# Collision rates between two molecules in a liquid

How would I calculate the collision rate between kaolinite and amylopectin particles in a liquid with a density of ($\pu{1.01g/m^3}$) and a viscosity of ($\pu{0.000434 Pa s}$)? I know this is related to orthokinetic flocculation, however, I do not know the exact equation. If anyone knows the equation, can you please inform me of it?

• Your particles are a good deal bigger than molecules. – Ivan Neretin May 10 '18 at 11:56

If you assume that the reaction is diffusion controlled then this is the fastest that a bimolecular solution phase reaction can be and the second order rate constant is $k=8000RT/(3\eta)$ (dm$^3$/mol/s) where $\eta$ is the solution viscosity and assuming that the molecules are approximately the same size and even if they are not its still a good estimation. In mobile solvents (hexane, water etc) $k\approx 10^{10} \to 10^{11}$ dm$^3$/mol/s.
If the species a, b are ions (charge $Z_{a,b}$) then the rate constant is multiplied by $\delta/(e^{\delta}-1)$ where $\displaystyle \delta = \frac{Z_aZ_bq^2}{(4\pi\epsilon_0)\epsilon k_BTd_{ab}}$ where $d_{ab}$ is the centre to centre molecules size, $q$ electronic charge, $k_B$ the Boltzmann constant, $\epsilon$ the solvent dielectric constant and $\epsilon_0$ the permittivity of free space.
[If the species are not the same size radius $r$ then $\displaystyle k= \frac{2000RT}{\eta}\frac{(r_a+r_b)^2}{r_ar_b}$. ]