Transport Of Tracer Particles Research Articles

Asymmetric vertical transport in weakly forced shallow flows

In this paper, we report on an investigation of the vertical transport of tracer particles released within a shallow, continuously-forced flow by means of numerical simulations. The investigation is motivated by the shallow flows encountered in many environmental situations and inspired by the laboratory experiments conducted in electromagnetically forced shallow fluid layers. The flow is confined to a thin fluid layer by stress-free top and no-slip bottom walls. The dynamics and the transport properties of the shallow flow are investigated under various flow conditions characterized by a Reynolds number related to the forcing, ReF, and the aspect ratio of vertical and horizontal length scales δ. The forcing generates an array of vortices that becomes unsteady when ReFδ2≳10. These vortices are accompanied by upwellings in their cores which are surrounded by narrower, stronger downwellings. Hence, upwellings occur where the horizontal flow is vorticity-dominated, while downwellings where it is strain-dominated. The magnitude of the asymmetry in strength and size of the vertical flows and their correlation with horizontal structures depends on the flow conditions and significantly influences the vertical spreading of particles within the fluid volume. Under conditions leading to a large asymmetry, particles within updrafts are transported slowly upwards, while particles within downdrafts rapidly move downwards. In addition, particles are trapped for longer within the updrafts than downdrafts because of their correlation with vorticity-dominated regions. However, when the flow becomes fully three-dimensional and highly unsteady for large ReFδ2 values, this transport asymmetry subsides because the updrafts and downdrafts exhibit similar strength and size in such flow conditions. Consequently, similar amounts of particles are transported upwards and downwards at similar rates.

Lagrangian flow networks for passive dispersal: Tracers versus finite-size particles.

The transport and distribution of organisms such as larvae, seeds, or litter in the ocean as well as particles in industrial flows is often approximated by a transport of tracer particles. We present a theoretical investigation to check the accuracy of this approximation by studying the transport of inertial particles between different islands embedded in an open hydrodynamic flow aiming at the construction of a Lagrangian flow network reflecting the connectivity between the islands. To this end, we formulate a two-dimensional kinematic flow field which allows the placement of an arbitrary number of islands at arbitrary locations in a flow of prescribed direction. To account for the mixing in the flow, we include a von Kármán vortex street in the wake of each island. We demonstrate that the transport probabilities of inertial particles making up the links of the Lagrangian flow network essentially depend on the properties of the particles, i.e., their Stokes number, the properties of the flow, and the geometry of the setup of the islands. We find a strong segregation between aerosols and bubbles. Upon comparing the mobility of inertial particles to that of tracers or neutrally buoyant particles, it becomes apparent that the tracer approximation may not always accurately predict the probability of movement. This can lead to inconsistent forecasts regarding the fate of marine organisms, seeds, litter, or particles in industrial flows.

Flow structure around a microswimmer at fluid–fluid interface

Living organisms such as bacteria and algae often form biofilms at air–liquid and/or liquid–liquid interfaces. Therefore, it is important to understand the hydrodynamic interaction between the fluid–fluid interface and microorganisms. In the present study, a squirmer model is employed to study the flow field structures around a symmetrically trapped spherical microswimmer at an interface separating two fluids with viscosity contrast. In these simulations, Reynolds ( Re ) and Capillary ( Ca ) numbers are very small, and hence the contribution of inertia and interface deformations are neglected. The squirmer model is validated against the analytical solution obtained by considering a source dipole. It is observed that the flow structure and vorticity distribution around the microswimmers are strongly influenced by the squirmer parameter (β) and viscosity contrast (λ). Furthermore, the interplay between force-dipole and source-dipole along with viscosity contrast leads to a range of flow structures such as symmetric four-lobe and asymmetric quadrupolar flow fields. This flow structure asymmetry around the swimmer is quantified with different steady state orientations (φ). The effect of flow profile on the passive tracer particle transport is explored in terms of trajectories. Specifically, larger values of φ result in more profound curly trajectories.

Anomalous diffusion of scaled Brownian tracers.

A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that an active bath transfers to the tracer; thus, the model proposed here extends active Brownian motion, for which the stochastic dynamics of the orientation of the propelling force is described by scaled Brownian motion (sBm), identified by time-dependent diffusivity of the form D_{β}∝t^{β-1},β>0. If β≠1, sBm is highly nonstationary and suitable to describe such nonequilibrium dynamics induced by complex media. In this paper, we provide analytical calculations and computer simulations to show that genuine anomalous diffusion emerges in the long-time regime, with a time scaling of the mean-squared displacement t^{2-β}, while ballistic transport t^{2}, characteristic of persistent motion, is found in the short-time regime. We also analyze the time dependence of the kurtosis, and the intermediate scattering function of the position distribution, as well as the propulsion autocorrelation function, which defines the effective persistence time.

Enzyme Catalysis Causes Fluid Flow, Motility, and Directional Transport on Supported Lipid Bilayers.

The dynamic interplay between the composition of lipid membranes and the behavior of membrane-bound enzymes is critical to the understanding of cellular function and viability, and the design of membrane-based biosensing platforms. While there is a significant body of knowledge about how lipid composition and dynamics affect membrane-bound enzymes, little is known about how enzyme catalysis influences the motility and lateral transport on lipid membranes. Using enzyme-attached lipids in supported bilayers (SLBs), we provide direct evidence of catalysis-induced fluid flow that underlies the observed motility on SLBs. Additionally, by using active enzyme patches, we demonstrate the directional transport of tracer particles on SLBs. As expected, enhancing the membrane viscosity by incorporating cholesterol into the bilayer suppresses the overall movement. These are the first steps in understanding diffusion and transport on lipid membranes due to active, out-of-equilibrium processes that are the hallmark of living systems. In general, our study demonstrates how active enzymes can be used to control diffusion and transport in confined 2-D environments.

On the transport of tracer particles in two-dimensional plasma edge turbulence

Shear flows in turbulent fluids have been known to act as transport barriers for some time. An example of a shear flow generating mechanism is the E×B shear in plasma, which has a substantial impact on the dynamics of magnetic confinement fusion devices. The influence of this may be seen in the scrape-off layer where blobs or filaments may be sheared and velocity impacted, and in the edge and core of the plasma, where the formation of transport barriers and suppression of turbulence is strongly associated with such shearing effects. A dynamical picture of transport through these effects has been elusive—the development of a reduced model would be beneficial. We consider the application of an “observational” random walk to such transport, in order to determine whether it is a suitable approach upon which to base the development of reduced models. The observational random walk is modification of the random walk approach, introducing an intrinsic time separating observations, which reproduces the basic results of previous random walk models given a Gaussian jump function, assuming spatially homogenous jump function. We demonstrate that the jump function can be inferred from the statistics of passive particles propagated by E×B drift on a synthetic turbulence field and that the transport equation found from the jump function matches the expected diffusive transport very well. We, then, consider passive particles on simulations of the classic and modified Hasagawa–Wakatani equations in a statistical steady state for a variety of adiabaticity values and find normal transport in the near-hydrodynamic limit. When zonal flows appear, we find jump functions with non-Gaussian features, which result in transport equations with fractional differential terms in addition to, or in place of, diffusion terms. We surmise that the non-local fractional terms are related to the zonal flows acting as transport barriers. Overall, we find that the approach developed is a suitable starting point for the development of reduced models.

Impact of cell-sized confinement on particle transport within a motor-driven cytoskeletal network.

Intracellular transport of small particles and macromolecules is affected by the degree of crowding, confinement, and motor-driven activity within the cell. In vitro studies have examined how transport dynamics depend on each of these factors. But studies have primarily focused on these factors in isolation. Previously, we showed how crowding and confinement synergistically couple to slow the diffusion of DNA molecules. Here, we explore the combined effects of crowding by a composite network of actin and microtubule filaments, activity driven by molecular motors, and confinement by a lipid membrane to cell-sized volumes. We quantify transport of tracer particles within this tunable in vitro environment using differential dynamic microscopy (DDM) and single particle tracking. We simultaneously measure the dynamics and spatial organization of the composite network to link transport dynamics to network properties. To what degree tracers exhibit subdiffusive motion due to caging within the network mesh or superdiffusive motion due to motor activity depends on network composition, motor concentration, and confinement size.

Dynamics of self-propelled tracer particles inside a polymer network.

The transport of tracer particles through mesh-like environments such as biological hydrogels and polymer matrices is ubiquitous in nature. These tracers can be passive, such as colloids, or active (self-propelled), for example, synthetic nanomotors or bacteria. Computer simulations in principle could be extremely useful in exploring the mechanism of the active transport of tracer particles through mesh-like environments. Therefore, we construct a polymer network on a diamond lattice and use computer simulations to investigate the dynamics of spherical self-propelled particles inside the network. Our main objective is to elucidate the effect of the self-propulsion on the tracer particle dynamics as a function of the tracer size and the stiffness of the polymer network. We compute the time-averaged mean-squared displacement (MSD) and the van-Hove correlations of the tracer. On the one hand, in the case of a bigger sticky particle, the caging caused by the network particles wins over the escape assisted by the self-propulsion. This results an intermediate-time subdiffusion. On the other hand, smaller tracers or tracers with high self-propulsion velocities can easily escape from the cages and show intermediate-time superdiffusion. The stiffer the network, the slower the dynamics of the tracer, and bigger tracers exhibit longer lived intermediate time superdiffusion, since the persistence time scales as ∼σ3, where σ is the diameter of the tracer. At the intermediate time, non-Gaussianity is more pronounced for active tracers. At the long time, the dynamics of the tracer, if passive or weakly active, becomes Gaussian and diffusive, but remains flat for tracers with high self-propulsion, accounting for their seemingly unrestricted motion inside the network.

Tracer particle transport dynamics in the diffusive sandpile cellular automaton

Abstract The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked grains experience a sudden change, thus revealing a dynamical transition, that is consistent with previous studies (Newman DE et al., Phys Rev Lett 2002;88(20):204304). Across this transition, the sandpile moves from a regime characterized by self-similarity and memory, where avalanches of all possible sizes dominate transport across the system, to another regime where transport is taken over by near system-size, quasi-periodic avalanches. Values for the fractional transport exponents that quantify effective transport across the sandpile prior to the transition are also obtained.

The rarefied (non-continuum) conditions of tracer particle transport in soils, with implications for assessing the intensity and depth dependence of mixing from geochronology

Abstract. We formulate tracer particle transport and mixing in soils due to disturbance-driven particle motions in terms of the Fokker–Planck equation. The probabilistic basis of the formulation is suitable for rarefied particle conditions, and for parsing the mixing behavior of extensive and intensive properties belonging to the particles rather than to the bulk soil. The significance of the formulation is illustrated with the examples of vertical profiles of expected beryllium-10 (10Be) concentrations and optically stimulated luminescence (OSL) particle ages for the benchmark situation involving a one-dimensional mean upward soil motion with nominally steady surface erosion in the presence of either uniform or depth-dependent particle mixing, and varying mixing intensity. The analysis, together with Eulerian–Lagrangian numerical simulations of tracer particle motions, highlights the significance of calculating ensemble-expected values of extensive and intensive particle properties, including higher moments of particle OSL ages, rather than assuming de facto a continuum-like mixing behavior. The analysis and results offer guidance for field sampling and for describing the mixing behavior of other particle and soil properties. Profiles of expected 10Be concentrations and OSL ages systematically vary with mixing intensity as measured by a Péclet number involving the speed at which particles enter the soil, the soil thickness, and the particle diffusivity. Profiles associated with uniform mixing versus a linear decrease in mixing with depth are distinct for moderate mixing, but they become similar with either weak mixing or strong mixing; uniform profiles do not necessarily imply uniform mixing.

Mixing and transport from combined stretching-and-folding and cutting-and-shuffling.

While structures and bifurcations controlling tracer particle transport and mixing have been studied extensively for systems with only stretching-and-folding, and to a lesser extent for systems with only cutting-and-shuffling, few studies have considered systems with a combination of both. We demonstrate two bifurcations for nonmixing islands associated with elliptic periodic points that only occur in systems with combined cutting-and-shuffling and stretching-and-folding, using as an example a map approximating biaxial rotation of a less-than-half-full spherical granular tumbler. First, we characterize a bifurcation of elliptic island containment, from containment by manifolds associated with hyperbolic periodic points to containment by cutting line tangency. As a result, the maximum size of the nonmixing region occurs when the island is at the bifurcation point. We also demonstrate a bifurcation where periodic points are annihilated by the cutting-and-shuffling action. Chains of elliptic and hyperbolic periodic points that arise when invariant tori surrounding an elliptic point break up [according to Kolmogorov-Arnold-Moser (KAM) theory] can annihilate when they meet a cutting line. Consequently, the Poincaré index (a topological invariant of smooth systems) is not preserved.

An Integrated Experimental and Modeling Approach to Predict Sediment Mixing from Benthic Burrowing Behavior.

Bioturbation is the dominant mode of sediment transport in many aquatic environments and strongly influences both sediment biogeochemistry and contaminant fate. Available bioturbation models rely on highly simplified biodiffusion formulations that inadequately capture the behavior of many benthic organisms. We present a novel experimental and modeling approach that uses time-lapse imagery to directly relate burrow formation to resulting sediment mixing. We paired white-light imaging of burrow formation with fluorescence imaging of tracer particle redistribution by the oligochaete Lumbriculus variegatus. We used the observed burrow formation statistics and organism density to parametrize a parsimonious model for sediment mixing based on fundamental random walk theory. Worms burrowed over a range of times and depths, resulting in homogenization of sediments near the sediment-water interface, rapid nonlocal transport of tracer particles to deep sediments, and large areas of unperturbed sediments. Our fundamental, parsimonious random walk model captures the central features of this highly heterogeneous sediment bioturbation, including evolution of the sediment-water interface coupled with rapid near-surface mixing and anomalous late-time mixing resulting from infrequent, deep burrowing events. This approach provides a general, transferable framework for explicitly linking sediment transport to governing biophysical processes.

Ageing Scher–Montroll Transport

We study the properties of ageing Scher–Montroll transport in terms of a biased subdiffusive continuous time random walk in which the waiting times $$\tau $$ between consecutive jumps of the charge carriers are distributed according to the power law probability $$\psi (t)\simeq t^{-1-\alpha }$$ with $$0<\alpha <1$$ . As we show, the dynamical properties of the Scher–Montroll transport depend on the ageing time span $$t_{a}$$ between the initial preparation of the system and the start of the observation. The Scher–Montroll transport theory was originally shown to describe the photocurrent in amorphous solids in the presence of an external electric field, but it has since been used in many other fields of physical sciences, in particular also in the geophysical context for the description of the transport of tracer particles in subsurface aquifers. In the absence of ageing ( $$t_{a}=0$$ ) the photocurrent of the classical Scher–Montroll model or the breakthrough curves in the groundwater context exhibit a crossover between two power law regimes in time with the scaling exponents $$\alpha -1$$ and $$-1-\alpha $$ . In the presence of ageing a new power law regime and an initial plateau regime of the current emerge. We derive the different power law regimes and crossover times of the ageing Scher–Montroll transport and show excellent agreement with simulations of the process. Experimental data of ageing Scher–Montroll transport in polymeric semiconductors are shown to agree well with the predictions of our theory.

Tracer trajectories and displacement due to a micro-swimmer near a surface

We study tracer particle transport due to flows created by a self-propelled micro-swimmer, such as a swimming bacterium, alga or a microscopic artificial swimmer. Recent theoretical work has shown that as a swimmer moves in the fluid bulk along an infinite straight path, tracer particles far from its path perform closed loops, whereas those close to the swimmer are entrained by its motion. However, in biologically and technologically important cases tracer transport is significantly altered for swimmers that move in a run-and-tumble fashion with a finite persistence length, and/or in the presence of a free surface or a solid boundary. Here we present a systematic analytical and numerical study exploring the resultant regimes and their crossovers. Our focus is on describing qualitative features of the tracer particle transport and developing quantitative tools for its analysis. Our work is a step towards understanding the ecological effects of flows created by swimming organisms, such as enhanced fluid mixing and biofilm formation.

Tracer dispersion in bedload transport

Abstract. Bedload particles entrained by rivers tends to disperse as they move downstream. In this paper, we use the erosion-deposition model of Charru et al. (2004) to describe the velocity and the spreading of a plume of tracer particles. We restrict our analysis to steady-state transport above a flat bed of uniform sediment. The transport of tracer particles is then controlled by downstream advection and particle exchange with the immobile bed. After a transitional regime dominated by initial conditions, the evolution of a plume of markers tends asymptotically towards classical advection-diffusion: its average position grows linearly with time, whereas it spreads like the square root of time.

The effects of nonuniform magnetic field strength on density flux and test particle transport in drift wave turbulence

The extended Hasegawa–Wakatani equations generate fully nonlinear self-consistent solutions for coupled density n and vorticity ∇2ϕ, where ϕ is electrostatic potential, in a plasma with background density inhomogeneity κ=−∂ ln n0/∂x and magnetic field strength inhomogeneity C=−∂ ln B/∂x. Finite C introduces interchange effects and ∇B drifts into the framework of drift turbulence through compressibility of the E×B and diamagnetic drifts. This paper addresses the direct computation of the radial E×B density flux Γn=−n∂ϕ/∂y, tracer particle transport, the statistical properties of the turbulent fluctuations that drive Γn and tracer motion, and analytical underpinnings. Systematic trends emerge in the dependence on C of the skewness of the distribution of pointwise Γn and in the relative phase of density-velocity and density-potential pairings. It is shown how these effects, together with conservation of potential vorticity Π=∇2ϕ−n+(κ−C)x, account for much of the transport phenomenology. Simple analytical arguments yield a Fickian relation Γn=(κ−C)Dx between the radial density flux Γn and the radial tracer diffusivity Dx, which is shown to explain key trends in the simulations.

Habitat modification mediated by motile surface stirrers versus semi-motile burrowers: potential for a positive feedback mechanism in a eutrophied ecosystem

We performed a 4 wk laboratory experiment with the semi-motile burrowers Macoma balthica and Marenzelleria spp. and the motile surface sediment stirrers Monoporeia affinis and Mysis mixta to study their effects on the transport of tracer particles (mean diameter () 1 µm) in the sediment, sediment parameters (depth of the oxidized layer, water content, organic matter content), water turbidity, and nutrient fluxes across the sediment-water interface (PO4 3- , NO2 - + NO3 - , NH4 + ; measured weekly). Two densities were included for each taxon, representing a low and a high field density. M. balthica significantly increased particle mixing, the rates being 59.6 and 61.9 × 10 -3 cm 2 d -1 . While all taxa increased turbidity in the overlying water, the strongest effects were caused by M. affinis and M. mixta, resulting in 112- and 45-fold increases, respectively. In addition, these 2 motile species increased oxidation of the sediment surface layers. A distinctive difference in the nutrient fluxes was observed between the semi-motile (M. balthica, Marenzelleria spp.) and the motile taxa (M. affinis, M. mixta). The former increased the efflux of both PO4 3- and NH4 + , while the latter sup- pressed the efflux of NH4 + and decreased the sediment uptake of NOx, indicating enhanced N removal. Higher nutrient exchange rates were observed at the higher animal densities. We conclude that a shift in the benthic communities from the 2 motile to the 2 semi-motile taxa, observed through- out the northern Baltic Sea, may notably alter the regime of benthic nutrient cycling and thereby the performance of the entire ecosystem.

Mesoscale transport properties induced by near critical resistive pressure-gradient-driven turbulence in toroidal geometry

Numerical calculations of resistive pressure-gradient-driven turbulence in toroidal geometry in a range of beta values where the pressure profile is close to critical show self-similarity of space and time scales. These self-similarity properties lead to a fractional diffusive equation for mesoscale tracer-particle transport. The indices of the fractional derivates are consistent with the ones found for resistive pressure-gradient-driven turbulence in cylindrical geometry.

Fractional diffusion in plasma turbulence

Transport of tracer particles is studied in a model of three-dimensional, resistive, pressure-gradient-driven plasma turbulence. It is shown that in this system transport is anomalous and cannot be described in the context of the standard diffusion paradigm. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit superdiffusive scaling. To model these results we present a transport model with fractional derivatives in space and time. The model incorporates in a unified way nonlocal effects in space (i.e., non-Fickian transport), memory effects (i.e., non-Markovian transport), and non-Gaussian scaling. There is quantitative agreement between the turbulence transport calculations and the fractional diffusion model. In particular, the model reproduces the shape and space-time scaling of the pdf, and the superdiffusive scaling of moments.

Passive particle transport in three-vortex flow

We study transport of tracer particles in a two-dimensional incompressible inviscid flow produced by three point vortices of equal strength. Time dependence of the flow caused by vortex motion gives rise to chaotic tracer trajectories, which fill parts of the flow plane referred to as mixing regions. For general vortex positions, a large connected mixing region (chaotic sea) is formed around vortices. It comprises a number of coherent fluid patches (islands), which do not mix with the rest of the chaotic sea, inside them particle motion is predominantly regular; three near-circular islands surrounding vortices are distinguished by their robust nature. Tracers in the chaotic sea rotate around the center of vorticity in an irregular way. Their trajectories are intermittent, long flights of almost regular motion are caused by trappings in the boundary regions of regular islands. The statistics of tracer rotation exhibits anomalous features, such as faster than linear growth of tracer ensemble variance and asymmetric probability distribution with long power tails. Exponent of the variance growth power law is different for different time ranges. Central part of the tracer distribution and its low (noninteger) moments evolve in a self-similar way, characterized by an exponent, which is different from that of the variance, and contrary to the latter is constant in time. Algebraic tails of the tracer distribution, controlling the behavior of the variance, are responsible for this effect. Long correlations in tracer motion lead to non-Poissonian distribution of Poincare recurrences in the mixing region. Analysis of long recurrences proves, that they are caused by tracer trappings inside boundary layers of islands of regular motion, which always exist inside the mixing region. Statistics of Poincare recurrences and trapping times exhibit power-law decay, indicating absence of a characteristic relaxation time. Values of the decay exponent for recurrences and for escape from the analyzed traps are very close to each other; long correlations are not dominated by a single trap, but are a cumulative effect of all of them, relative importance of a trap is determined by its size, and by its rotation frequency with respect to the background.