Lagrangian Stochastic Simulation Research Articles

Taming Taylor-Aris dispersion through chaotic advection

Taylor-Aris dispersion represents an undesired phenomenon in pressure-driven liquid chromatography, often responsible for the unchecked increase of the Height Equivalent of the Theoretical Plate (HETP) when high throughput operating conditions are sought. Previous work on the subject showed how it is possible to contain the augmented dispersion in empty microchannels by inducing cross-sectional velocity components yielding an overall helical structure of the flow streamlines. Here, we explore the possibility of further reducing axial dispersion by devising flow conditions that give rise to chaotic streamlines. A three-dimensional steady flow generated by the combination of a pressure-driven Poiseuille flow and an electroosmotically-induced spatially periodic flow is used as a case study. Brenner’s macrotransport approach is used to predict the axial dispersion coefficient of a diffusing solute in flows possessing regular, partially chaotic and globally chaotic kinematic features. Accurate Lagrangian-stochastic simulations of particle ensembles are used to validate the predictions obtained through Brenner’s paradigm. Our findings suggest that the Taylor-Aris phenomenon can be altogether suppressed in the limit of globally chaotic kinematics. A theoretical interpretation of this outcome is developed by combining macrotransport theory with established results of the spectral approach to mixing in advecting-diffusing chaotic flows.

Brownian Sieving Effect for Boosting the Performance of Microcapillary Hydrodynamic Chromatography. Proof of Concept.

Microcapillary hydrodynamic chromatography (MHDC) is a well-established technique for the size-based separation of suspensions and colloids, where the characteristic size of the dispersed phase ranges from tens of nanometers to micrometers. It is based on hindrance effects which prevent relatively large particles from experiencing the low velocity region near the walls of a pressure-driven laminar flow through an empty microchannel. An improved device design is here proposed, where the relative extent of the low velocity region is made tunable by exploiting a two-channel annular geometry. The geometry is designed so that the core and the annular channel are characterized by different average flow velocities when subject to one and the same pressure drop. The channels communicate through openings of assigned cut-off length, say A. As they move downstream the channel, particles of size bigger than A are confined to the core region, whereas smaller particles can diffuse through the openings and spread throughout the entire cross section, therein attaining a spatially uniform distribution. By using a classical excluded-volume approach for modeling particle transport, we perform Lagrangian-stochastic simulations of particle dynamics and compare the separation performance of the two-channel and the standard (single-channel) MHDC. Results suggest that a quantitative (up to thirtyfold) performance enhancement can be obtained at operating conditions and values of the transport parameters commonly encountered in practical implementations of MHDC. The separation principle can readily be extended to a multistage geometry when the efficient fractionation of an arbitrary size distribution of the suspension is sought.

Nonlocal Turbophoresis of Particles in the Logarithmic Layer of Wall Turbulence

The dynamics of high-inertia particles in the logarithmic layer of a wall turbulent flow has been studied using Lagrangian stochastic simulation. Because of the linear dependence of the turbulent time scale on the distance to the wall in the logarithmic layer, turbophoresis, i.e., the migration of particles toward the wall, is observed. It has a nonlocal character in the wall region because of a significant contribution of ballistic motion of particles. The profiles of the concentration and second moment of particle velocities have been obtained for an arbitrary inertia parameter of a particle and different values of the restitution coefficient of the particle velocity at rebound from the wall. It has been shown that the probability density distribution of particle velocities has “heavy tails” in the wall region. These tails exhibit a power-law behavior in the inelastic collapse regime for particle trajectories, which is observed at restitution coefficients below a critical value of 0.163 in agreement with the results reported in Belan et al., Phys. Rev. E 93, 052206 (2016).

Physical processes controlling passive larval transport at the Patagonian Shelf Break Front

The largest beds of the Patagonian scallop (Zygochlamys patagonica) have been associated with high chlorophyll-a concentration observed along the Patagonian Shelf Break Front but there is no supported hypothesis about how this benthic-pelagic connection is maintained. In this work we address the main physical processes driving the benthic-pelagic linkages through oriented numerical experiments derived from a realistic, high-resolution numerical model, and Lagrangian stochastic simulations. The results support the hypothesis of an important dynamical control of the slope current on the fate of surface released passive particles and their subsequent bottom settlement. A high percentage of the particles released at the surface settled over the scallop beds. The particles remaining at the surface layer followed a prevailing NE flow direction with low cross-shelf dispersion. Additional experiments show that the secondary cross-shelf circulation forced by the slope current promotes downwelling and hence the settlement of particles on the westward side (onshore) of the shelf break. The percent of particles settling over the scallop beds exceeded 80% by the addition of vertical stochastic turbulence and tidal forcing. These results highlight the importance of including the vertical diffusivity in particle tracking experiments to better estimate benthic-pelagic interaction processes.

Timestep Buffering to Preserve the Well-Mixed Condition in Lagrangian Stochastic Simulations

Using one or more physical time scales as a basis for timestep (\(\Delta t\)) selection is common in Lagrangian stochastic simulations of particle dispersion. This approach generally works well when the velocity statistics (and thus \(\Delta t\)) vary slowly but problems such as the \(\Delta t\) bias and imbalanced particle fluxes at interfaces can occur when the velocity statistics vary rapidly. These problems can result in violations of the well-mixed condition (WMC) and inaccurate predictions. An additional problem is that unrealistically high (or rogue) particle velocities can occur if \(\Delta t\) is too large. A small constant timestep can be used to reduce or eliminate these problems but incurs the penalty of considerable computational cost. A timestep-buffering technique that eliminates abrupt changes in a variable timestep through linear interpolation is demonstrated to be effective at satisfying the WMC and minimizing rogue velocities for particle dispersion in an idealized one-dimensional turbulence regime with a steep gradient. The technique is also shown to be effective when applied to a more realistic three-dimensional system.

Impact of Sea Spray on Air–Sea Fluxes. Part II: Feedback Effects

Abstract This paper presents estimations for the transfer of momentum, heat, and water mass between the air and the sea. The results from Lagrangian stochastic simulations of sea spray drops (see Part I), along with two sea spray generation functions, are used to calculate the spray-mediated flux components of the air–sea fluxes. When the spray-mediated fluxes constitute a significant fraction of the total fluxes under certain conditions, their feedback effect on the atmosphere cannot be neglected. The authors derive a simplified feedback model to investigate such cases, finding that the spray-mediated fluxes may be especially sensitive to the size distribution of the drops. The total effective air–sea fluxes lead to drag and enthalpy coefficients that increase modestly with wind speed. The rate of increase for the drag coefficient is greatest at moderate wind speeds, while the rate of increase for the enthalpy coefficient is greatest at higher wind speeds where the spray is ubiquitous.

Lagrangian Stochastic Simulation of Atmospheric Dispersion from Sources near the Ground

Lagrangian Stochastic Simulation of Atmospheric Dispersion from Sources near the Ground

Tracking the potato late blight pathogen in the atmosphere using unmanned aerial vehicles and Lagrangian modeling

A means for determining the aerial concentration, C (sporangia m −3), of plant pathogenic spores at various distances from a source of inoculum is needed to quantify the potential spread of a plant disease. Values of C for Phytophthora infestans sporangia released from an area source of diseased plants in a potato canopy was quantified in three ways: (1) by using Rotorods to sample the air just above the source, (2) by using unmanned aerial vehicles to sample the air at altitudes up to 90 m above the source and at downwind distances up to 500 m from the source, and (3) by using a Lagrangian stochastic simulation of sporangia flight trajectories to tie these two measurements together. Experiments were conducted using three potato crops over two years. Model predictions of time-average, crosswind-integrated concentrations were highly correlated ( r = 0.9) with values of C measured using the unmanned aerial vehicles. The model describes the release and dispersal of sporangia from a potato canopy to a downwind distance of 500 m. Thus, it may have utility as a part of an area-wide decision support system by helping to predict risk of disease spread between neighboring or distant potato fields.

Comparison between measured tracer fluxes and footprint model predictions over a homogeneous canopy of intermediate roughness

Fast response tracer flux measurements are compared against flux footprint predictions from both a Lagrangian stochastic simulation and an analytical solution to the equation of diffusion over a canopy of intermediate roughness. A turbulent tracer flux experiment was conducted over a peach orchard for a range of mildly unstable to very unstable conditions. For this purpose, a line source was used to release sulfur hexafluoride at treetop and fast response tracer flux instrumentation placed in the roughness sub-layer was mounted on four towers perpendicular to the line source to measure the vertical tracer flux. There was excellent agreement between Lagrangian simulated fluxes and their experimental counterparts. The analytical solution to the advection–diffusion equation used also shows a good agreement with the tracer fluxes particularly far from the tracer source. These results suggest that for canopies of intermediate roughness, the flux footprint predictions from both models presented work very well, despite their simplifying assumptions.

809 ラグランジュ確率モデルによる平行平板間乱流中のパッシブスカラ拡散場の数値シミュレーション

809 ラグランジュ確率モデルによる平行平板間乱流中のパッシブスカラ拡散場の数値シミュレーション

Lagrangian stochastic simulation of turbulent dispersion of heat markers in a channel flow

A modified Langevin equation is developed to represent the dispersion of heat markers from point sources that originate at different locations in a channel through which a fluid is flowing turbulently. Of particular interest is the description of wall sources. Since a heated (or cooled) wall may be represented as a distribution of point sources (or sinks), these results can be used to describe heat transfer problems which have different configurations of heat transfer surfaces.

Quantifying the Rate of Release and Escape of Phytophthora infestans Sporangia from a Potato Canopy

ABSTRACT A means for determining the rate of release, Q (spores per square meter per second), of spores from a source of inoculum is paramount for quantifying their further dispersal and the potential spread of disease. Values of Q were obtained for Phytophthora infestans sporangia released from an area source of diseased plants in a potato canopy by comparing the concentrations of airborne sporangia measured at several heights above the source, with the concentrations predicted by a Lagrangian Stochastic simulation model. An independent estimate of Q was obtained by quantifying the number of sporangia per unit area of source at the beginning of each sampling day by harvesting diseased plant tissue and enumerating sporangia from these samples. This standing spore crop was the potential number of sporangia released per area of source during the day. The standing spore crop was apportioned into time segments corresponding to sporangia concentration measurement periods using the time trace of sporangia sampled above the source by a Burkard continuous suction spore sampler. This apportionment of the standing spore crop yielded potential release rates that were compared with modeled release rates. The two independent estimates of Q were highly correlated (P = 0.003), indicating that the model has utility for predicting release rates for P. infestans sporangia and the spread of disease between fields.

G702 確率モデルによるチャネル乱流中粒子拡散場の数値シミュレーション

G702 確率モデルによるチャネル乱流中粒子拡散場の数値シミュレーション

An analysis of the asymptotic behavior of cross-wind-integrated ground-level concentrations using Lagrangian stochastic simulation

This paper examines the asymptotic behavior as a function of downwind distance of ground-level cross-wind-integrated concentration (CWIC) caused by a continuous ground-level source in the atmospheric surface layer. We first present asymptotic expressions obtained from an analysis of data from Project Prairie Grass (PPG, Barad, 1958), and then derive corresponding formulae from data generated using Lagrangian stochastic (LS) model simulations. Under stable and neutral stratification, the formulae derived from PPG data agree well with that from LS simulations. Assuming that the Lagrangian stochastic model represents current understanding of dispersion, this agreement suggests that the formulations for stable and neutral conditions are credible. On the other hand, for unstable stratification, we find that while the LS model yields a “− 3 2 ” law, the PPG data suggest a fall-off with distance that is closer to a “ − 2” slope. At the present time, we cannot identify the reasons for this disagreement.

A Lagrangian stochastic model for aerial spray transport above an oak forest

An aerial spray droplets' transport model has been developed by applying recent advances in Lagrangian stochastic simulation of heavy particles. A two-dimensional Lagrangian stochastic model was adopted to simulate the spray droplet dispersion in atmospheric turbulence by adjusting the Lagrangian integral time scale along the drop trajectory. The other major physical processes affecting the transport of spray droplets above a forest canopy, the aircraft wingtip vortices and the droplet evaporation, were also included in each time step of the droplets' transport. The model was evaluated using data from an aerial spray field experiment. In generally neutral stability conditions, the accuracy of the model predictions varied from run-to-run as expected. The average root-mean-square error was 24.61 IU cm −2, and the average relative error was 15%. The model prediction was adequate in two-dimensional steady wind conditions, but was less accurate in variable wind condition. The results indicated that the model can simulate successfully the ensemble; average transport of aerial spray droplets under neutral, steady atmospheric wind conditions.