Brownian motion can be see in starch grains that are approx 1micrometre in diameter.

What is the maximum size of particle before they can no longer exhibit Brownian Motion?

Platelets are 2 micrometres in diameter and are only marginally more dense than plasma. There are studies of the effects of Brownian Motion in flowing  fluids to mimic its effect in vivo, but I cannot find any reference to it being studied in plasma at rest. 

Has anybody seen any studies of Brownian Motion in Platelets at rest in non-flowing plasma? 

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