The effects of hindered mobility and depletion of particles in near-wall shear flows and the implications for nanovelocimetry

Abstract

The behaviour of spherical Brownian particles in a near-wall shear flow is explored using Langevin simulations and experimental measurements, focusing on the effects of anisotropic hindered particle mobility and the formation of a particle depletion layer due to repulsive forces. The results are discussed in the context of particle velocity distributions obtained by near-wall image-based velocimetry. It is observed that the shear force and dispersion dominate at high Péclet number (Pe > 3), and the asymmetric shapes of particle velocity distributions are attributed to broken symmetry due to the presence of the wall. Furthermore, the excursions outside the observation depth between image acquisitions and the shear-induced slowdowns of tracer particles cause significant measurement bias for long and short inter-frame time intervals, respectively. Also impeding the measurement accuracy is the existence of a near-wall particle depletion layer that leads to an overestimation of the fluid velocity. An analytical protocol to infer the correct fluid velocity from biased measurements is presented.

Effect of finite sampling time on estimation of Brownian fluctuation

“…The effect also becomes more pronounced as the domain size (H) shrinks. The diffusion-induced bias just described for the near-wall diffusion coefficient has also been observed in near-wall velocimetry studies, where the asymmetric diffusion leads to a larger apparent mean velocity that increases with delay time (Sadr et al 2007;Pouya et al 2008;Huang et al 2009). …”

“…The simulation of Brownian motion using Langevin equations has been successfully demonstrated (Adamczyk, Siwek & Szyk 1995;Sholl et al 2000;Sadr, Li & Yoda 2005;Unni & Yang 2005;Huang, Guasto & Breuer 2009). The Langevin equation for a Brownian particle immersed in a fluid medium can be written as (Unni & Yang 2005):…”

“…The trajectory of each individual particle is tracked over an infinite domain (−∞ < x, y, z < ∞) using (2.1), where all the terms are updated in each time step. Following previous studies (Ermak & Mccammon 1978;Huang et al 2009), the (non-dimensional) integration time step δt is chosen as 10 −3 , which is small enough to ensure numerical accuracy and large enough compared to the particle relaxation time (≈10 −5 ), as necessary for validity of the diffusion model. For the near-wall simulations, due to the discrete and finite nature of the computational process, a particle may attempt to enter the solid wall during the integration time step even with a short time step (despite the fact that with the assumption of a no-slip boundary condition, the diffusion coefficient vanishes and particles come to rest at the surface of the solid).…”

Nanoparticle image velocimetry at topologically structured surfaces

“…For all data, there are only a few tracer particles detected with a height lower than ϳ110 nm, while the tracer particles with height higher than ϳ220 nm have intensity levels that are as low as the CCD camera's noise and are consequently eliminated in the image analysis. These data are consistent with earlier works based on experiments 20 and calculations, 29 where the nonuniform tracer distribution over the surface can be explained by the combination of electrostatic and van der Waals interactions between the particles and the wall. Note that in Fig.…”

Electrokinetic characterization of individual nanoparticles in nanofluidic channels

“…We hypothesize that two of these effects could be (1) double layer interactions and (2) particle rotation due to shear. In the latter case, shear effects can cause particles to move slower than the local fluid velocity Huang et al (2009) which effectively increases the electrophoretic mobility. In thinner double layer systems, the shear is greater, consistent with our results.…”