spectra under various conditions.