Particle Tracking Simulations Research Articles

Numerical analysis of thermal and mechanical stress profile during the extrusion processing of plasticized starch by non-isothermal flow simulation

Abstract The non-isothermal, non-Newtonian, transient flow of plasticized starch in a co-rotating twin-screw extruder is simulated by using 3-dimensional (3D) computational fluid dynamics (CFD) accompanied by particle tracking simulation. The results show that the maximum stresses are generated at the tip of the screws. These maxima lead to local hot spots with temperatures up to 10 K higher than material temperature at low shear regions. The particle tracking simulation allowed calculating maximum stress distribution among the extruded material, which vary significantly. The results further suggest that increasing screw speed can lead to lower mechanical stresses due to decreased matrix viscosity. Despite the lower mechanical stresses, increasing screw speed still results in the exposure of material to significantly higher material temperature. Overall, results reveal the significance and the necessity of the in-depth analysis of local extrusion conditions by non-isothermal CFD and particle tracking simulations.

Physical Processes Determine Spatial Structure in Water Temperature and Residence Time on a Wide Reef Flat

AbstractOn coral reefs, flow determines residence time of water influencing physical and chemical environments and creating observable microclimates within the reef structure. Understanding the physical mechanisms driving environmental variability on shallow reefs, which distinguishes them from the open ocean, is important for understanding what contributes to thermal resilience of coral communities and predicting their response to future anomalies. In June 2014, a field experiment conducted at Dongsha Atoll in the northern South China Sea investigated the physical forces that drive flow over a broad shallow reef flat. Instrumentation included current and pressure sensors and a distributed temperature sensing system, which resolved spatially and temporally continuous temperature measurements over a 3‐km cross‐reef section from the lagoon to reef crest. Spectral analysis shows that while diurnal variability was significant across the reef flat—a result expected from daily solar heating—temperature also varied at higher frequencies near the reef crest. These spatially variable temperature regimes, or thermal microclimates, are influenced by circulation on the wide reef flat, with spatially and temporally variable contributions from tides, wind, and waves. Through particle tracking simulations, we find the residence time of water is shorter near the reef crest (3.6 h) than near the lagoon (8.6 h). Tidal variability in flow direction on the reef flat leads to patterns in residence time that are different than what would be predicted from unidirectional flow. Circulation on the reef also determines the source (originating from offshore vs. the lagoon) of the water present on the reef flat.

Analytical model of the streaking process in a single split-ring resonator for sub-ps electron pulse

The use of THz-driven split-ring resonator (SRR) for temporal characterization of sub-ps electron pulse has been proposed for a few years and was experimentally demonstrated recently. The dependence of the streaking performance on the dimensions of SRR is to be further discussed here. For SRRs with simple structures, the resonance frequency can be derived through an equivalent LC circuit, which reveals the quantitative dependence of the resonance frequency on its geometric dimensions. Besides, the geometric dimensions of SRR determine its streaking region and field enhancement factor, which have a substantial impact on the streaking process and the temporal resolution. We analyze the existing equivalent LC circuit model for SRRs and propose an analytical beam dynamics model to describe the streaking process of electron pulse. Formulas for the streaking angle, the post-streaking beam divergence, the spot size on the detector and the temporal resolution of SRR are derived. The analytical results are compared with the particle tracking simulation to discuss its applicability. The restriction of the bunch length measurement due to the space charge effect are discussed as a complement to the analytical model. This analytical model provides a link between the temporal resolution and the geometric dimensions of SRR, which can be utilized for performance evaluation and structural optimization.

Acoustophoretic agglomeration patterns of particulate phase in a host fluid

Ultrasound-assisted processing of particulate phase in a host fluid relies on the induced acoustic force field. Understanding the agglomeration phenomenon in the particulate phase under acoustic forces will provide better insight about the acoustophoresis quality and a way to design a well-controlled process. In this work, a dynamic model consisting of acoustic and hydrodynamic forces is proposed for tracking the motion of micro-spheres under ultrasound fields with planar and non-planar wave fronts. The agglomeration of particles at the nodal plane was simulated taking into account the contact and collisions between spheres. The numerical simulations were conducted for both sound hard and compressible spheres to investigate the behaviors of single and multiple-phase particle populations. For the case of a plane standing-wave, the interaction between solid-bubble allows the solid particles to stay at the velocity node which is their unstable equilibrium location. With a Bessel standing wave as a non-planar pressure field, the agglomeration patterns of particles are generally different from the case of plane standing wave, which implies the significance of the particle tracking simulations for predicting the agglomeration patterns and locations under ultrasound fields with arbitrary wave fronts.

Beaching patterns of plastic debris along the Indian Ocean rim

Abstract. A large percentage of global ocean plastic waste enters the Northern Hemisphere Indian Ocean (NIO). Despite this, it is unclear what happens to buoyant plastics in the NIO. Because the subtropics in the NIO are blocked by landmass, there is no subtropical gyre and no associated subtropical garbage patch in this region. We therefore hypothesize that plastics “beach” and end up on coastlines along the Indian Ocean rim. In this paper, we determine the influence of beaching plastics by applying different beaching conditions to Lagrangian particle-tracking simulation results. Our results show that a large amount of plastic likely ends up on coastlines in the NIO, while some crosses the Equator into the Southern Hemisphere Indian Ocean (SIO). In the NIO, the transport of plastics is dominated by seasonally reversing monsoonal currents, which transport plastics back and forth between the Arabian Sea and the Bay of Bengal. All buoyant plastic material in this region beaches within a few years in our simulations. Countries bordering the Bay of Bengal are particularly heavily affected by plastics beaching on coastlines. This is a result of both the large sources of plastic waste in the region and the ocean dynamics that concentrate plastics in the Bay of Bengal. During the intermonsoon period following the southwest monsoon season (September, October, November), plastics can cross the Equator on the eastern side of the NIO basin into the SIO. Plastics that escape from the NIO into the SIO beach on eastern African coastlines and islands in the SIO or enter the subtropical SIO garbage patch.

Independent reaction times method in Geant4‐DNA: Implementation and performance

The simulation of individual particle tracks and the chemical stage following water radiolysis in biological tissue is an effective means of improving our knowledge of the physico-chemical contribution to the biological effect of ionizing radiation. However, the step-by-step simulation of the reaction kinetics of radiolytic species is the most time-consuming task in Monte Carlo track-structure simulations, with long simulation times that are an impediment to research. In this work, we present the implementation of the independent reaction times (IRT) method in Geant4-DNA Monte Carlo toolkit to improve the computational efficiency of calculating G-values, defined as the number of chemical species created or lost per 100eV of deposited energy. The computational efficiency of IRT, as implemented, is compared to that from available Geant4-DNA step-by-step simulations for electrons, protons and alpha particles covering a wide range of linear energy transfer (LET). The accuracy of both methods is verified using published measured data from fast electron irradiations for • OH and for time-dependent G-values. For IRT, simulations in the presence of scavengers irradiated by cobalt-60 γ-ray and 2MeV protons are compared with measured data for different scavenging capacities. In addition, a qualitative assessment comparing measured LET-dependent G-values with Geant4-DNA calculations in pure liquid water is presented. The IRT improved the computational efficiency by three orders of magnitude relative to the step-by-step method while differences in G-values by 3.9% at 1μs were found. At 7ps, • OH and yields calculated with IRT differed from recent published measured data by 5%±4% and 2%±4%, respectively. At 1μs, differences were 9%±5% and 6%±7% for • OH and , respectively. Uncertainties are one standard deviation. Finally, G-values at different scavenging capacities and LET-dependent G-values reproduced the behavior of measurements for all radiation qualities. The comprehensive validation of the Geant4-DNA capabilities to accurately simulate the chemistry following water radiolysis is an ongoing work. The implementation presented in this work is a necessary step to facilitate performing such a task.

Density ratio effects on the topology of coherent turbulent structures in two-way coupled particle-laden channel flows

This investigation considers the effect of density ratio on the modification of coherent turbulent structures in particle-laden channel flows at a shear Reynolds number of Reτ = 180. Direct numerical simulation and Lagrangian particle tracking are used to accurately predict the motion of particles dispersed within the flow at three Stokes numbers, St+ = 0.1, 50, and 92. Particle–fluid coupling is achieved through a local element-based force feedback field in the Navier–Stokes equations, which are solved using a seventh-order accurate spectral element method. After an initial transitory period wherein the effects of particle–fluid interaction are emphasized, the low density ratio particles are found to enhance the turbulence field, increasing the frequency of Q-criterion satisfying regions, while the inertial particles suppress the turbulence, reducing the number of quasistreamwise vortices. Results indicate that the topology of the quasistreamwise vortices is altered by the presence of the particles in the viscous sublayer, the buffer layer, and the log-law region such that the distribution of the third invariant of the deviatoric tensor, R, is widened by the presence of tracer-like particles and made thinner by the inertial particles. This effect reduces the amount of unstable focus/compressing regions and stable focus/stretching regions, which account for the streamwise vortical structures observed in these types of flow. Investigating the instantaneous coupling force field surrounding turbulent structures and low speed streaks shows that particles exert their greatest influence on the fluid in the regions noted, and mechanisms by which the particulate phase interacts with turbulent vortices are analyzed.

Productive detours – Atlantic water inflow and acoustic backscatter in the major troughs along the Svalbard shelf

Atlantic Water (AW) flowing along the western and northern Svalbard shelf-break extends the Atlantic domain into the Arctic and is the region’s major source of heat, nutrients and advected plankton. We investigated the inflow and recirculation of AW into four major troughs that cut into the Svalbard shelf, the Isfjorden, Kongsfjorden, Hinlopen and Kvitøya Troughs, and related the circulation patterns to acoustic backscatter observed with echosounders and Acoustic Doppler Current Profilers. The acoustic observations showed higher levels of backscatter from fish in the Hinlopen Trough compared to the shelf and shelf-break north of Svalbard. This coincides with a steady inflow of nutrients, biomass and heat into the trough with the AW. Trough circulation was characterized using output from a high-resolution regional ocean model and particle tracking simulations. All four troughs experience topographically steered recirculation (in-and-outflow) of AW, but the troughs on the western Svalbard shelf showed a stronger seasonality than the troughs on the northern shelf. The Hinlopen Trough receives the strongest AW inflow and the most direct inflow from the shelf-break boundary current. The troughs form hybrid habitats between the shelf and shelf-break that extend the Atlantic advective domain closer to the Svalbard coastline.

Process intensification through staggered herringbone micro-channels: Mass transfer enhancement to a reactive wall

In the present study, the flow behaviour through different micro-herringbone channels configurations (1-peak, 2-peak, 1–2 alternated peak herringbone channel and a flow inversion geometry) have been numerically analysed as a mean of intensifying mass transfer to a reactive boundary. Results showed that the mass transfer coefficients were higher for the 1–2 alternated herringbone structure than those with, either, 1-peak or 2-peak structures. Moreover, the flow inversion structure mass transfer coefficients were double those obtained for the staggered herringbone channel. The alternated herringbone channel combines a different set of herringbone structures that are efficient at removing the boundary layer at different parts of the channel. The combination of these structures provide an enhanced mass transfer performance as compared to a standard herringbone channel. The obtained results showed that a 2D simplified model which uses hydrodynamic data from CFD simulations is a reasonable substitute for full 3D particle tracking simulations in terms of the mass transfer behavior of the 1PSHC with a 97.5 % of accuracy related to the asymptotic Sherwood number. The mixing capacity of the herringbones was accounted for by an apparent effective diffusion coefficient. The agreement between the 3D and 2D simulation was reasonable.

Efficient discrete-event based particle tracking simulation for high energy physics

This work presents novel discrete event-based simulation algorithms based on the Quantized State System (QSS) numerical methods. QSS provides attractive features for particle transportation processes, in particular a very efficient handling of discontinuities in the simulation of continuous systems. We focus on High Energy Physics (HEP) particle tracking applications that typically rely on discrete time-based methods, and study the advantages of adopting a discrete event-based numerical approach that resolves efficiently the crossing of geometry boundaries by a traveling particle. For this purpose we follow two complementary strategies. First, a new co-simulation technique connects the Geant4 simulation toolkit with a standalone QSS solver. Second, a new native QSS numerical stepper is embedded into Geant4. We compare both approaches against the latest Geant4 default steppers in different HEP setups, including a complex realistic scenario (the CMS particle detector at CERN). Our techniques achieve relevant simulation speedups in a wide range of scenarios, particularly when the intensity of discrete-event handling dominates performance in the solving of the continuous laws of particle motion.

A Method to Represent a Well in a Three-Dimensional Discrete Fracture Network Model.

In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three-dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high-resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real-world case study.

Microstructures refinement and mechanical properties enhancement of aluminum and magnesium alloys by combining distributary-confluence channel process for semisolid slurry preparation with high pressure die-casting

Abstract A simple and efficient semisolid slurry preparation technique, called distributary-confluence channel (DCC), was developed to prepare high-quality semisolid slurries of aluminum and magnesium alloys. The DCC process was coupled with the use of a high pressure die-casting (HPDC) machine to successfully achieve near-net forming and implement production applications with rheological high pressure die-casting (Rheo-HPDC) for various Al and Mg alloy castings. The changes in the flow state and in the physical field of the melt during the slurry preparation via the DCC technique were investigated by numerical simulations. The nucleation mechanism and the growth law of the primary grain during the DCC process were discussed. The microstructures, porosities, and mechanical properties of the aluminum and magnesium alloys prepared via DCC Rheo-HPDC were studied. The results show that semisolid slurries containing a large amount of primary grains with an average size 0.8, and uniformly dispersed in the liquid matrix can be prepared via DCC. The simulation results indicate that the melt exhibits opposite velocity vectors on the upper part and on the lower part of the DCC. Moreover, it encounters and collides at the confluence to generate convection, which is beneficial to obtain uniform melt temperature, composition fields, nuclei exfoliation, and spherical growth. The random particle tracking simulation results show that the DCC process improves the composition field of the slurry. The DCC process facilitates the melt nucleation by using multi-channel chilling and increasing the nucleation area. The self-stirring generated during the flow of the melt produces a large amount of free nuclei inside the melt. There exist two main mechanisms behind the formation of the spherical primary grains. The one is the mechanism of explosive nucleation and spheroidal growth, the other is the dendrite arm necking, fusing, grain ripening, and rounding. Furthermore, by comparing identical alloy castings produced via traditional HPDC and other Rheo-HPDC processes, the DCC Rheo-HPDC castings present finer and rounder grains, a lower porosity, and more performant mechanical properties.

Supersonic antigravity aerodynamic atomization dusting nozzle based on the Laval nozzle and probe jet

To improve the trapping efficiency of respiratory dust by aerodynamic atomization and to maintain the health and safety of workers, a numerical simulation (droplet fragmentation and particle tracking in a high Mach number flow) and an aerodynamic atomization experiment were adopted on the basis of the existing supersonic aerodynamic atomization nozzles that utilize the Laval nozzle as the core. A new type of this kind of nozzle based on a probe structure was designed and optimized. Both the simulation and experimental results have shown that the probe injection method is more suitable for the progress of supersonic aerodynamic atomization. The new nozzle inherits the characteristics of fast droplet speed, conservation of water and pressure, long-range and slow attenuation. The atomization performance of the new nozzle is better than that of traditional nozzles at the same power, and the new nozzle has a larger atomization angle, smaller atomization granularity, lower noise and a more stable atomization output. For the first time, the process of breaking particles by using supersonic gas in the field of dust removal is truly realized. When the pressure is more than 0.1 MPa, antigravity water absorption can be realized. The dust removal rate can be approximately twice as high as that of the traditional ultrasonic atomization method. Compared with the traditional ultrasonic atomization method (84.75%), the dust isolation efficiency can reach 94.07%. The droplets of ultra-fine size with high-speed produced by the new nozzle will have a strong trapping effect on respiratory dust and will save more energy by the vacuum force siphon than currently used nozzles (the amount of gas saved by the same efficiency is 40% and the amount of water saved is 45%).

Depth-Dependent Correction for Wind-Driven Drift Current in Particle Tracking Applications

Predicting the trajectories of buoyant objects drifting at the ocean surface is important for a variety of different applications. To minimise errors in predicted trajectories, the dominant transport mechanisms have to be considered. In addition to the background surface currents (i.e. geostrophic, tidal, baroclinic currents), the wind-driven drift current can have a significant influence on the dynamics of buoyant objects. The drift current consists of two components: Stokes drift and a wind-induced shear current. The drift current has a strong vertical profile that can have a large influence on the transport of buoyant objects. However, few practical methods exist that consider the vertical profile of the drift current when predicting particle pathways on the ocean surface. The aim of this paper is to introduce a depth-dependent drift current correction factor (``drift factor''). We test the usefulness of this drift factor by simulating the transport of two types of ocean surface drifters, released simultaneously within the coverage of a high-frequency ocean radar (HFR) system. Our results show velocity differences between the two types of drifters and the HFR measured ocean surface currents. We suggest that these differences are the result of the drift current vertical profile. Our particle tracking simulations provide an illustrative example, indicating the importance of accounting for a drift factor that takes the variation of the drift current with depth into account.

Multiple spawning events promote increased larval dispersal of a predatory fish in a western boundary current

AbstractTransport of larvae by ocean currents is an important dispersal mechanism for many species. The timing and location of spawning can have a large influence on settlement location. Shifts in the known spawning habitat of fish, whether due to climate or the discovery of new spawning stock, can influence the distribution of juveniles and our understanding of connectivity. The globally distributed species; Pomatomus saltatrix, is one such example where a previously unrecognised summer spawning event and a more southern latitudinal extent was recently reported for the southwest Pacific population. Although restrictions are in place to protect the traditional spawning event, the importance of the newly recognised summer spawning event is uncertain. Here, we investigate larval dispersal of P. saltatrix using particle tracking simulations to identify the contributions of the different spawning events to settlement. By modelling dispersal of larvae released in northern and mid‐latitude regions over the Austral spring and summer, we show that the newly recognised mid‐latitude summer spawning event contributes over 50% of the larvae reaching southern latitudes. This is due to a reduced (1–2 days) pelagic larval duration (associated with temperature), resulting in reduced larval mortality, and the seasonal (summer) strengthening of the East Australian Current (EAC) transporting particles ~50 km further south. These findings demonstrate that in dynamic boundary current systems such as the EAC, the final settlement location of larvae that are transported by ocean currents can vary considerably depending on the timing and location of spawning and that multiple spawning events are important for maximum dispersal.

Numerical simulation of ellipsoidal particles deposition in the human nasal cavity under cyclic inspiratory flow

In this study, a computational fluid dynamics model of a 53-year-old nonsmoking Caucasian male was used to simulate the deposition of ellipsoidal particles under cyclic inhalation in the nasal cavity. A sinusoidal pattern (frequency: 0.25 Hz, maximum volume flow rate: 20 L/min) was set to simulate the realistic breathing pattern under a rest condition. In order to find the trajectory of inhaled particles, a series of unsteady particle tracking simulations using a Lagrangian approach were performed and ellipsoidal particles between 1 and 20 µm in size and 1–50 in aspect ratio were injected in the fluid domain. Results showed that for small particles (d = 1 µm), the deposition pattern follows the airflow pattern, and it increases/decreases by an increase/decrease in the inlet volume flow rate. Besides, the deposition is highly sensitive to the shape of the particles, and it rises by an increase in the aspect ratio. Interestingly, for particles in the range of 5–20 µm, the deposition is mainly dependent on the diameter. Also, the deposition pattern of particles with a diameter of 20 µm is entirely different from the deposition pattern of smaller particles, and it does not follow the inlet airflow pattern. Moreover, it was seen that the deposition fraction under cyclic breathing pattern in the acceleration and deceleration phases of the inhalation is not equal. Finally, it was shown that the inertial force has more contribution to the deposition of ellipsoidal particles, and as a result, tracking these particles under the equivalent mean airflow rate (Q = 12.7 L/min) causes significant errors in the total deposition fraction.

Entropy: (1) The former trouble with particle-tracking simulation, and (2) A measure of computational information penalty

Traditional random-walk particle-tracking (PT) models of advection and dispersion do not track entropy, because particle masses remain constant. However, newer mass-transfer particle tracking (MTPT) models have the ability to do so because masses of all compounds may change along trajectories. Additionally, the probability mass functions (PMF) of these MTPT models may be compared to continuous solutions with probability density functions, when a consistent definition of entropy (or similarly, the dilution index) is constructed. This definition reveals that every discretized numerical model incurs a computational entropy. Similar to Akaike’s (1974, 1992) entropic penalty for larger numbers of adjustable parameters, the computational complexity of a model (e.g., number of nodes or particles) adds to the entropy and, as such, must be penalized. Application of a new computational information criterion reveals that increased accuracy is not always justified relative to increased computational complexity. The MTPT method can use a particle-collision based kernel or an adaptive kernel derived from smoothed-particle hydrodynamics (SPH). The latter is more representative of a locally well-mixed system (i.e., one in which the dispersion tensor equally represents mixing and solute spreading), while the former better represents the separate processes of mixing versus spreading. We use computational means to demonstrate the fitness of each of these methods for simulating 1-D advective-dispersive transport with uniform coefficients.

Simulations of particle tracking in the oligociliated mouse node and implications for left-right symmetry-breaking mechanics.

The concept of internal anatomical asymmetry is familiar-usually in humans the heart is on the left and the liver is on the right; however, how does the developing embryo know to produce this consistent laterality? Symmetry-breaking initiates with left-right asymmetric cilia-driven fluid mechanics in a small fluid-filled structure called the ventral node in mice. However, the question of what converts this flow into left-right asymmetric development remains unanswered. A leading hypothesis is that flow transports morphogen-containing vesicles within the node, the absorption of which results in asymmetrical gene expression. To investigate how vesicle transport might result in the situs patterns observe in wild-type and mutant experiments, we extend the open-source Stokes flow package, NEAREST, to consider the hydrodynamic and Brownian motion of particles in a mouse model with flow driven by one, two and 112 beating cilia. Three models for morphogen-containing particle released are simulated to assess their compatibility with observed results in oligociliated and wild-type mouse embryos: uniformly random release, localized cilium stress-induced release and localized release from motile cilia themselves. Only the uniformly random release model appears consistent with the data, with neither localized release model resulting in significant transport in the oligociliated embryo. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

Mitigation of intensity limitation in the CERN SPS using a double RF system

The Super Proton Synchrotron (SPS) at CERN is the injector of the Large Hadron Collider (LHC). Multi-bunch instabilities limit the intensity of the beam that can be accelerated to 450 GeV in the SPS and transferred to the LHC. Without mitigation measures, the threshold of bunch intensity of the longitudinal instability is three times below the nominal bunch intensity of the LHC beam. The High Luminosity LHC project (HL-LHC), which requires a doubling of the nominal bunch intensity, relies on improvement of beam stability in the SPS. A fourth harmonic RF system allows, presently, to stabilize the beam up to nominal LHC intensity. It increases the synchrotron frequency spread inside the bunch, providing more efficient Landau damping of beam instability. However, nonlinearities of the synchrotron frequency distribution inside the bunch pose a limitation on bunch length. This paper explores possible intensity increase in the SPS by studying the effect on beam stability of the voltage ratio between two RF systems. The results are substantiated by beam measurements and particle-tracking simulations. An optimized voltage program of the second RF system during the cycle has been tested in operation and beam stability and the quality have been successfully improved.

Matrix Diffusion in Fractured Media: New Insights Into Power Law Scaling of Breakthrough Curves

AbstractWe develop a theoretical model for power law tailing behavior of transport in fractured rock based on the relative dominance of the decay rate of the advective travel time distribution, modeled using a Pareto distribution (with tail decaying as ∼ time−(1+α)), versus matrix diffusion, modeled using a Lévy distribution. The theory predicts that when the advective travel time distribution decays sufficiently slowly (α<1), the late‐time decay rate of the breakthrough curve is −(1+α/2) rather than the classical −3/2. However, if α>1, the −3/2 decay rate is recovered. For weak matrix diffusion or short advective first breakthrough times, we identify an early‐time regime where the breakthrough curve follows the Pareto distribution, before transitioning to the late‐time decay rate. The theoretical predictions are validated against particle tracking simulations in the three‐dimensional discrete fracture network simulator dfnWorks, where matrix diffusion is incorporated using a time domain random walk.