A thermo-diffusion system with Smoluchowski interactions: well-posedness   and homogenization
  We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients. 
Oleh Krehel and Adrian Muntean and Toyohiko Aiki
math.AP