unit m. is the relative diffusion constant between A and B, unit m2/s, and . and are the number concentrations of molecules A and B in the solution respectively, unit #molecule/m3. or where: is in unit mole collisions/s in 1 L of solution. is the Avogadro's number. is the relative diffusion constant between A and B, unit m2/s. and are the molar concentration of A and B respectively, unit mol/L. is the diffusive collision rate constant, unit L mol-1 s-1. There have been a lot of extensions and modifications to the Smoluchowski model since it was proposed in 1916. In 2022, Chen rationales that because the diffusive flux is evolving over time and the distance between the molecules has a finite value at a given concentration, there should be a critical time to cut off the evolution of the flux that will give a value much larger than the infinite solution Smoluchowski has proposed. So he proposes to use the average time for two molecules to switch places in the solution as the critical cut-off time, i.e., first neighbor visiting time, although an alternative time could be the mean free path time or the average first passenger time. This hypothesis yields a fractal reaction kinetic rate equation of diffusive collision in a diluted solution: where: is in unit mole collisions/s in 1 L of solution. is the Avogadro's number. is the area of the collision cross-section in unit m2. is the product of the unitless fractions of reactive surface area on A and B. is the relative diffusion constant between A and B, unit m2/s. and are the molar concentration of A and B respectively, unit mol/L. is the diffusive collision rate constant, unit L4/3 mol-4/3 s-1. See also Two-dimensional gas Rate equation References External links Introduction to Collision Theory Chemical kinetics