2014/12/17 by Guolong Li, Li, Guolong
Economics, Econometrics and Finance · Environmental Science · Mathematics · #Coagulation and Flocculation Studies #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1412.5645
openalex publication_date 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider two different models for colloidal particles. In the first model, we consider their free motion to be diffusion while in the second model we take it to be integrated Ornstein-Uhlenbeck process. In both models, we derived collision estimates for pairs of particles. In particular, we found that these estimates would be different to the Brownian case even when the particles' free motion is Brownian at macroscopic scales. As a consequence, the coagulation kernel and diffusivity in the coagulation-diffusion equations would also be affected accordingly. We then proved that there exists a unique solution to the coagulation-diffusion equations in these cases under physically reasonable assumptions.