Free and confined Brownian motion in viscoelastic Stokes-Oldroyd B fluids

We linearize the Stokes-Oldroyd B model for small perturbations and instantaneous hydrodynamic friction to simulate the environment for a free and confined Brownian particle. We use the standard Green's function approach to determine the viscoelasticity, and show that the expression obtained for the frequency dependent viscosity is similar to that given by the Jeffrey's model, though the latter describes viscoelasticity by the bulk storage and loss moduli that is represented by a complex elastic modulus [Formula: see text] of the fluid concerned. In contrast, we consider the characteristics of the polymer chains and the Newtonian solvent of the complex fluid individually, and determine an expression for frequency-dependent viscosity that would be useful for microrheology performed from Brownian trajectories measured in experiments. Finally, we evaluate the trajectory of a free Brownian particle in a viscoelastic environment using our formalism, and calculate various important parameters quantifying Brownian dynamics, which we then extend to the particle confined in a harmonic potential as provided by optical tweezers.