Hydrodynamic Diffusion Research Articles

From local to hydrodynamic friction in Brownian motion: A multiparticle collision dynamics simulation study.

The friction and diffusion coefficients of rigid spherical colloidal particles dissolved in a fluid are determined from velocity and force autocorrelation functions by mesoscale hydrodynamic simulations. Colloids with both slip and no-slip boundary conditions are considered, which are embedded in fluids modeled by multiparticle collision dynamics with and without angular momentum conservation. For no-slip boundary conditions, hydrodynamics yields the well-known Stokes law, while for slip boundary conditions the lack of angular momentum conservation leads to a reduction of the hydrodynamic friction coefficient compared to the classical result. The colloid diffusion coefficient is determined by integration of the velocity autocorrelation function, where the numerical result at shorter times is combined with the theoretical hydrodynamic expression for longer times. The suitability of this approach is confirmed by simulations of sedimenting colloids. In general, we find only minor deviations from the Stokes-Einstein relation, which even disappear for larger colloids. Importantly, for colloids with slip boundary conditions, our simulation results contradict the frequently assumed additivity of local and hydrodynamic diffusion coefficients.

Numerical study of the anode boundary layer in atmospheric pressure arc discharges

The anode boundary layer in atmospheric pressure arc discharges is studied numerically on the basis of the hydrodynamic (diffusion) equations for plasma components. The governing equations are formulated in a unified manner without the assumptions of thermal equilibrium, ionization equilibrium or quasi-neutrality. For comparison, a quasi-neutral model of the anode layer is also considered. The numerical computations are performed for an argon arc at typical values of the current density in anode layers (500–2000 A cm−2). The results of numerical modelling show that the common collisionless model of the sheath fails to describe the sheath region for the problem under consideration. For this reason, a detailed analysis of the anode sheath is performed using the results of unified modelling. In addition, the distributions of plasma parameters in the anode layer are analysed and the basic characteristics of the layer (anode voltage drop, sheath voltage drop, anode layer thickness, sheath thickness, heat flux to the anode) are calculated. Our results are found to be in good agreement with the existing theoretical predictions and experimental data. The dependence of the anode layer characteristics on the current density is also discussed.

An Imaging Flow Cytometer for Introductory Physics

Over the past year, Princeton has been developing a new one-semester survey-style Physics for the Life Sciences course as a possible alternative pathway for life science majors. This course will engage students on selected topics commonly encountered in the life sciences including forces and motion on the cellular scale, fluids, light, and imaging. The class will also be offered with a full laboratory. Several successful introductory science and engineering courses at Princeton have a laboratory component centered on completion of a single extended project comprised of multiple components, each of which explore a topic central to the learning goals of the class. Building on this successful model, we have developed a modular project appropriate for the new life science initiative (an imaging light-sheet flow cytometer) that combines elements of the major topics into a single project that can be completed over the semester and used as the basis for a final lab project. Here we describe construction and function of the imaging cytometer including sources for the components and course-appropriate analysis to measure fluorescence intensity distributions and hydrodynamic diffusion properties.

Numerical simulations of instabilities in the implosion process of inertial confined fusion in 2D cylindrical coordinates

In this paper, we introduce a multi-material arbitrary Lagrangian and Eulerian method for the hydrodynamic radiative multi-group diffusion model in 2D cylindrical coordinates. The basic idea in the construction of the method is the following: In the Lagrangian step, a closure model of radiation-hydrodynamics is used to give the states of equations for materials in mixed cells. In the mesh rezoning step, we couple the rezoning principle with the Lagrangian interface tracking method and an Eulerian interface capturing scheme to compute interfaces sharply according to their deformation and to keep cells in good geometric quality. In the interface reconstruction step, a dual-material Moment-of-Fluid method is introduced to obtain the unique interface in mixed cells. In the remapping step, a conservative remapping algorithm of conserved quantities is presented. A number of numerical tests are carried out and the numerical results show that the new method can simulate instabilities in complex fluid field under large deformation, and are accurate and robust.

Hydrodynamic diffusion in active microrheology of non-colloidal suspensions: the role of interparticle forces

Hydrodynamic diffusion in the absence of Brownian motion is studied via active microrheology in the ‘pure-hydrodynamic’ limit, with a view towards elucidating the transition from colloidal microrheology to the non-colloidal limit, falling-ball rheometry. The phenomenon of non-Brownian force-induced diffusion in falling-ball rheometry is strictly hydrodynamic in nature; in contrast, analogous force-induced diffusion in colloids is deeply connected to the presence of a diffusive boundary layer even when Brownian motion is very weak compared with the external force driving the ‘probe’ particle. To connect these two limits, we derive an expression for the force-induced diffusion in active microrheology of hydrodynamically interacting particles via the Smoluchowski equation, where thermal fluctuations play no role. While it is well known that the microstructure is spherically symmetric about the probe in this limit, fluctuations in the microstructure need not be – and indeed lead to a diffusive spread of the probe trajectory. The force-induced diffusion is anisotropic, with components along and transverse to the line of external force. The latter is identically zero owing to the fore–aft symmetry of pair trajectories in Stokes flow. In a naïve first approach, the vanishing relative hydrodynamic mobility at contact between the probe and an interacting bath particle was assumed to eliminate all physical contribution from interparticle forces, whereby advection alone drove structural evolution in pair density and microstructural fluctuations. With such an approach, longitudinal force-induced diffusion vanishes in the absence of Brownian motion, a result that contradicts well-known experimental measurements of such diffusion in falling-ball rheometry. To resolve this contradiction, the probe–bath-particle interaction at contact was carefully modelled via an excluded annulus. We find that interparticle forces play a crucial role in encounters between particles in the hydrodynamic limit – as they must, to balance the advective flux. Accounting for this force results in a longitudinal force-induced diffusion $D_{\Vert }=1.26aU_{S}{\it\phi}$, where $a$ is the probe size, $U_{S}$ is the Stokes velocity and ${\it\phi}$ is the volume fraction of bath particles, in excellent qualitative and quantitative agreement with experimental measurements in, and theoretical predictions for, macroscopic falling-ball rheometry. This new model thus provides a continuous connection between micro- and macroscale rheology, as well as providing important insight into the role of interparticle forces for diffusion and rheology even in the limit of pure hydrodynamics: interparticle forces give rise to non-Newtonian rheology in strongly forced suspensions. A connection is made between the flow-induced diffusivity and the intrinsic hydrodynamic microviscosity which recovers a precise balance between fluctuation and dissipation in far from equilibrium suspensions; that is, diffusion and drag arise from a common microstructural origin even far from equilibrium.

Assessment of the best flow model to characterize diffuse correlation spectroscopy data acquired directly on the brain.

Diffuse correlation spectroscopy (DCS) is a non-invasive optical technique capable of monitoring tissue perfusion. The normalized temporal intensity autocorrelation function generated by DCS is typically characterized by assuming that the movement of erythrocytes can be modeled as a Brownian diffusion-like process instead of by the expected random flow model. Recently, a hybrid model, referred to as the hydrodynamic diffusion model, was proposed, which combines the random and Brownian flow models. The purpose of this study was to investigate the best model to describe autocorrelation functions acquired directly on the brain in order to avoid confounding effects of extracerebral tissues. Data were acquired from 11 pigs during normocapnia and hypocapnia, and flow changes were verified by computed tomography perfusion (CTP). The hydrodynamic diffusion model was found to provide the best fit to the autocorrelation functions; however, no significant difference for relative flow changes measured by the Brownian and hydrodynamic diffusion models was observed.

Constrained Random Walk Models for Euro/Swiss Franc Exchange Rates: Theory and Empirics

We study the performance of the euro/Swiss franc exchange rate in the extraordinary period from September 6, 2011 and January 15, 2015 when the Swiss National Bank enforced a minimum exchange rate of 1.20 Swiss francs per euro. Within the general framework built on geometric Brownian motions (GBM), the first-order effect of such a steric constraint would enter a priori in the form of a repulsive entropic force associated with the paths crossing the barrier that are forbidden. It turns out that this naive theory is proved empirically to be completely mistaken. The clue is to realise that the random walk nature of financial prices results from the continuous anticipations of traders about future opportunities, whose aggregate actions translate into an approximate efficient market with almost no arbitrage opportunities. With the Swiss National Bank stated commitment to enforce the barrier, trader's anticipation of this action leads to a volatility of the exchange rate that depends on the distance to the barrier. This effect described by Krugman's model [P.R. Krugman. Target zones and exchange rate dynamics. The Quarterly Journal of Economics, 106(3):669-682, 1991] is supported by non-parametric measurements of the conditional drift and volatility from the data. To the best of our knowledge, our results are the first to provide empirical support for Krugman's model, likely due to the exceptional pressure on the euro/Swiss franc exchange rate that made the barrier effect particularly strong. Despite the obvious differences between brainless physical Brownian motions and complex financial Brownian motions resulting from the aggregated investments of anticipating agents, we show that the two systems can be described with the same mathematics after all. Using a recently proposed extended analogy in terms of a colloidal Brownian particle embedded in a fluid of molecules associated with the underlying order book, we derive that, close to the restricting boundary, the dynamics of both systems is described by a stochastic differential equation with a very small constant drift and a linear diffusion coefficient. As a side result, we present a simplified derivation of the linear hydrodynamic diffusion coefficient of a Brownian particle close to a wall.

Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid.

We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation.

Two-Aperture Microfluidic Probes as Flow Dipole: Theory and Applications.

A microfluidic probe (MFP) is a mobile channel-less microfluidic system under which a fluid is injected from an aperture into an open space, hydrodynamically confined by a surrounding fluid, and entirely re-aspirated into a second aperture. Various MFPs have been developed, and have been used for applications ranging from surface patterning of photoresists to local perfusion of organotypic tissue slices. However, the hydrodynamic and mass transfer properties of the flow under the MFP have not been analyzed, and the flow parameters are adjusted empirically. Here, we present an analytical model describing the key transport properties in MFP operation, including the dimensions of the hydrodynamic flow confinement (HFC) area, diffusion broadening, and shear stress as a function of: (i) probe geometry (ii) aspiration-to-injection flow rate ratio (iii) gap between MFP and substrate and (iv) reagent diffusivity. Analytical results and scaling laws were validated against numerical simulations and experimental results from published data. These results will be useful to guide future MFP design and operation, notably to control the MFP “brush stroke” while preserving shear-sensitive cells and tissues.

Radiative Transfer in Two Adjoining Media: The Continuity of Thermal Flux and the Existence and Uniqueness of Solutions

The spatial transport of radiation in two adjoining media and the continuity of flux at the interface are considered. As usual, we assume that the material is in local thermodynamic equilibrium. First in the absence of hydrodynamic motion and thermal diffusion, the existence and uniqueness of a global solution of the classical radiative transfer equations with the absorbing boundary condition is derived. But the continuity of thermal flux at the interface of two materials cannot be preserved in this classical model. To preserved the continuity of thermal flux at the interface, we consider radiative transfer equations modified by thermal diffusion. The existence and uniqueness of a global solution of this modified radiative transfer equation is also derived.

Hydrodynamic and Mass Transport Coupled through the Viscosity: Analysis of Steady-State and EHD Impedance

A mathematical model for electrohydrodymanic impedance was developed in which hydrodynamic and convective diffusion equations were coupled by a relationship between viscosity and concentration. This procedure allows better understanding the physical problem separating the mass transport and the hydrodynamic effects and the model fit to previously reported experimental results revealed a larger viscosity gradient than previously inferred. These results are consistent with the hypothesized formation of a colloidal suspension of ferrous sulfate particles.

Palladium Nanoparticles Decorated on Reduced Graphene Oxide Rotating Disk Electrodes toward Ultrasensitive Hydrazine Detection: Effects of Particle Size and Hydrodynamic Diffusion

Although metal nanoparticle/graphene composites have been widely used as the electrode in electrochemical sensors, two effects, consisting of the particle size of the nanoparticles and the hydrodynamic diffusion of analytes to the electrodes, are not yet fully understood. In this work, palladium nanoparticles/reduced graphene oxide (PdNPs/rGO) composites were synthesized using an in situ polyol method. Palladium(II) ions and graphene oxide were reduced together with a reducing agent, ethylene glycol. By varying the concentration of palladium(II) nitrate, PdNPs with different sizes were decorated on the surface of rGO sheets. The as-fabricated PdNPs/rGO rotating disk electrodes (RDEs) were investigated toward hydrazine detection. Overall, a 3.7 ± 1.4 nm diameter PdNPs/rGO RDE exhibits high performance with a rather low limit of detection of about 7 nM at a rotation speed of 6000 rpm and provides a wide linear range of 0.1-1000 μM with R(2) = 0.995 at 2000 rpm. This electrode is highly selective to hydrazine without interference from uric acid, glucose, ammonia, caffeine, methylamine, ethylenediamine, hydroxylamine, n-butylamine, adenosine, cytosine, guanine, thymine, and l-arginine. The PdNPs/rGO RDEs with larger sizes show lower detection performance. Interestingly, the detection performance of the electrodes is sensitive to the hydrodynamic diffusion of hydrazine. The as-fabricated electrode can detect trace hydrazine in wastewater with high stability, demonstrating its practical use as an electrochemical sensor. These findings may lead to an awareness of the effect of the hydrodynamic diffusion of analyte that has been previously ignored, and the 3.7 ± 1.4 nm PdNPs/rGO RDE may be useful toward trace hydrazine detection, especially in wastewater from related chemical industries.

Hydrodynamic Interaction of Elastic Capsules in Bounded Shear Flow

AbstractThis paper presents a modified Loop’s subdivision algorithm for studying the deformation of a single capsule, the hydrodynamic interaction between two capsules and the hydrodynamic diffusion of a suspension of capsules in bounded shear flow. A subdivision thin-shell model is employed to compute the forces generated on the surface of the elastic capsule during deformation. The capsule surface is approximated using the modified Loop’s subdivision scheme which guarantees bounded curvature and C1 continuity everywhere on the limit surface. The present numerical technique has been validated by studying the deformation of a spherical capsule in shear flow. Computations are also performed for a biconcave capsule over a wide range of shear rates and viscosity ratios to investigate its dynamics. In addition, the hydrodynamic interaction between two elastic capsules in bounded shear flow is studied. Depending on the wall separation distance, the trajectory-bifurcation points that separate reversing and crossing motions for both spherical and biconcave capsules can be found. Compared to the spherical capsules, the biconcave capsules exhibit additional types of interaction such as rotation and head-on collision. The head-on collision results in a large trajectory shift which contribute to the hydrodynamic diffusion of a suspension. A suspension of a large number of biconcave capsules in shear flow is also simulated to show the ability of the modified scheme in running a large-scale simulation over a long period of time.

Hydrodynamic correlations and diffusion coefficient of star polymers in solution.

The center-of-mass dynamics of star polymers in dilute solution is analyzed by hybrid mesoscale simulations. The fluid is modeled by the multiparticle collision dynamics approach, a particle-based hydrodynamic simulation technique, which is combined with molecular dynamics simulations for the polymers. Star polymers of various functionalities are considered. We determine the center-of-mass velocity correlation functions, the corresponding mean square displacements, and diffusion coefficients. The velocity correlation functions exhibit a functionality-dependent and structure-specific intermediate time regime, with a slow decay. It is followed by the long-time tail t(-3/2), which is solely determined by the fluid. Infinite-system-size diffusion coefficients are determined from the velocity correlation function by a combination of simulation and analytical results, as well as from the center-of-mass mean square displacement for various systems sizes and extrapolation. In terms of the hydrodynamic radius, the star polymer hydrodynamic diffusion coefficient exhibits the same universal system-size dependence as a spherical colloid. The functionality dependence of the ratio of hydrodynamic radii and the radii of gyration agrees well with experimental predictions.

Time-Dependent and Shear-Dependent Transient Viscosity of an Alumina Suspension

The transient viscosity of a well-dispersed Alumina–polyvinyl butyral tape-casting slurry have been investigated at the shear domain of 1–8 s−1 with the help of a conventional Couette device. The slurry under these shear rates shows a combination of shear dependence and time dependence based upon the applied shear. Attempts have been made to explain the diverse rheological behavior of the slurry. Many studies involving powder loading, milling time, extended shear up ramp, extended shear down ramp, time- and shear-dependent viscosities of the supernatant, and continual shearing have been conducted to explore the probable reasons behind such diverse behavior of the slurry. The findings of these studies strongly suggest that at the shear rates, shear-induced hydrodynamic diffusion plays a major role in dictating the time-dependent viscosity profile of the suspension. Further analysis of the results points out that the observed viscosity profiles are the resultant of the two major competitive processes of shear-induced hydrodynamic disffusion and shear rejuvenation. The results obtained in the present investigation also strongly indicate that the time-dependent behavior of the suspensions under shear opens up an alternative route of characterization of well-dispersed ceramics suspensions.

Modelling of RO installations for wastewater treatment plants

Abstract The investigation results of the processes involved in the combined plants for water and drainage cleaning, including an RO and UF membrane apparatus for magnetic water treatment, are presented in this paper. The potential of the magnetic water treatment method for correcting the nanofiltration processes is highlighted. New schemes are proposed for using the magnetic water treatment apparatus for the purpose of preventing the formation of colloid and salt deposits on the membrane surface of the RO and UF apparatuses. The membrane system mathematical model that enables the evaluation of the intensity of formation of deposits in the membrane apparatus were considered by accounting for the hydrodynamic flow and diffusion processes. The membrane system model accounts for the influence of the magnetic water treatment on the nanofiltration processes. The data of the experiments performed at the laboratory stand with water desalination via a RO membrane apparatus equipped with the additional group for influencing the water cleaned by the magnetic field are introduced in the current paper.

Diffusion of colloidal particles in swimming suspensions

Previously, we have proposed to analyse the hydrodynamic interactions in a suspension of swimmers with respect to an effective hydrodynamic diffusion coefficient, which only considers the fluctuating motion caused by the stirring of the fluid. In this work, we study the diffusion of colloidal particles immersed in a bath of swimmers. To accurately resolve the many-body hydrodynamic interactions responsible for this diffusion, we use a direct numerical simulation scheme based on the smooth profile method. We consider a squirmer model for the self-propelled swimmers, as it accurately reproduces the flow field generated by real microorganisms, such as bacteria or spermatozoa. We show that the diffusion coefficients of the colloids are comparable with the effective diffusion coefficients of the swimmers, provided that the concentration of swimmers is high enough. At low concentrations, the difference in the way colloids and swimmers react to the flow leads to a reduction in the diffusion coefficient of the colloids. This is clearly seen in the appearance of a negative-correlation region for the velocity-correlation function of the colloids, which does not exist for the swimmers.

Mathematical model on grain-size distribution in suspension over sand-gravel bed

In this study, the grain-size distribution in suspension over a sand-gravel bed in an open channel turbulent flow is investigated from theoretical point of view. On the basis of diffusion equation, a model on grain-size distribution is developed incorporating the effect of stratification and hindered settling due to increased suspension concentration. The hydrodynamic diffusion related to particle–particle interaction is considered in the computation of reference level and the influence of incipient motion probability, non-ceasing probability and pick-up probability of the sediment particles are considered in the computation of reference concentration. Due to inclusion of several factors, the proposed model predicts well the grain-size distribution of suspended load when compared with the experimental data and also shows its prediction superiority with respect to other existing models.

A unifying mode-coupling theory for transport properties of electrolyte solutions. II. Results for equal-sized ions electrolytes

On the basis of a versatile mode-coupling theory (MCT) method developed in Paper I [C. Contreras Aburto and G. Nägele, J. Chem. Phys. 139, 134109 (2013)], we investigate the concentration dependence of conduction-diffusion linear transport properties for a symmetric binary electrolyte solution. The ions are treated in this method as charged Brownian spheres, and the solvent-mediated ion-ion hydrodynamic interactions are accounted for also in the ion atmosphere relaxation effect. By means of a simplified solution scheme, convenient semi-analytic MCT expressions are derived for the electrophoretic mobilities, and the molar conductivity, of an electrolyte mixture with equal-sized ions. These expressions reduce to the classical Debye-Falkenhagen-Onsager-Fuoss results in the limit of very low ion concentration. The MCT expressions are numerically evaluated for a binary electrolyte, and compared to experimental data and results by another theoretical method. Our analysis encloses, in addition, the electrolyte viscosity. To analyze the dynamic influence of the hydration shell, the significance of mixed slip-stick hydrodynamic surface boundary conditions, and the effect of solvent permeability are explored. For the stick boundary condition employed in the hydrodynamic diffusivity tensors, our theoretical results for the molar conductivity and viscosity of an aqueous 1:1 electrolyte are in good overall agreement with reported experimental data for aqueous NaCl solutions, for concentrations extending even up to two molar.

Hydrodynamic diffusion of sedimenting point particles in a vertical shear flow

AbstractThe hydrodynamic diffusion of sedimenting point particles in a vertically sheared periodic system is investigated numerically and theoretically. In both the velocity-gradient direction and the vorticity direction, the rate of hydrodynamic diffusion is reduced as the shear rate is increased. In the velocity-gradient direction, two-particle interactions cause no net displacement, and three-particle interactions are necessary for diffusive behaviour. In contrast to an unsheared system, the resulting diffusion coefficient is only weakly dependent upon the size of the system and ${\widehat{D}}_{xx} \sim 4. 2\times 1{0}^{- 4} \hspace{0.167em} {n}^{2} {(f/ \mu )}^{4} {\dot {\gamma } }^{- 3} \ln (0. 42\widehat{L}{(\mu \dot {\gamma } / f)}^{1/ 2} )$, where $n$ is the particle number density, $f$ the force per particle, $\mu $ the fluid viscosity, $\dot {\gamma } $ the imposed shear rate, and $\widehat{L}$ the system size. In the vorticity direction, although individual two-particle interactions cause no net displacement, a superposition of interactions is sufficient to cause diffusion-like linear growth of the ensemble-averaged square particle displacements. The associated diffusion coefficient is given by ${\widehat{D}}_{yy} \sim 9. 47\times 1{0}^{- 4} \hspace{0.167em} n{(f/ \mu )}^{2} \widehat{L}\hspace{0.167em} {\dot {\gamma } }^{- 1} $. At sufficiently long times, the effect of multi-particle interactions cannot be neglected and there is a transition to another regime in which the diffusion coefficient is similar in form, but slightly reduced from this value. The dependence of ${\widehat{D}}_{xx} $ and ${\widehat{D}}_{yy} $ on the number density and dimensionless shear rate is explained using theoretical scaling arguments and analyses.