Anisotropic Memory Effects in Confined Colloidal Diffusion

Abstract

The motion of an optically trapped sphere constrained by the vicinity of a wall is investigated at times where hydrodynamic memory is significant. First, we quantify, in bulk, the influence of confinement arising from the trapping potential on the sphere's velocity autocorrelation function C(t). Next, we study the splitting of C(t) into C_{parallel}(t) and C_{perpendicular}(t), when the sphere is approached towards a surface. Thereby, we monitor the crossover from a slow t{-3/2} long-time tail, away from the wall, to a faster t{-5/2} decay, due to the subtle interplay between hydrodynamic backflow and wall effects. Finally, we discuss the resulting asymmetric time-dependent diffusion coefficients.

Brownian motion at short time scales

“…Hinch obtained an analytical solution of the VACF for free particles from the original Langevin analysis [74]. Clercx and Schram calculated the MSD and VACF of a Brownian particle in a harmonic potential in an incompressible liquid [75], which can be used to describe the Brownian motion of an optically trapped microsphere in a liquid directly [24,30,76].…”

“…The intermediate regime t c < t < 100t c is poorly understood. A recent experiment has measured the VACF of a Brownian particle in water at VACF< 0.35 [24,30]. A measurement of the VACF between 1 and 0.35 is required in order to better understand the hydrodynamic effects and compressibility effects of water on Brownian motion [81][82][83][84].…”

“…The instantaneous velocity of a Brownian particle trapped in a gas has been measured [21]. Recently, the velocity autocorrelation function of a Brownian particle in water was measured successfully for v(t)v(0) v 2 < 0.35 [24,30,79]. The instantaneous velocity of a Brownian particle in liquid is much more difficult to measure, and has not been measured to date.…”

“…For example, several groups reported anisotropic Brownian motion of particles near interfaces [28][29][30][31][32], and Brownian motion of anisotropic particles such as ellipsoids [33,34], nanotubes [35,36] and helical bacteria [37]. Brownian motion in nonequilibrium systems is of particular interest because it is directly related to the transport of molecules and cells in biological systems.…”

In situ viscometry by optical trapping interferometry

“…The Brownian sphere is typically positioned at a distance h Ӎ 50 m away from the glass surface to avoid any boundary effects. 14,15 The equation of motion gives the positions of the bead in the lab-trap system as the sum of its thermal fluctuations and its response to imposed oscillations in fluid velocity, x͑t͒ = x therm ͑t͒ + x resp ͑t͒. Accordingly, the resulting power spectral density P͑f͒ = ͉͗x͑f͉͒ 2 ͘ / t msr , with t msr the measurement time, splits up into two components; P͑f͒ = P therm ͑f͒ + P resp ͑f͒.…”