I am trying to study diffusion and Brownian motion, I found that diffusion is the macroscopic version of Brownian motion and also that if particle in a fluid medium is really small then the force excreted by the random motion of molecules will be unequal in some dimensions leading to net force and net motion. My question is related to this concept: Do we have a formula or quantitative analysis to tell that particle of 'this' size in terms of molecules' size of fluid media or Diffusion coefficient, or some other quantities, can undergo Brownian motion but not larger than that? Please also include your references.
The colloidal particels of a colloidal solution when viewed through a ultramicroscope show a constant zig-zag motion known as Brownian movement.
$Size\space of\space colloidal\space particles :1nm - 100nm$
Brownian movement is a characteristic property of colloidal particles. This motion is independent of the nature of the colloid but depends in the size of particles and the viscosity of the solution. Smaller the size and lesser the viscosity, faster the motion. The motion becomes intense at higher temperature.
The Brownian movement is due to the unbalanced bombardment of the particles by the molecules of the dispersion medium. As the size of particles increases, the probability of uneven bombardment decreases and the Brownian movement becomes slow. (Here particles refer to colloidal particles)
The Brownian movement has a string effect which does not permit the particles to settle and thus, is responsible for the stability of sols.