Brownian motion in a Maxwell fluid

Abstract

The equilibrium dynamics of a spherical particle immersed in a complex Maxwell fluid is analyzed in terms of velocity autocorrelation function (VACF), mean-square displacement (MSD), and power spectral density (PSD). We elucidate the role of hydrodynamic memory and its interplay with medium viscoelasticity for a free and a harmonically confined particle. The elastic response at high frequencies introduces oscillations in the VACF, which are found to be strongly damped by the coupling to the fluid. We show that in all Maxwell fluids hydrodynamic memory eventually leads to a power-law decay in the VACF as is already known for Newtonian fluids. The MSD displays asymptotically an intermediate plateau reflecting the elastic restoring forces of the medium. In the frequency domain, the PSD exhibits at high frequencies a step due to the trapping, whereas the low-frequency decay reflects the viscoelastic relaxation. Our results suggest that high-frequency microrheology is well-suited to infer the elastic modulus, which is sensitive over a wide range of Maxwell times.

Effect of Magnetic Field on the Fluctuations of Charged Oscillators in Viscoelastic Fluids

“…In the present work an exact analytical solution of the generalized Langevin equation (LE) has been found for the motion of the particle trapped in a harmonic potential well and exposed to a constant magnetic eld in the case when the thermal force is exponentially correlated in the time. This model is consistent with the assumption that the solvent has weakly viscoelastic properties, which corresponds to the theory, originally proposed by Maxwell and later substantiated coming from rst principles [5,6]. The calculated time correlation functions describing the particle motion are more general than the previous results from the literature and are obtained in a way applicable to many other problems of the Brownian motion with memory.…”

Determination of viscoelastic properties by analysis of probe-particle motion in molecular simulations

“…The second term is the Basset force [24], arising from medium inertia, which is a frictional force from the radiational dissipation of particle energy by elastic waves [17,25]. The third term is the effective inertial force of the particle.…”

Brownian motion at short time scales

“…The ability to measure the instantaneous velocity of a Brownian particle will be invaluable in studying nonequilibrium statistical mechanics [85,86]. The Brownian motion of a suspended particle can be used for microrheology to probe the properties of fluids, such as viscoelastic fluids [87][88][89], and surrounding environments [90][91][92]. He recently developed general methods to control the motion of atoms and molecules, and studied Brownian motion with unprecedented precision.…”