Singular self-preserving regimes of coagulation processes

Area of Science:

• Physical Chemistry
• Chemical Engineering
• Statistical Mechanics

Background:

• Disperse systems evolve over time due to processes like coagulation and condensation.
• Understanding the late-stage evolution of particle mass spectra is crucial for various applications.

Purpose of the Study:

• To investigate the asymptotic behavior of particle mass distributions in disperse systems.
• To analyze systems with coagulation alone, source-enhanced coagulation, and simultaneous coagulation-condensation.
• To determine universal scaling functions and their exponents.

Main Methods:

• Application of the renormalization-group approach.
• Analysis of systems with homogeneous condensation efficiencies and coagulation kernels.
• Derivation of asymptotic particle mass distributions of the form N(A)(g,t)=A(t)psi(gB(t)).

Main Results:

• Identified universal scaling functions psi(x) describing particle growth in three types of systems.
• Found that time-dependent functions A(t) and B(t) are power functions of time.
• Exponents of A(t) and B(t) are functions of homogeneity exponents lambda and gamma.
• Demonstrated that particle mass distributions can be singular (psi(x) ~ x(-sigma)) at small masses.

Conclusions:

• The asymptotic behavior of particle mass distributions in diverse coagulating and condensing systems can be described by universal scaling functions.
• The derived exponents sigma, lambda, and gamma provide insights into the dynamics of particle growth.
• The study offers a theoretical framework illustrated by exactly soluble models.