Experimental study of the Stokes-Einstein relation by using oscillating optical tweezers and a position tracking method

Transportation and delivery of microscopic materials in very small and complex systems such as biological organisms are mainly done by physical diffusion. This phenomenon in a fluid system with a low Reynolds number can be explained using the Stokes-Einstein relation D = k B T/β , where D is the diffusion coefficient, T is the temperature of the system, and β is the viscous friction coefficient of the background fluid. For a spherical particle with radius a in a fluid of viscosity η , β = 6 πηa . As far as we know, all the experimental tests of this relation before ours measured only D, η, a , and T due to the experimental difficulties in measuring β directly. In this research, we tested this relation from a different perspective. The diffusion coefficient D and the viscous friction coefficient β were experimentally measured in the same system by using a position tracking method and an oscillating optical tweezers technique, respectively. We found that our experimental results supported the Stokes-Einstein relation very well.