Effect of finite sampling time on estimation of Brownian fluctuation

Abstract

We present a study of the effect of finite detector integration/exposure time E, in relation to interrogation time interval t, on analysis of Brownian motion of small particles using numerical simulation of the Langevin equation for both free diffusion and hindered diffusion near a solid wall. The simulation result for free diffusion recovers the known scaling law for the dependence of estimated diffusion coefficient on E/ t, i.e. for 0 E/ t 1 the estimated diffusion coefficient scales linearly as 1 − (E/ t)/3. Extending the analysis to the parameter range E/ t 1, we find a new nonlinear scaling behaviour given by (E/ t) −1 [1 − ((E/ t) −1 )/3], for which we also provide an exact analytical solution. The simulation of near-wall diffusion shows that hindered diffusion of particles parallel to a solid wall, when normalized appropriately, follows with a high degree of accuracy the same form of scaling laws given above for free diffusion. Specifically, the scaling laws in this case are well represented by 1 − ((1 + )(E/ t))/3, for E/ t 1, and (E/ t) −1 [1 − ((1 + )(E/ t) −1 )/3], for E/ t 1, where the small parameter depends on the size of the near-wall domain used in the estimation of the diffusion coefficient and value of E. For the range of parameters reported in the literature, we estimate < 0.03. The near-wall simulations also show a bias in the estimated diffusion coefficient parallel to the wall even in the limit E = 0, indicating an overestimation which increases with increasing time delay t. This diffusion-induced overestimation is caused by the same underlying mechanism responsible for the previously reported overestimation of mean velocity in near-wall velocimetry.

Efficacy of single-component MTV to measure turbulent wall-flow velocity derivative profiles at high resolution

“…MTV data can also experience a temporal filtering effect associated with the averaging that occurs over the exposure period of the ICCD. This effect is physically similar to that found by Pouya et al (2015) in the context of experimentally estimating the intensity of Brownian fluctuations with finite sampling time sensors. In this regard, there are trade-offs associated with the camera time delay and exposure duration relative to accurately measuring the u ′ profiles.…”

Three-dimensional particle tracking around microstructures in water via total internal reflection fluorescence microscopy and refractive-index-matching method

“…Because the height of the microstructures fabricated by using T-NIL was less than 500 nm, MnPIV can therefore be applied in 3D flow measurements around these microstructures. We examined the hindrance factor for Brownian motion normal to the glass plate using the TIRFM (Pouya et al 2015), which is approximated by the following equation (Bevan and Prieve 2000):…”

Effect of finite spatial and temporal resolutions on super-resolution particle tracking velocimetry for pressure-driven flow in a nanochannel

“…Recently, we conducted simulations of single particle tracking in a nanochannel and revealed that a longer temporal resolution makes the apparently observed particle dynamics (particle diffusion coe cient, distribution of particle number density) different from the original particle dynamics due to the Brownian motion during the nite temporal resolution (Hanasaki et al 2018). Previous studies have also reported that anisotropic Brownian displacement near the surface by hydrodynamic interaction with the nite temporal resolution can cause a bias error of the measured nanoparticle position (Eichmann & Bevan 2010;Sadr et al 2007;Huang et al 2009;Pouya et al 2015). However, these artifacts owing to the nite temporal resolution have not been su ciently veri ed by experiments.…”