Spherical Tracer Research Articles

Superdiffusion and heterogeneous dynamics in liquid crystals by microrheology

Microrheology (MR) has emerged as a powerful tool for unraveling the intricate local viscoelastic properties of various soft materials. By tracking the free (passive MR) or forced (active MR) diffusion of a tracer, valuable insights into the mechanical characteristics of the host system can be obtained. In this study, we investigate the forced diffusion of a spherical tracer within isotropic and smectic liquid crystal phases of hard rod-like particles. Our findings reveal superdiffusive behaviour induced by external forces, particularly pronounced when these are aligned parallel to the nematic director. Analysis of the dynamical susceptibility unveils heterogeneities strongly correlated with the magnitude and orientation of applied forces, highlighting the system's critical dependence on structural ordering. Intriguingly, we observe that tracer superdiffusion, driven by external forces and evident across all relevant system directions, does not demonstrate a strong correlation with resulting dynamical heterogeneities.

Tracer dynamics in polymer networks: Generalized Langevin description.

Tracer diffusion in polymer networks and hydrogels is relevant in biology and technology, while it also constitutes an interesting model process for the dynamics of molecules in fluctuating, heterogeneous soft matter. Here, we systematically study the time-dependent dynamics and (non-Markovian) memory effects of tracers in polymer networks based on (Markovian) implicit-solvent Langevin simulations. In particular, we consider spherical tracer solutes at high dilution in regular, tetrafunctional bead-spring polymer networks and control the tracer-network Lennard-Jones (LJ) interactions and the polymer density. Based on the analysis of the memory (friction) kernels, we recover the expected long-time transport coefficients and demonstrate how the short-time tracer dynamics, polymer fluctuations, and the viscoelastic response are interlinked. Furthermore, we fit the characteristic memory modes of the tracers with damped harmonic oscillations and identify LJ contributions, bond vibrations, and slow network relaxations. Tuned by the LJ interaction parameter, these modes enter the kernel with an approximately linear to quadratic scaling, which we incorporate into a reduced functional form for convenient tracer memory interpolation and extrapolation. This eventually leads to highly efficient simulations utilizing the generalized Langevin equation, in which the polymer network acts as an additional thermal bath with a tunable intensity.

Radar-Based Particle Localization in Densely Packed Granular Assemblies

Particle tracking in densely packed granular assemblies is of great interest in mechanical process engineering. In this contribution, a radar-based system for particle localization as an initial step towards tracking is presented. This system comprises six transmitting and receiving antennas forming a “multiple-input multiple-output” setup positioned around a cuboidal reactor. The reactor is a standard batch grate system, which contains stationary spherical polyoxymethylene particles with a 10 mm diameter and a spherical steel tracer particle with a 20 mm diameter. The tracer is positioned at various locations at an optically transparent reactor wall. Electromagnetic waves must pass through the remaining three reactor walls to detect the tracer particle. Operating in the Frequency Modulated Continuous Wave mode within a 1.5 to 8.5 GHz frequency range, we compared radar-detected tracer positions with those from camera images. The results demonstrate a vertical localization accuracy with a standard deviation of σvert= 0.86 cm and a horizontal position accuracy with σhor= 0.17 cm. This study not only presents the achievements of radar-based particle localization but also delves into the potential and challenges of applying this technology to a specific measurement scenario within mechanical process engineering.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations.

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Dynamics of a spherical self-propelled tracer in a polymeric medium: interplay of self-propulsion, stickiness, and crowding.

We employ computer simulations to study the dynamics of a self-propelled spherical tracer particle in a viscoelastic medium, made of a long polymer chain. Here, the interplay between viscoelasticity, stickiness, and activity (self-propulsion) brings additional complexity to the tracer dynamics. Our simulations show that on increasing the stickiness of the tracer particle to the polymer beads, the dynamics of the tracer particle slows down as it gets stuck to the polymer chain and moves along with it. But with increasing self-propulsion velocity, the dynamics gets enhanced. In the case of increasing stickiness as well as activity, the non-Gaussian parameter (NGP) exhibits non-monotonic behavior, which also shows up in the re-scaled self part of the van-Hove function. Non-Gaussianity results owing to the enhanced binding events and the sticky motion of the tracer along with the chain with increasing stickiness. On the other hand, with increasing activity, initially non-Gaussianity increases as the tracer moves through the heterogeneous polymeric environment but for higher activity, the tracer escapes resulting in a negative NGP. For higher values of stickiness, the trapping time distributions of the passive tracer particle broaden and have long tails. On the other hand, for a given stickiness with increasing self-propulsion force, the trapping time distributions become narrower and have short tails. We believe that our current simulation study will be helpful in elucidating the complex motion of activity-driven probes in viscoelastic media.

Effective drag on spheres immersed in a fluidized bed at minimum fluidization—Influence of bulk solids properties

AbstractThe aims of this work are to elucidate the effects that bulk solids properties have on the effective drag experienced by large spheres immersed in an emulsion of group‐B solids under minimum fluidization conditions and to analyze the ways in which the different suspensions react towards different applied shear rates. To investigate this, magnetic particle tracking was applied to resolve the trajectory of falling‐sphere measurements in which the size, density, and sphericity of the bulk solids were varied as well as the size and density of the spherical tracers. The resulting experimental scope included both rising and sinking tracers as well as full segregation and in‐bed stagnation of the tracers. The set‐up provided highly resolved tracer trajectories, from which the drag experienced by the sphere can be calculated. For sinking tracers, the results showed that an increase in bulk solids size, angularity, and density reduced the terminal velocity of the sphere. This effect correlated well with the bed expansion and Hausner ratio, indicating that a reduced void space among the bulk solids is the main reason for the increase in motion resistance. At lower shear rates, namely, during the de‐acceleration towards the stagnant state, beds of larger, more angular, or denser bulk solids yield lower levels of shear stress. The angle of repose of the bulk solids correlated with the rate at which the emulsion thins with increasing shear rate. For rising tracers, shear stress did not show any significant dependency on the properties of the bulk solids.

The structure of cellulose nanofibril networks at low concentrations and their stabilizing action on colloidal particles

The structure and dynamics of networks formed by rod-shaped particles can be indirectly investigated by measuring the diffusion of spherical tracer particles. This method was used to characterize cellulose nanofibril (CNF) networks in both dispersed and arrested states, the results of which were compared with coarse-grained Brownian dynamics simulations. At a CNF concentration of 0.2 wt% a transition was observed where, below this concentration tracer diffusion is governed by the increasing macroscopic viscosity of the dispersion. Above 0.2 wt%, the diffusion of small particles (20–40 nm) remains viscosity controlled, while particles (100–500 nm) become trapped in the CNF network. Sedimentation of silica microparticles (1–5 μm) in CNF dispersions was also determined, showing that sedimentation of larger particles is significantly affected by the presence of CNF. At concentrations of 0.2 wt%, the sedimentation velocity of 5 μm particles was reduced by 99 % compared to pure water.

Activation energy, spatial confinement, and mean first passage and escape times of a tracer in a wormlike micellar fluid: an effective potential approach

Wormlike micelles are long semiflexible cylindrical polymer structures formed by amphiphiles. In solution, these linear micelles percolate in multiconected entangled networks, where cross-links can break and recombine dynamically. Technological applications of wormlike micellar fluids include tunable encapsulation/delivery of molecules or colloids in biomedicine, oil industry, and/or cleaning processes. In this work, we propose that the experimental activation energy, the spatial confinement, and the mean first passage and escape times of a spherical tracer immersed in wormlike micellar network, in which caging effects are observed, can be estimated from economic Brownian dynamics simulations of a single particle interacting with an effective one-dimensional cosine-like potential of amplitude U 0 and periodicity L. The proposed one-fitting parameter method has been used to characterize the long-time dynamics of wormlike micellar solutions formed by the self-assembly of a mixture of zwitterionic and anionic surfactants at several temperatures and different concentrations of surfactant and brine. The amplitude U 0 has displayed a good agreement regarding the corresponding experimental activation energy at different temperatures. The periodicity L has shown to be an upper bound of the mesh size ξ and of the same order of magnitude regarding the entanglement length l e, obtained from rheology and microrheology experiments. The escape time of the tracer in the effective potential τ escape and the time t*, at which a change of curvature in the mean square displacement occurs, are upper and lower limits, respectively, of the experimental relaxation time. Our method is simple and fast, and we foresee that it should be applicable to model the long-time behaviour of tracers in other polymer systems, in which caging effects are present.

On the determination of 3D position and orientation of spheroidal particles using defocusing and deep learning

Tracking the 3D position of tracer particles or small objects like cells or unicellular organisms in miniaturized lab-on-a-chip or biomedical devices is complicated since it is often not possible in these setups to use multi-camera approaches. Most successful single-camera approaches for these applications are based on holography or defocusing. Holographic methods have been used to track complex objects such has bacteria (Bianchi et al. (2019)) and even to estimate their orientation (Wang et al. (2016)). However, these methods require a complex and expensive experimental setup which is not always available in research laboratories. On the other hand, defocusing methods work with conventional microscopic optics, are easy to implement, and have shown excellent results in 3D PTV experiments (Qiu et al. (2019)). One main drawback is that they normally work only with spherical and mono-dispersed tracer particles. A defocusing method that has potential to measure non-spherical particles is the General Defocusing Particle Tracking (Barnkob and Rossi (2020)) which is based on pattern recognition and can be conceptually extended to more complex tasks by extending the reference library of particle images, including not only spherical particles at different depth positions, but also non-spherical particles at different orientations. However, whether this approach could work in practice is still unknown. First, is the information contained in simple defocused images sufficient to reconstruct depth and orientation of non-spherical particles, and eventually under which circumstances? Second, how to practically collect the labelled reference images?

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses.

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical "slaving onset" stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.

Microrheology of colloidal suspensions via dynamic Monte Carlo simulations

Understanding the rheology of colloidal suspensions is crucial in the formulation of a wide selection of industry-relevant products, such as paints, foods and inks. To characterise the viscoelastic behaviour of these soft materials, one can analyse the microscopic dynamics of colloidal tracers diffusing through the host fluid and generating local deformations and stresses. This technique, referred to as microrheology, links the bulk rheology of fluids to the microscopic dynamics at the particle scale. If tracers are subjected to external forces, rather than freely diffusing, it is called active microrheology. Motivated by the impact of microrheology in providing information on local structure in complex systems such as colloidal glasses, active matter or biological systems, we have extended the dynamic Monte Carlo (DMC) technique to investigate active microrheology in colloidal suspensions. The original DMC theoretical framework, able to accurately describe the Brownian dynamics of colloids at equilibrium, is here reconsidered and expanded to describe the effects of an external force pulling a tracer embedded in isotropic colloidal suspensions at different densities. To this end, we studied the dynamics of a spherical tracer dragged by a constant external force through a bath of spherical and rod-like particles of comparable size. We could extract valuable details on its effective friction coefficient, being constant at small and large values of the external force, but otherwise displaying a nonlinear behaviour that indicates the occurrence of a force-thinning regime. Our DMC simulation results are in excellent quantitative agreement with past Langevin dynamics simulations and theoretical works for the bath of spherical colloids. The bath of rod-like particles is studied in the isotropic phase, and displays an example where DMC is more convenient than Brownian or Langevin dynamics, in this case, in dealing with particle rotation.

Diffusion of globular macromolecules in liquid crystals of colloidal cuboids

Macromolecular diffusion in dense colloidal suspensions is an intriguing topic of interdisciplinary relevance in Science and Engineering. While significant efforts have been undertaken to establish the impact of crowding on the dynamics of macromolecules, less clear is the role played by long-range ordering. In this work, we perform Dynamic Monte Carlo simulations to assess the importance of ordered crowding on the diffusion of globular macromolecules, here modelled as spherical tracers, in suspensions of colloidal cuboids. We first investigate the diffusion of such guest tracers in very weakly ordered host phases of cuboids and, by increasing density above the isotropic-to-nematic phase boundary, study the influence of long-range orientational ordering imposed by the occurrence of liquid–crystalline phases. To this end, we analyse a spectrum of dynamical properties that clarify the existence of slow and fast tracers and the extent of deviations from Gaussian behaviour. Our results unveil the existence of randomly oriented clusters of cuboids that display a relatively large size in dense isotropic phases, but are basically absent in the nematic phase. We believe that these clusters are responsible for a pronounced non-Gaussian dynamics that is much weaker in the nematic phase, where orientational ordering smooths out such structural heterogeneities.

Simulation study of passive rod diffusion in active bath: Nonmonotonic length dependence and abnormal translation-rotation coupling

Diffusion of tracer particles in active bath has attracted extensive attention in recent years. So far, most studies have considered isotropic spherical tracer particles, while the diffusion of anisotropic particles has rarely been involved. Here we investigate the diffusion dynamics of a rigid rod tracer in a bath of active particles by using Langevin dynamics simulations in a two-dimensional space. Particular attention is paid to how the translation (rotation) diffusion coefficient DT (DR) change with the length of rod L and active strength Fa. In all cases, we find that rod exhibits superdiffusion behavior in a short time scale and returns to normal diffusion in the long time limit. Both DT and DR increase with Fa, but interestingly, a nonmonotonic dependence of DT (DR) on the rod length has been observed. We have also studied the translation-rotation coupling of rod, and interestingly, a negative translation-rotation coupling is observed, indicating that rod diffuses more slowly in the parallel direction compared to that in the perpendicular direction, a counterintuitive phenomenon that would not exist in an equilibrium counterpart system. Moreover, this anomalous (diffusion) behavior is reentrant with the increase of Fa, suggesting two competitive roles played by the active feature of bath particles.

Visual analysis of three-dimensional flow field based on WebVR

Abstract With the rapid development of internet technologies, it is possible to provide computing services and visualize calculated results on the internet. A three-dimensional flow field visualization method based on WebVR is presented in this paper. We devised and built an immersive and interactive three-dimensional virtual reality scene employing web-standard technologies (i.e., HTML5, JavaScript, WebGL, and Ajax) and computing services provided by hydrodynamic software, using GPUs to accelerate the display of flow field in the browser, without the use of plug-ins. On the basis of three-dimensional topography and surface flow field, a three-dimensional flow field presentation method of superimposing multiple sections into the original computational domain was proposed. Furthermore, the description of tracer sphere and path line was adopted to describe the structure characteristics of the flow field. Replacing complete three-dimensional sphere models with textured stylized particles improved the frame rate of the browser greatly when rendering animations. This research enables developers and users of the hydrodynamic model to be immersed in their data of flow field using Google Cardboard. As far as we know, this is the first time that WebVR technology has been applied in three-dimensional hydrodynamic simulation.

Settling tracer spheroids in vertical turbulent channel flows

The motion of particles settling in turbulence is an intriguing problem, which is relevant to an in-depth understanding of planktons in marine flows or the design of photobioreactors. This work studies the motion, orientation and distribution of inertia-less spheroidal particles settling in vertical channel flows by direct numerical simulations. We show that, compared to spherical tracers, the settling velocity of spheroidal tracers is enhanced due to preferential orientation and local clustering (not due to particle inertia, in the present case). Prolate spheroids tend to align their symmetry axes in the direction of gravity while oblate ones align perpendicular to it. Both kinds of particles attain a larger slip velocity in the direction of gravity and, therefore, settle faster. We also show that particles sample preferentially regions of high fluid velocity in downward flow and regions of low fluid velocity in upward flow. Such preferential sampling, which also contributes to the enhancement of settling, is the result of clustering. Besides, tracer particles are observed to accumulate in the channel center in downward flow and near the wall in upward flow: We show that tracer transport in the wall-normal direction is controlled by the particle-to-fluid slip velocity and by clustering. The slip velocity dominates the transport initially, but tracers increasingly cluster in regions with opposite flow direction as they accumulate either in the channel center or near the wall. Clustering appears to be associate with the coherent structures that characterize wall turbulence, and tracer distribution in the wall-normal direction is found to reach a steady state when the two qualitatively different mechanisms balance each other.

Novel Activated Microbubbles-based Strategy to Coat Nanoparticles on Root Canal Dentin: Fluid Dynamical Characterization

IntroductionActivated microbubbles (MBs) have the potential to deliver nanoparticles in complex microspaces such as root canals. The objective of the study is to determine the fluid dynamical parameters associated with ultrasonic, sonic, and manual activation of MBs in simulated root canals and to assess the effectiveness of surface coating formed by delivering chitosan nanoparticles using activated MBs within root canals in extracted teeth. MethodsIn stage 1, polydimethylsiloxane models were fabricated to determine the physical effects of MBs agitated manually (MM), sonically (MS), and ultrasonically (MU). Spherical tracer particles were used to visualize and record the fluid motion using an inverted microscope linked to a high-speed camera. The velocity, wall stress, and penetration depth were analyzed at regions of interest. In stage 2, 35 extracted human incisors were divided into 7 groups to evaluate the effectiveness of chitosan nanoparticle delivery using activated MBs (MM, MS, and MU groups). Field emission scanning electron microscopy and energy-dispersive X-rays were used to characterize the nanoparticle coating on root canal dentin and the degree of dentinal tubule occlusion. ResultsIn stage 1, velocity, wall stress, and penetration depth increased significantly in the MB groups compared with the control (P < .01). In stage 2, 70% of the dentin surface was coated, and 65% of the dentinal tubule was occluded with nanoparticle-based coating in the MM, MU, and water ultrasonic groups. Element analysis displayed the presence of dentin smear on the root canal surface for the MU and water ultrasonic groups. ConclusionsActivated MBs enhanced fluid dynamical parameters when compared with water in simulated root canal models. Manual activation of MBs resulted in uniform and significant nanoparticle-based surface coating and tubule blockage in root canal dentin without dentin smear formation.

Effect of bed characteristics on separation behavior of coal particles in a gas-solid fluidized bed

Air dense medium fluidized bed can achieve effective separation of −50 + 6 mm coal. However, the bed characteristics significantly affect the separation behavior of coal particles. The results indicated that the bed critical expansion degree decreased with increase in static bed height, and the axial distribution coefficient of low-density particles increased from 0.798 at Hs = 60 mm to 0.950 at Hs = 180 mm with raising concentration of emulsified-phase particles, which revealed low bed height is advantageous for particles floatation, while bed density is not the main action factor in this process. As for bubble dimension calculation model, the Kato and Wen formula is favored for smaller relative error for 0.3–0.25 mm bed particles. In addition, separation was difficult when the density difference between the bed and the tracer spheres was more than 0.3 g/cm3, and the λ value was almost constant with increase in fluidization number for each sphere whose density difference was less than 0.3 g/cm3. With increasing Δρ from 0.07 g/cm3 to 0.27 g/cm3, the λ values for d = 38, 25, and 15 mm increased from 0.44, 0.69, and 1.54 to 0.64, 1.00, and 2.01, respectively.

Real-space imaging of translational and rotational dynamics of hard spheres from the fluid to the crystal.

Using real-space imaging of single particles, we investigate the interplay between translational and rotational motion of tracer particles in suspensions of colloidal particles over a wide range of volume fractions from dilute fluid to densely packed crystal. To this end, we introduce a new type of spherical colloidal tracer particles containing two differently labelled fluorescent cores. The tracer particles can be combined with host particles enclosing a single fluorescent core and chemical and physical properties identical to the tracers. This leads to a system of spherical colloidal particles, in which spatio-temporal trajectories of rotation and translation of individual particles can be recorded simultaneously with full 360° resolution of rotational dynamics. Our analysis shows that translation and rotation of colloidal particles are uncorrelated and decoupled for all volume fractions irrespective of the phase of the particle system.

Dynamics of ellipsoidal tracers in swimming algal suspensions.

Enhanced diffusion of passive tracers immersed in active fluids is a universal feature of active fluids and has been extensively studied in recent years. Similar to microrheology for equilibrium complex fluids, the unusual enhanced particle dynamics reveal intrinsic properties of active fluids. Nevertheless, previous studies have shown that the translational dynamics of spherical tracers are qualitatively similar, independent of whether active particles are pushers or pullers-the two fundamental classes of active fluids. Is it possible to distinguish pushers from pullers by simply imaging the dynamics of passive tracers? Here, we investigated the diffusion of isolated ellipsoids in algal C. reinhardtii suspensions-a model for puller-type active fluids. In combination with our previous results on pusher-type E. coli suspensions [Peng et al., Phys. Rev. Lett. 116, 068303 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.068303], we showed that the dynamics of asymmetric tracers show a profound difference in pushers and pullers due to their rotational degree of freedom. Although the laboratory-frame translation and rotation of ellipsoids are enhanced in both pushers and pullers, similar to spherical tracers, the anisotropic diffusion in the body frame of ellipsoids shows opposite trends in the two classes of active fluids. An ellipsoid diffuses fastest along its major axis when immersed in pullers, whereas it diffuses slowest along the major axis in pushers. This striking difference can be qualitatively explained using a simple hydrodynamic model. In addition, our study on algal suspensions reveals that the influence of the near-field advection of algal swimming flows on the translation and rotation of ellipsoids shows different ranges and strengths. Our work provides not only new insights into universal organizing principles of active fluids, but also a convenient tool for detecting the class of active particles.

Tracer motion in an active dumbbell fluid

The diffusion properties of spherical tracers coupled through a repulsive potential to a system of active dumbbells are analyzed. We model the dumbbells’ dynamics with Langevin equations and the activity with a self-propulsive force of constant magnitude directed along the main axis of the molecules. Two types of tracers are considered. Thermal tracers are coupled to the same bath as the dumbbells while athermal tracers are not; both interact repulsively with the dumbbells. We focus our attention on the intruders’ mean square displacement and how it compares to the one of the dumbbells. We show that the dynamics of thermal intruders, with mass similar to the one of the dumbbells, display the typical four time-lag regimes of the dumbbells’ mean square displacement. The thermal tracers’ late-time diffusion coefficient depends on their mass very weakly and it is close to the one of the dumbbells at low Péclet only. Athermal tracers only have ballistic and late-time diffusive regimes. The late time diffusion coefficients of athermal tracers and dumbbells have similar values at high Péclet number when their masses are of the same order, while at low Péclet number this coefficient gets close to the one of the dumbbells only when the tracers are several order of magnitude heavier than the dumbbells. We propose a generalization of the Enskog law for dilute hard disks, that describes the athermal tracers’ mean square displacement in the form of a scaling law in terms of their mass.