scholarly journals Quantification of Brownian motion under presence of flow using particle diffusometry

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Dong Hoon Lee ◽  
Steven T. Wereley
Keyword(s):  
Diffusion Coefficient ◽  
Brownian Motion ◽  
Diffusion Coefficients ◽  
Environmental Samples ◽  
Imaging Techniques ◽  
Fluid Flows ◽  
Waterborne Pathogen ◽  
Quantification Method ◽  
Sequential Images ◽  
Quiescent Fluid

Particle diffusometry (PD), a quantification method for the Brownian motion, is performed by recording temporally sequential images and using correlation analysis to obtain an ensemble diffusion coefficient for all particles captured in the imaging region (Clayton et al., 2017). PD is proven to be successful in the detection of the waterborne pathogen V. cholerae in environmental samples using different imaging techniques, including an inverted fluorescence microscope as well as a handheld hardware device operated with a smartphone (Clayton et al., 2019; Moehling et al., 2020). Although we intend to use PD to calculate diffusion coefficients in quiescent fluid, oftentimes unintentional fluid flows occur, creating measurement error when calculating the diffusion coefficient. In previous work, recordings under the presence of flow were discarded to avoid incorrect measurements of the sample. 

scholarly journals Confined Brownian Motion Tracked With Motion Blur: Estimating Diffusion Coefficient and Size of Confining Space

2021 ◽  
Vol 8 ◽  
Author(s):  
Kim I. Mortensen ◽  
Henrik Flyvbjerg ◽  
Jonas N. Pedersen
Keyword(s):  
Diffusion Coefficient ◽  
Brownian Motion ◽  
Exposure Time ◽  
Diffusion Coefficients ◽  
Brownian Particle ◽  
Quantitative Description ◽  
Time Lapse ◽  
Motion Blur ◽  
Single Particle Tracking ◽  
A Cell

Mesoscopic environments and particles diffusing in them are often studied by tracking such particles individually while their Brownian motion explores their environment. Environments may be, e.g., a domain in a cell membrane, an interior compartment of a cell, or an engineered nanopit. Particle trajectories are typically determined from time-lapse recorded movies. These are recorded with sufficient exposure time per frame to be able to detect and localize particles in each frame. Since particles move during this exposure time, particles image with motion blur. This motion blur can compromise estimates of diffusion coefficients and the size of the confining domain if not accounted for correctly. We do that here. We give explicit and exact expressions for the variance of measured positions and the mean-squared displacement of a Brownian particle confined in, respectively, a 1D box, a 2D box, a 2D circular disc, and a 3D sphere. Our expressions are valid for all exposure times, irrespective of the size of the confining space and the value of the diffusion coefficient. They apply also in the common case where the exposure time is smaller than the time-lapse due, e.g., to “dead time” caused by the readout process in the camera. These expressions permit determination of diffusion coefficients and domain sizes for given movies for the simple geometries we consider. More important, the trends observed in our exact results when parameter values are varied are valid also for more complex geometries for which no exact analytical solutions exist. Wherever the underlying physics is the same, the exact quantitative description of its consequences provided here is portable as a qualitative and semi-quantitative understanding of its consequences in general. The results may also be useful for other types of reflected Brownian motion than those occurring in single-particle tracking, e.g., in nuclear magnetic resonance imaging techniques. For use in that particular context, we briefly discuss the effects of confinement on anisotropic Brownian motion imaged with motion blur.

scholarly journals Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 4030
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Surface Effect ◽  
Bulk Water ◽  
Self Diffusion ◽  
Average Diffusion Coefficient ◽  
Average Diffusion ◽  
Chain Lengths ◽  
Fluid Diffusion ◽  
Self Diffusion Coefficient

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH2)3CH3, –(CH2)7CH3, and –(CH2)11CH3 nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.

scholarly journals Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 99 ◽  
Author(s):  
Kazuma Yamanaka ◽  
Takayuki Narumi ◽  
Megumi Hashiguchi ◽  
Hirotaka Okabe ◽  
Kazuhiro Hara ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Diffusion Coefficients ◽  
Coarse Graining ◽  
Chaotic Advection ◽  
Time Dependent ◽  
Local Order ◽  
Weak Turbulence ◽  
Normal Diffusion ◽  
Convective Rolls

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

Diffusion of Zinc in Two-Phase Mg-Al Alloy

2007 ◽  
Vol 263 ◽  
pp. 189-194
Author(s):  
Ivo Stloukal ◽  
Jiří Čermák
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Residual Activity ◽  
Diffusion Path ◽  
Al Alloy ◽  
Serial Sectioning ◽  
Two Phase ◽  
Interphase Boundaries ◽  
The Mean

Coefficient of 65Zn heterodiffusion in Mg17Al12 intermetallic and in eutectic alloy Mg - 33.4 wt. % Al was measured in the temperature region 598 – 698 K using serial sectioning and residual activity methods. Diffusion coefficient of 65Zn in the intermetallic can be written as DI = 1.7 × 10-2 m2 s-1 exp (-155.0 kJ mol-1 / RT). At temperatures T ≥ 648 K, where the mean diffusion path was greater than the mean interlamellar distance in the eutectic, the effective diffusion coefficient Def = 2.7 × 10-2 m2 s-1 exp (-155.1 kJ mol-1 / RT) was evaluated. At two lower temperatures, the diffusion coefficients 65Zn in interphase boundaries were estimated: Db (623 K) = 1.6 × 10-12 m2 s-1 and Db (598 K) = 4.4 × 10-13 m2 s-1.

Molten Slag Structure and Diffusion Coefficients of Cr3+ and Si4+ during Micro-Carbon Cr-Fe Alloy Production

2011 ◽  
Vol 79 ◽  
pp. 77-82
Author(s):  
Yi Min ◽  
Jian Huang ◽  
Cheng Jun Liu ◽  
Mao Fa Jiang
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Molten Slag ◽  
Optimization Method ◽  
Structure Theory ◽  
Average Diffusion Coefficient ◽  
Slag Structure ◽  
Initial Stage ◽  
Silicate Structure ◽  
Average Diffusion

Based on the silicate structure theory, the molten slag structure and the existential state of and during micro-carbon Cr-Fe alloy production process were analysised, and then their diffusion coefficients were calculated. The results showed that, during the initial stage, the average diffusion coeffecient of and is close to the , the reaction process is controlled by the diffusion of () and corporately, during the later stage, the diffusion coefficient of is less than average diffusion coefficient of and , the controlling step is the diffusion of . According to the evolution of diffusion coefficient, molten slag composition optimization method was advised to increase the diffusion ability of and for enhancing the reaction efficiency and the recovery rate of chromium.

Induced polarization and pore radius — A discussion

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D519-D526 ◽  
Author(s):  
Andreas Weller ◽  
Zeyu Zhang ◽  
Lee Slater ◽  
Sabine Kruschwitz ◽  
Matthias Halisch
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Diffusion Coefficients ◽  
Pore Radius ◽  
Mercury Porosimetry ◽  
Induced Polarization ◽  
Reliable Estimate ◽  
Characteristic Relaxation Time ◽  
A Value ◽  
Apparent Diffusion

Permeability estimation from induced polarization (IP) measurements is based on a fundamental premise that the characteristic relaxation time [Formula: see text] is related to the effective hydraulic radius [Formula: see text] controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We have examined the link between a widely used single estimate of [Formula: see text] and [Formula: see text] for an extensive database of sandstone samples, in which mercury porosimetry data confirm that [Formula: see text] is reliably determined from a modification of the Hagen-Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of one or two distinct representative diffusion coefficients but instead demonstrates strong evidence for six orders of magnitude of variation in an apparent diffusion coefficient that is well-correlated with [Formula: see text] and the specific surface area per unit pore volume [Formula: see text]. Two scenarios can explain our findings: (1) the length scale defined by [Formula: see text] is not equal to [Formula: see text] and is likely much longer due to the control of pore-surface roughness or (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g., silica and clays) making up the rock. In either case, the estimation of [Formula: see text] (and hence permeability) is inherently uncertain from a single characteristic IP relaxation time as considered in this study.

Diffusion of Water in Composite Filling Materials

1976 ◽  
Vol 55 (5) ◽  
pp. 730-732 ◽  
Author(s):  
M. Braden ◽  
E.E. Causton ◽  
R.L. Clarke
Keyword(s):  
Diffusion Coefficient ◽  
Composite Materials ◽  
Diffusion Coefficients ◽  
Diffusion Processes ◽  
Resin Phase ◽  
Filling Materials ◽  
Irreversible Breakdown

The absorption and desorption of water by seven composite materials are diffusion processes, with the diffusion coefficient decreasing with concentration. The magnitude of the diffusion coefficients were consistent with diffusion occurring in the resin phase. Although most materials showed reversible behavior during repeated sorption-desorption cycles, one material showed irreversible breakdown.

Activation barriers for oxygen diffusion in polystyrene and polycarbonate glasses: effects of codissolved argon, helium, and nitrogen

1995 ◽  
Vol 73 (11) ◽  
pp. 1831-1840 ◽  
Author(s):  
Bojie Wang ◽  
Peter R. Ogilby
Keyword(s):  
Diffusion Coefficient ◽  
Polymer Matrix ◽  
Diffusion Coefficients ◽  
Oxygen Diffusion ◽  
Arrhenius Plot ◽  
Activation Barrier ◽  
Spectroscopic Technique ◽  
Activation Barriers ◽  
Data Yield ◽  
Diffusion Activation

A recently developed spectroscopic technique was used to determine oxygen diffusion coefficients as a function of temperature for polystyrene and polycarbonate films. Data were recorded at total pressures <300 Torr over the temperature range 5–45 °C under conditions in which argon, helium, and nitrogen, respectively, were copenetrants. In all cases, the presence of the additional gas caused an increase in the oxygen diffusion coefficient. Arrhenius plots of the data yield (a) a diffusion activation barrier, Eact, and (b) a diffusion coefficient, D0, that represents the condition of "barrier-free" gas transport for the temperature domain over which the Arrhenius plot is linear. For all cases examined in both polystyrene and polycarbonate, D0 increased with an increase in the partial pressure of added gas. In polystyrene, the presence of an additional gas did not change Eact. In polycarbonate, Eact obtained in the presence of helium and argon likewise did not differ from that obtained in the absence of the copenetrant. When nitrogen was the added gas, however, a larger value of Eact was obtained. This latter observation is interpreted to reflect the plasticization of polycarbonate by nitrogen. Eact and D0 data are discussed within the context of a model that distinguishes between dynamic and static elements of free volume in the polymer matrix. Keywords: oxygen diffusion, polystyrene, polycarbonate, activation barrier.

Diffusion-Based Modeling of Gas Transport in Organic-Rich Ultratight Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-26
Author(s):  
Zizhong Liu ◽  
Hamid Emami-Meybodi
Keyword(s):  
Diffusion Coefficient ◽  
Adsorption Capacity ◽  
Surface Diffusion ◽  
Diffusion Coefficients ◽  
Gas Transport ◽  
Knudsen Diffusion ◽  
Gas Production ◽  
Hydrocarbon Transport ◽  
The Impact ◽  
And Storage

Summary The complex pore structure and storage mechanism of organic-rich ultratight reservoirs make the hydrocarbon transport within these reservoirs complicated and significantly different from conventional oil and gas reservoirs. A substantial fraction of pore volume in the ultratight matrix consists of nanopores in which the notion of viscous flow may become irrelevant. Instead, multiple transport and storage mechanisms should be considered to model fluid transport within the shale matrix, including molecular diffusion, Knudsen diffusion, surface diffusion, and sorption. This paper presents a diffusion-based semianalytical model for a single-component gas transport within an infinite-actingorganic-rich ultratight matrix. The model treats free and sorbed gas as two phases coexisting in nanopores. The overall mass conservation equation for both phases is transformed into one governing equation solely on the basis of the concentration (density) of the free phase. As a result, the partial differential equation (PDE) governing the overall mass transport carries two newly defined nonlinear terms; namely, effective diffusion coefficient, De, and capacity factor, Φ. The De term accounts for the molecular, Knudsen, and surface diffusion coefficients, and the Φ term considers the mass exchange between free and sorbed phases under sorption equilibrium condition. Furthermore, the ratio of De/Φ is recognized as an apparent diffusion coefficient Da, which is a function of free phase concentration. The nonlinear PDE is solved by applying a piecewise-constant-coefficient technique that divides the domain under consideration into an arbitrary number of subdomains. Each subdomain is assigned with a constant Da. The diffusion-based model is validated against numerical simulation. The model is then used to investigate the impact of surface and Knudsen diffusion coefficients, porosity, and adsorption capacity on gas transport within the ultratight formation. Further, the model is used to study gas transport and production from the Barnett, Marcellus, and New Albany shales. The results show that surface diffusion significantly contributes to gas production in shales with large values of surface diffusion coefficient and adsorption capacity and small values of Knudsen diffusion coefficient and total porosity. Thus, neglecting surface diffusion in organic-rich shales may result in the underestimation of gas production.

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