Why viscosity changes the spread
Combining ideal osmotic pressure with mobility and diffusive balance relates diffusivity to temperature, viscosity and radius.
Read · Brownian motion: from wandering to a measurable law · Results
§3 · The diffusion of small suspended spheres
Particles just large enough to see under a microscope must wander, Einstein argues, and how far they wander in a given time would let us count molecules. Read the argument, and open any step it leaves out.