Increasing Particle Radius Research Articles

Compensating loss via non-Hermiticity in optically trapped and bounded particles.

The non-Hermiticity in the optical trapping and binding originates from their open nature. Once the non-Hermiticity is sufficiently large such that it pushes the system across the exceptional point, the non-Hermitian force will provide an effective gain to the systems. In this scenario, the trapped particles acquire additional energies as a consequence of the non-Hermitian force field, which effectively serve as a gain. Conversely, these trapped or bound particles can also dissipate energy as a result of the damping effect experienced during oscillation within optical trapping or binding. People usually employ vacuum extraction to extend the lifetime of particles' vibrational modes. However, low-pressure environments can induce instability in the systems. Here, we propose using the "non-Hermitian gain" to compensate for damping loss and enhance the quality factor (lifetime, Q-factor) of vibrational modes. Our study also takes into account the Brownian motion in optical trapping. Nevertheless, even after taking the Brownian motion into account, the Q-factors remained high. We further unveil the physical mechanism that can enhance or diminish non-Hermitian forces, such as increasing particle radius and refractive index and utilizing propagating or standing waves.

Essential magnetosome proteins MamI and MamL from magnetotactic bacteria interact in mammalian cells

To detect cellular activities deep within the body using magnetic resonance platforms, magnetosomes are the ideal model of genetically-encoded nanoparticles. These membrane-bound iron biominerals produced by magnetotactic bacteria are highly regulated by approximately 30 genes; however, the number of magnetosome genes that are essential and/or constitute the root structure upon which biominerals form is largely undefined. To examine the possibility that key magnetosome genes may interact in a foreign environment, we expressed mamI and mamL as fluorescent fusion proteins in mammalian cells. Localization and potential protein-protein interaction(s) were investigated using confocal microscopy and fluorescence correlation spectroscopy (FCS). Enhanced green fluorescent protein (EGFP)-MamI and the red fluorescent Tomato-MamL displayed distinct intracellular localization, with net-like and punctate fluorescence, respectively. Remarkably, co-expression revealed co-localization of both fluorescent fusion proteins in the same punctate pattern. An interaction between MamI and MamL was confirmed by co-immunoprecipitation. In addition, changes in EGFP-MamI distribution were accompanied by acquisition of intracellular mobility which all Tomato-MamL structures displayed. Analysis of extracts from these cells by FCS was consistent with an interaction between fluorescent fusion proteins, including an increase in particle radius. Co-localization and interaction of MamI and MamL demonstrate that select magnetosome proteins may associate in mammalian cells.

Study on the effects of electrode volume fraction and electrode particle radius on dynamic electrochemical-thermal-aging coupling characteristics of lithium cell based on cylindrical cell design method

Electrode volume fraction and electrode particle radius are important electrode parameters for the lithium cell design and deeply influence the electrochemical-physical processes inside lithium cell, which is still insufficiently clear. In order to obtain the effects of electrode parameters on lithium cell, a combine method of the dynamic electrochemical-thermal-aging coupling model and cylindrical cell design was proposed. Simulation was conducted at charge rate 1C. Cell temperature, current density and Solid-Electrolyte-Interface at ambient temperature 25 °C, and total strain energy density and lithium plating at ambient temperature −5 °C were analyzed. As electrode volume fraction or electrode particle radius increases, maximum temperature and maximum temperature difference of lithium cell increase. When electrode volume fraction increases from 0.3 to 0.7, maximum temperature of cell increases by 2.6 °C at least. Current density peak increases with the increase of the positive electrode volume fraction or electrode particle radius. When electrode volume fraction increases from 0.3 to 0.7, current density peak increases by 44 %∼74 %. As electrode volume fraction increases, total strain energy density Ws decreases in the early stage of charge, while increases in the late stage of charge. As the negative (or positive) electrode particle radius increases, Ws of the negative (or positive) electrode increase, while Ws of the positive (or negative) electrode decreases. Solid-Electrolyte-Interface thickness increases with the increase of the electrode volume fraction or electrode particle radius. The effect range of negative electrode volume on lithium plating is 0.5 ∼ 0.7. The lithium metal thickness increase with the increase of the positive electrode volume fraction. As the negative or positive electrode particle radius increases, the lithium metal thickness increase or decrease, respectively.

Molecular dynamics simulations of head-on low-velocity collisions between particles.

The particle contact model is important for powder simulations. Although several contact models have been proposed, their validity has not yet been well established. Therefore, we perform molecular dynamics (MD) simulations to clarify the particle interaction. We simulate head-on collisions of two particles with impact velocities less than a few percent of the sound velocity to investigate the dependence of the interparticle force and the coefficient of restitution on the impact velocity and particle radius. In this study, we treat particles with a radius of 10-100nm and perform simulations with up to 0.2 billion atoms. We find that the interparticle force exhibits hysteresis between the loading and unloading phases. Larger impact velocities result in strong hysteresis and plastic deformation. For all impact velocities and particle radii, the coefficient of restitution is smaller than that given by the Johnson-Kendall-Robert theory, which is a contact model that gives the force between elastic spherical particles. A contact model of inelastic particles cannot reproduce our MD simulations. In particular, the coefficient of restitution is significantly reduced when the impact velocity exceeds a certain value. This significant energy dissipation cannot be explained even by the contact models including plastic deformation. We also find that the coefficient of restitution increases with increasing particle radius. We also find that the previous contact models including plastic deformation cannot explain the strong energy dissipation obtained in our MD simulations, although they agree with the MD results for very low impact velocities. Accordingly, we have constructed a new dissipative contact model in which the dissipative force increases with the stress generated by collisions. The new stress-dependent model successfully reproduces our MD results over a wider range of impact velocities than the conventional models do. In addition, we proposed another, simpler, dissipative contact model that can also reproduce the MD results.

Optomechanical effects caused by non-zero field quantities in multiple evanescent waves.

Evanescent waves, with their high energy density, intricate local momentum, and spatial distribution of spins, have been the subject of extensive recent study. These waves offer promising applications in near-field particle manipulation. Consequently, it becomes imperative to gain a deeper understanding of the impacts of scattering and gradient forces on particles in evanescent waves to enhance and refine the manipulation capabilities. In this study, we employ the multipole expansion theory to present analytical expressions for the scattering and gradient forces exerted on an isotropic sphere of any size and composition in multiple evanescent waves. The investigation of these forces reveals several unusual optomechanical phenomena. It is well known that the scattering force does not exist in counter-propagating homogeneous plane waves. Surprisingly, in multiple pairs of counter-propagating evanescent waves, the scattering force can arise due to the nonzero orbital momentum (OM) density and/or the curl part of the imaginary Poynting momentum (IPM) density. More importantly, it is found that the optical scattering force can be switched on and off by simply tuning the polarization. Furthermore, optical forces typically vary with spatial position in an interference field. However, in the interference field generated by evanescent waves, the gradient force becomes a spatial constant in the propagating plane as the particle's radius increases. This is attributed to the decisive role of the non-interference term of the electromagnetic energy density gradient. Our study establishes a comprehensive and rigorous theoretical foundation, propelling the advancement and optimization of optical manipulation techniques harnessed through multiple evanescent waves. Specifically, these insights hold promise in elevating trapping efficiency through precise control and manipulation of optical scattering and gradient forces, stimulating further explorations.

Phase-field analysis of the effects of particle size, diffusivities, and mechanical properties on the cracking of silicon nanoparticle

In this study, a multiphysics model that reproduces the cracking of Si nanoparticle for a battery application was demonstrated. Two types of cracks appear on Si nanoparticle during lithiation. An essential condition for surface crack (SC) nucleation and propagation is a fast charging rate to form a high concentration gradient of lithium ions near the surface. A slower charging rate induces internal cracks (ICs) radiating from the center of the particle. The critical charging rates, at which SC or IC occurs, decrease rapidly with increasing particle radius. This indicates the difficulty of cracking of small nanoparticles, which is in a good agreement with the previous experimental results. Multiple cracks can appear in the particle, especially when the diffusivity is high. These cracks can be combined during the charging process, leading to the fracture or isolation of the particles. Additionally, two different peak stresses and Young's moduli from the literature were used considering their effects on the cracking of Si nanoparticle films. We believe our results provide a guideline for the fabrication and operation of Si nanoparticle-based anodes for lithium ion batteries.

Optical sorting by trajectory tracking with high sensitivity near the exceptional points

Exceptional points (EPs) in non-Hermitian systems embody abundant new physics and trigger various novel applications. In the optical force system, the motion of a particle near its equilibrium position is determined by the optical force stiffness matrix (OFSM), which is inherently non-Hermitian when the particle is illuminated by vortex beams. In this study, by exploiting the rapid variations in eigenvalues and the characteristics of particle motion near EPs of the OFSM, we propose a method to sort particles with subtle differences in their radii or refractive indices based on their trajectories in air. We demonstrate that the trajectory of a particle with parameters slightly larger than those corresponding to certain EPs closely resembles an ellipse. The increase in the major axis of the ellipse can be several orders of magnitude larger than the increase in particle radius. Furthermore, even a slight change in the refractive index can not only significantly alter the size of the ellipse but also rotate its orientation angle. Hence, particles with subtle differences can be distinguished by observing the significant disparities in their trajectories. This approach holds promise as a technique for the precise separation of micro and nanoscale particles.

A Trans-Scale Study on the Influence of Water Content and Particle Size on Matric Suction

Exploring the water retention properties of unsaturated soil from the perspective of a liquid bridge has been a popular issue in recent years. This study first measures the soil–water characteristic curves (SWCCs) of granular specimens to determine the influence of particle size on matric suction from a macroscopic perspective. Then, the internal mechanism of the influence of particle size and volumetric water content on matric suction is analyzed from the mesoscopic perspective by using the Young–Laplace (Y–L) equation to calculate matric suction between two equal spheres. The macroscopic and mesoscopic experiments both show that matric suction decreases with an increase in particle radius. Moreover, identifying the internal mechanism of SWCC from the liquid bridge perspective is only applicable when the influence of gravity can be disregarded or is in the transitional stage. The influence of volumetric water content and sphere radius on matric suction is mostly caused by the variation in the outer radius of the liquid bridge ( r 1 ) and the neck radius of the liquid bridge ( r 2 ). With an increase in volumetric water content and sphere diameter, the increasing rate of r 1 is much higher than r 2 , and the macroscopical matric suction gradually decreases.

The dynamics of magnetic nanoparticle motion in a straight microvessel

In this study, we investigate the trajectory of magnetic nanoparticle flowing through a microvessel in the presence of cylindrical magnet. By using the equation of motion of particle in the presence of magnetic and fluidic forces, the motion trajectory of magnetic particle in the microvessel is calculated. Our numerical results show that the probability of trapping magnetic particles in the straight microvessel is a function of the intensity of the magnetic field, particle radius, particle magnetization, and diameter of vessel. In this study, we investigate the effect of particle radius, magnet magnetization, particle saturation magnetization and vessel radius on the trajectory of magnetic nanoparticle flowing through the straight vessel. The results show that with increasing particle radius, magnet magnetization, particle saturation magnetization and also with decreasing vessel radius, the probability of trapping a floating particle in the channel increases

Characteristic curves and relationships for surface charging parameters of nonelectrolyte-immersed aqueous cavities

Most properties of charged particles’ dispersions are closely related to the amount of charge residing on the surface of particles. Very few works have been done so far to investigate curvature-dependence of surface potential and charge density of dispersed charged particles. Although there are some experimental studies in the literature on this subject, only a few of them have examined the mathematical relationship between particle size and surface charging parameters, resulting in contradictory findings. Indeed, a universal behavior is yet to be inferred from analysis of the outcomes of these studies since they reported either a roughly constant or decreasing trend of surface charge density with increasing particle radius. Unfortunately, the majority of the limited research efforts on surface charging have focused on dispersion of charged particles in aqueous solutions, but there are systems in biological and engineering worlds where an electrolyte solution is encapsulated in the core of charged particles and immersed in a background non-electrolyte medium. In an attempt to fill this scientific gap and gain a better understanding of surface charging, analytical models are developed in the present work for prediction of surface potential, surface charge, and surface charge density for cylindrical and spherical particles in such systems.First, the problem under investigation is non-dimensionalized to facilitate the modeling process, consider the simultaneous effects of key variables, and generalize the results and behaviors. Then, the mutual relationship between every pair of variables is extracted by employing Gauss's law and combining it with the electro-neutrality condition in an aqueous cavity. Afterwards, the resulting generalized seemingly simple, but inherently complex, integral equations are solved to build the characteristic curves and regressed to derive explicit characteristic equations. Finally, the derived characteristic equations are transformed into a dimensional form to obtain simple formulas for explicit calculations of charging parameters on the surface of electrolyte-encapsulating charged particles in terms of easily measurable properties of the electrolyte solution, the size of the cavity, and thermodynamic conditions. This predictive capability of the new models will significantly reduce the time, costs, and efforts required to simultaneously characterize the size and charging parameters of particles because it removes the need for such a challenging measurement as charging parameters are explicitly related to particle size through thermodynamic conditions, as well as available or easy-to-measure properties of the solution.

Hysteresis characteristics of oxidation-thermodynamic for residual coal in goaf under uniaxial stress

During coal-mining processes underground, the coal spontaneous combustion caused by air leakage of narrow coal pillars and residual coal in goaf under pressure not only threatens the safety of mining of coal resources, but also leads to serious casualties. Therefore, the research of multi-field coupling for broken coal could be helpful to reveal the spontaneous combustion law of narrow coal pillars and residual coal in goaf and find the key for coal-fire prevention and control. Therefore, the uniaxial compression equipped with a temperature-programmed device is applied to conduct stress-heating tests on five types of coal particle sizes. Moreover, based on the Hertz contact deformation principle under the three-particle model, the thermodynamic hysteresis characteristics of broken coal under uniaxial stresses are theoretically analyzed. The results are shown as follows: (i) Uniaxial stress leads to significant hysteresis effects on the critical temperature of coal spontaneous combustion, heating rate, Graham’s Ratio-R2 temperature coefficient and pyrolysis temperature. (ii) As the particle radius increases, the growth rate of the exothermic intensity is suppressed, while it has no inhibitory effect on the critical temperature of the minimum exothermic intensity. (iii) The extreme point for the limit parameter of coal spontaneous combustion and the critical temperature shows the same corresponding hysteresis under uniaxial stress. The particle size ratio changes the limit parameter of coal spontaneous combustion obviously, and coal with a large particle size would reduce the risk of spontaneous combustion. (iv) The stress–strain curves and the stress-porosity curves are divided into stages, and it is found that the critical uniaxial stress of the porosity and strain of each coal sample is up to 4 MPa. Moreover, the temperature is the main reason for the hysteresis of permeability. The stress sensitivity of permeability declines with the effective stress rising, increases with the temperature going up, and decreases with the coal particle size reducing. (v) The hysteresis effect of uniaxial stress on coal spontaneous combustion first increases, then decreases, and finally increases.

Spatiotemporal changes in aerosol properties by hygroscopic growth and impacts on radiative forcing and heating rates during DISCOVER-AQ 2011

Abstract. This work focuses on the characterization of vertically resolved aerosol hygroscopicity properties and their direct radiative effects through a unique combination of ground-based and airborne remote sensing measurements during the Column and Vertically Resolved Observations Relevant to Air Quality (DISCOVER-AQ) 2011 field campaign in the Baltimore–Washington DC metropolitan area. To that end, we combined aerosol measurements from a multiwavelength Raman lidar located at NASA Goddard Space Flight Center and the airborne NASA Langley High Spectral Resolution Lidar-1 (HSRL-1) lidar system. In situ measurements aboard the P-3B airplane and ground-based Aerosol Robotic Network – Distributed Regional Aerosol Gridded Observational Network (AERONET-DRAGON) served to validate and complement quantifications of aerosol hygroscopicity from lidar measurements and also to extend the study both temporally and spatially. The focus here is on 22 and 29 July 2011, which were very humid days and characterized by a stable atmosphere and increasing relative humidity with height in the planetary boundary layer (PBL). Combined lidar and radiosonde (temperature and water vapor mixing ratio) measurements allowed the retrieval of the Hänel hygroscopic growth factor which agreed with that obtained from airborne in situ measurements and also explained the significant increase of extinction and backscattering with height. Airborne measurements also confirmed aerosol hygroscopicity throughout the entire day in the PBL and identified sulfates and water-soluble organic carbon as the main species of aerosol particles. The combined Raman and HSRL-1 measurements permitted the inversion for aerosol microphysical properties revealing an increase of particle radius with altitude consistent with hygroscopic growth. Aerosol hygroscopicity pattern served as a possible explanation of aerosol optical depth increases during the day, particularly for fine-mode particles. Lidar measurements were used as input to the libRadtran radiative transfer code to obtain vertically resolved aerosol radiative effects and heating rates under dry and humid conditions, and the results reveal that aerosol hygroscopicity is responsible for larger cooling effects in the shortwave range (7–10 W m−2 depending on aerosol load) near the ground, while heating rates produced a warming of 0.12 K d−1 near the top of PBL where aerosol hygroscopic growth was highest.

Surface stress of gold nanoparticles revisited

The surface energy has been one of the topics of atomistic research for nanoparticles in the last decades. However, the physical role of surface stress and its quantification have been a lot less an object of research. Assumptions for the surface stress, going back to the thermodynamic basis of continua, have been popular. As an example the surface stress (state) follows as derivatives of the surface energy with a rather “classical” evolution equation for the deformation energy. The current concept introduces a combination of atomistic modelling and continuum mechanics for a core–shell system. Considering crystalline and amorphous gold nanoparticles with radii in the range of 1 nm to 12 nm, we are finally able to independently calculate the values of surface stress and surface energy, both slightly decreasing with the increasing particle radius. Surprisingly large values of surface stress are predicted for the case of amorphous nanoparticles.

A Unified Approach to Disjoining Pressure in Liquid and Vapor Interlayer within the Framework of the Density Functional Theory

The classical density functional theory makes it possible to explicitly calculate the local density profiles, the components of the pressure tensor, and the thicknesses of thin interlayers between a lyophilic or lyophobic solid surface and, accordingly, gas or liquid phases at different values of the chemical potentials of the phases. Within the framework of a unified approach based on the gradient approximation of the classical density functional theory, it has been shown that, at certain values of parameters characterizing the wettability or nonwettability of a solid, equilibrium liquid films or vapor layers of a uniform thickness are formed around a spherical particle, if its surface is lyophilic or lyophobic, respectively. Mechanical and thermodynamic definitions have been given for the disjoining pressure in the spherical liquid or vapor interlayer around a solid particle, and the agreement between the definitions has been proven by calculations at different interlayer thicknesses and particle radii. It has been shown that the disjoining pressure in a vapor interlayer around a nanosized lyophobic particle decreases with an increase in particle radius, with this phenomenon being opposite to the situation with liquid films.

Application of Multiple Detection Data in the Analysis of Snowstorm Processes in Xinjiang during the Central Asia Extreme Precipitation Observation Test (CAEPOT)

At present, there is insufficient research on the refinement of the vertical structure of winter snowstorm systems in arid areas, and, compared with the central and eastern China, the observation sites in arid areas of northwestern China are scarce. To deepen the understanding of dynamics and microphysical processes and improve the level of forecasting and warning of snowstorms in northwestern China, the Institute of Desert Meteorology, China Meteorological Administration, Urumqi, carried out the Central Asia Extreme Precipitation Observation Test (CAEPOT) in Yili, Xinjiang, a typical arid region in China in February 2020. This paper uses multiple fine detection datasets obtained from the CAEPOT, including radar wind profiler, ground-based microwave radiometer, and millimeter-wave cloud radar to analyze macroscopic characteristics and microphysical changes of snowstorm system in Xinjiang. Studies have shown that the low trough with sufficient moisture, heat, power conditions, and weakening banded cloud system, which moved eastward from the Aral Sea to the west of Xinjiang during the snowstorm, were the key influencing system of this snowstorm. Before the snowstorm, the vertical shear of the horizontal wind field was severe, which aggravated the instability of the atmosphere, and there was upward motion in the lower atmosphere. A variety of physical quantities related to moisture showed a tendency to increase at the lower level and could be used as an early warning signal for snowstorm about 8 hours in advance, and the cloud and snow particles observed by millimeter-wave cloud radar were simultaneously developing upward and downward from 4 km, providing snowstorm warning 12 hours in advance. During the snowstorm, the horizontal wind speed and vertical speed were obviously enhanced, and the physical quantities related to moisture further increased, and, with the blocking and uplifting of the Tianshan Mountains, the snowstorm increased. The particles collided and grew while falling, resulting in a decrease in particle concentration and an increase in particle radius from high altitude to the ground, eventually resulting in near-ground reflectivity factor up to 30 dBz. In addition, reflectivity factor, physical quantities related to moisture, wind field, particle concentration, and particle radius all had a good correspondence with the beginning, end, and intensity of snowstorm, so when the physical quantities mentioned above weakened and stopped, snowstorm also weakened and stopped. In a word, this research is an important and meaningful work that provides more backgrounds and references for the forecast and warning of snowstorm in northwestern China.

A mathematic model for the soil freezing characteristic curve: the roles of adsorption and capillarity

The relationship between the unfrozen water content in frozen soil and negative temperature is defined as the soil freezing characteristic curve (SFCC). The SFCC plays a crucial role in understanding the hydrothermal migration, frost heaving and constitutive relations of frozen soil. The mechanism of the SFCC is less understood, especially in the low-temperature range. Considering the adsorption and capillary action between soil particles and the ice interface, a new SFCC model for saturated frozen soil is proposed from the pore scale. The predicted results of the model show that the unfrozen water content gradually decreases with the increasing particle radius at the same temperature. The SFCC of monodisperse silica microspheres and quartz sand samples were tested based on nuclear magnetic resonance technology. The experimental results were compared with the mathematical model, which showed that the new SFCC model is in good agreement with the experimental results. The new model has a clear physical meaning and can provide a theoretical basis for understanding the phase change process in frozen soils, which is of great significance to the application of the proposed model.

The photothermal property of zinc oxide nanoparticles in the infrared spectrum

Based on the discrete dipole approximation (DDA) algorithm, the absorption spectra and near electric field of ZnO nanospheres with the radius of 10−30 nm in the infrared band were calculated. The position of absorption peak is slight blue-shift when the particle radius increases, and it is red-shift with the ambient refractive index. The near-field enhancement was calculated at the resonance wavelength, the results show that it increases with the particle radius, but it decreases with the ambient refractive index. The spatial distribution of temperature was analyzed when ZnO nanoparticle was incident by infrared light, and it was found that the maximum of temperature rising inside the particle increases with the absorption cross-section of the particle.

Performance Analysis of the Shore-to-Reef Atmospheric Continuous-Variable Quantum Key Distribution

The effects of sea salt concluded in oceanic atmosphere are ubiquitous in practical wireless optical links. Here a shore-to-reef atmospheric continuous-variable quantum key distribution (CVQKD) model is established on the basis of Mie scattering theory, with the aim to characterize the complex case of beam propagation in the atmosphere caused by sea salt particles. The effects on performance of shore-to-reef atmospheric CVQKD under the sea salt particles and relative humidity are also studied. Simulation results show that the increase of particle radius and relative humidity will lead to the degeneration of secret key rate. Extending the channel distance also reduces the secret key rate. This paper provides a basis for the establishment of practical shore-to-reef atmospheric CVQKD model. The research of this paper also gives momentous reference for the study of optical communication channel models with other suspended particles over the ocean.

Numerical Simulation of Plasma‐Propellant Interaction Under the Non‐Fourier Model

AbstractDue to the signicant characteristics of shorter and more reproducible ignition delay, plasma ignition becomes one of the key technologies of electrothermal‐chemical (ETC) propulsion. Plasma ignition is a complex heat transfer process, characterized by high temperature, high pressure, micro‐scale and extremely short duration. Under such extreme conditions, the assumption that the propagation speed of thermal disturbance is infinite in Fourier's law is no longer applicable. As such, for accurate prediction the non‐Fourier model with dual‐phase‐lag (DPL) is adopted to describe the interaction process between the plasma and the propellant. The temperature history of propellant is obtained by Dufort‐frankel numerical difference method. The numerical results obtained by DPL model are compared with the results by the Fourier model and Cattaneo‐Vernotte (C−V) model, it shows that the DPL model occupies preferable prediction performance. Additionally, the effects of plasma temperature, particle radius and absorber thickness on ignition delay are discussed. It finds that the ignition delay decreases with the increase of plasma temperature, increases with the increase of particle radius, and increases with the increase of absorber thickness. The numerical results based on DPL model are verified by the experimental results as well.

Numerical study on shock–dusty gas cylinder interaction

The interaction of a planar shock wave with a dusty-gas cylinder is numerically studied by a compressible multi-component solver with an adaptive mesh refinement technique. The influence of non-equilibrium effect caused by the particle relaxation, which is closely related to the particle radius and shock strength, on the evolution of particle cylinder is emphasized. For a very small particle radius, the particle cloud behaves like an equilibrium gas cylinder with the same physical properties as those of the gas–particle mixture. Specifically, the transmitted shock converges continually within the cylinder and then focuses at a region near the downstream interface, producing a local high-pressure zone followed by a particle jet. Also, noticeable secondary instabilities emerge along the cylinder edge and the evident particle roll-up causes relatively large width and height of the shocked cylinder. As the particle radius increases, the flow features approach those of a frozen flow of pure air, e.g., the transmitted shock propagates more quickly with a weaker strength and a smaller curvature, resulting in an increasingly weakened shock focusing and particle jet. Also, particles would escape from the vortex core formed at late stages due to the larger inertia, inducing a greater particle dispersion. It is found that a large particle radius as well as a strong incident shock can facilitate such particle escape. The theory of Luo et al. (J. Fluid Mech., 2007) combined with the Samtaney–Zabusky (SZ) circulation model (J. Fluid Mech., 1994) can reasonably explain the high dependence of particle escape on the particle radius and shock strength.