Free Molecular Regime Research Articles

A stochastic particle model for aggregate morphology and particle size distributions under coagulation process

A new simple and efficient particle model is proposed in the present study based on the ballistic cluster–cluster agglomeration (BCCA) mechanism. The proposed Random Orientation-Tangent Point (ROTP-BCCA) model is implemented into the Monte Carlo method to investigate the aggregate coagulation process under the free molecular regime. The proposed ROTP-BCCA model is firstly used to predict the fractal characteristics of aggregates composed of monodispersed primary particles and validated by the previously reported results and is compared with the method of Lindberg et al. (L-BCCA model). Then the effects of primary particle polydispersity on the fractal characteristics, the first three order moments and the particle size distributions (PSD) of the aggregates are also investigated. The results show that the obtained fractal characteristics, the first three order moments and the particle size distributions of the aggregates for monodispersed and polydispersed primary particles from the present ROTP-BCCA model agree well with the results of L-BCCA model. Furthermore, the computational efficiency of the present proposed ROTP-BCCA model is proved to be much higher than the L-BCCA model.

Radiometric forces exerted on a perforated membrane

The radiometric force exerted on a thin perforated membrane and the heat flux from the membrane to a surrounding gas are calculated by the direct simulation Monte Carlo method over wide ranges of the gas rarefaction and membrane porosity. Ab initio potentials are used to model the intermolecular collisions. We find that perforations increase the force several times in the viscous regime of flow but decrease the force in the free-molecular and transitional regimes. The influence of the accommodation coefficients is studied by applying the Cercignani–Lampis model. The effects of gas species, degree of non-equilibrium, and environment temperature are found to have relatively small effects on dimensionless quantities such that the reported results can be applied to wide ranges of these factors and, hence, to numerous practical situations such as the levitation of centimeter-scale membranes at upper atmospheric altitudes.

Enhanced SERS signal in the hybrid substrate through electronic modulation of CVD grown single-layer graphene

The ever-growing demand for sensitive and reliable detection of hazardous material in the food chain and trace detection of chemical entities in a variety field attracted advanced Surface Enhanced Raman Spectroscopy (SERS) active material such as graphene-based hybrid SERS. The graphene‑silver nanostructures (AgNS) based hybrid SERS substrates are explored to understand the critical role of pristine graphene grown by chemical vapor deposition (CVD) on SERS signal and its possible mechanism. A lithography-free fabrication process has been developed for growth of uniform array of AgNS with varying both particle sizes and inter-particle gaps. The optimal AgNS with feature size ~40 nm and inter-particle spacing of ~13 nm demonstrated the maximum SERS enhancement with Rhodamine 6G (R6G). The single-layer graphene (SLG) grown by CVD with the aid of controlling the reaction geometry with growth under a free molecular regime leads to the highest quality graphene with I2D/IG ratio of ~3.58 and ID/IG ratio of 0.1539. The flow regime-controlled CVD-grown SLG integrated with AgNS and its SERS enhancement mechanism is explored for trace detection of R6G. The graphene with its ability to modulate the electronic structure and tune it relative to the highest occupied molecular orbital-lowest occupied molecular orbital (HOMO-LUMO) levels of R6G molecules resulted in improved SERS signal by about an order for graphene-AgNS hybrid structure as compared to bare AgNS. The obtained findings paved the way for the futuristic and reliable hybrid SERS substrate for trace-level detection of a wide range of chemical entities.

Numerical investigation of non-equilibrium condensation of carbon dioxide from a gas mixture of carbon dioxide and argon in a supersonic nozzle under cryogenic conditions

This study involved a numerical investigation of the homogeneous nucleation of CO2 from a CO2–Ar gas mixture in a supersonic nozzle with a throat size of 2.11 mm, a total pressure of 61.15 kPa, and a total temperature of 293.15 K. The flow conditions covered the cryogenic temperature range (∼75 K). Therefore, the surface tension of the clusters was calculated using the Tolman–Tanaka correction, and nucleation growth was evaluated considering both free molecular and continuum regimes. Numerical simulations were conducted for a wide range of CO2 mole fractions (3%–39%). In particular, the effect of the CO2 mole fraction on the condensation-shock position—approximately the Wilson point—was investigated. For 3%, 12%, 24%, and 39%, the condensation shock occurred at 0.048, 0.043, 0.046, and 0.054 m from the throat, respectively. When the mole fraction was low (≤10%), the condensation-shock position moved downstream as the mole fraction decreased. This trend was attributed to a lower nucleation rate. In contrast, when the mole fraction was high (≥10%), the condensation-shock position moved downstream as the mole fraction increased. This was because the CO2 equilibrium pressure rose more rapidly than the CO2 vapor pressure as the mole fraction increases.

Sedimentation and photophoretic levitation of aerosol clusters in the free molecular regime

Sedimentation of fractal aerosol clusters in rarefied gas medium in the dark and under external illumination similar to sunlight is studied in a numerical experiment taking into account orientation effects, depending on fractal dimension varying within a broad range. The calculation of forces and their moments, including friction forces and photophoretic forces, was carried out on the basis of approximation of free molecular gas kinetic regime and previously developed Monte-Carlo algorithms. Calculation involved 10000 clusters, each of them containing 160 primary spherical particles and efficiently absorbing sunlight and IR radiation, similarly to the particles of soot aggregates.The velocity of multi-particle cluster settling in the absence of illumination, when particle temperatures are equal to the temperature of the gaseous environment, is a distinct function of fractal dimension and is rather close to the velocity of settling of single spherical particles. The settling velocity approximation depending on fractal dimension has been obtained.Illumination brings dramatic changes into sedimentation pattern. The range of cluster sedimentation rate variations broadens substantially, which is a manifestation of gravito-photophoretic effect, so that some clusters even start to levitate. The proportion of levitating clusters is essentially dependent on fractal dimension. For soot-like clusters under irradiation similar to sunlight and pressure equal to atmospheric at the altitude of 30 km, the proportion of levitating aggregates is approximately 7%, which is in good agreement with the experimental data. In the dark and under irradiation, the aggregates rotate, and their trajectories are shaped as spirals.In the context of photophoretic phenomena, a result of principle has been obtained: under irradiation with sunlight, gravito-photophoretic levitation of aerosol soot-like aggregates composed of identical primary particles is possible at a pressure corresponding to the stratospheric altitudes. This result points to the possibility of substantial influence of gravito-photophoretic effect on transport and localization of soot aerosol in the Earth’s stratosphere and mesosphere.

A design optimization method for rarefied and continuum gas flows

A design optimization method applicable to both rarefied and continuum gas flows with good efficiency is proposed in the framework of gas-kinetic theory. The method follows the methodology of topology optimization where the areas of gas and solid are marked by the material density, based on which a fictitious porosity model is used to reflect the effect of the solid on the gas and mimic the diffuse boundary condition on the gas-solid interface. The formula of this fictitious porosity model is modified to make the model work well from the free-molecular flow regime to the continuum flow regime. To find the optimized material density, a gradient-based optimizer is adopted and the design sensitivity is obtained by the continuous adjoint method. To solve the primal kinetic equation and the corresponding adjoint equation, efficient multiscale numerical schemes are constructed. Several airfoil optimization problems are solved to demonstrate the performance of the present design optimization method in wide ranges of flow speed and gas rarefaction. It is found that the thickness of the optimized airfoil first increases and then decreases as the Knudsen number increases, and on the supersonic condition the optimized airfoil has quite different shapes of leading edge for different degrees of gas rarefaction.

Tilt effect on squeeze-film damping in electrostatic micro-actuators

In this study, we theoretically explore the impact of tilt on the switching dynamics of a MEMS device operated by a pair of electrostatic actuators and subject to pronounced squeeze-film damping in the transition and free molecular flow regimes. Our investigation reveals that inducing tilt, achieved through the application of uneven voltages on the electrodes, introduces additional source terms in the modified Reynolds equation governing the pressure distribution in the squeeze-film gap. These added terms result in an accelerated decay of the squeeze film force, facilitating faster device switching between the initial and target configurations.To analyze the device dynamics, we develop a coupled numerical model and employ evolutionary multi-objective optimization to determine an optimal actuation scheme. This optimization is carried out for scenarios where initially different voltages are applied to the electrodes during a certain pre-defined time interval before transitioning to the steady voltage corresponding to the target gap size at equilibrium. Our findings highlight that the suggested actuation strategy leads to substantial improvements in the switching time of the device. Furthermore, we provide insights into the conditions favoring tilt actuation over parallel-motion actuation where the initially applied voltages are equal.

Rarefied cylindrical Couette problem: Effect of a very sharp transition from weakly rarefied flow near the inner cylinder to free molecular flow at very low average Knudsen numbers

We consider the rarefied cylindrical Couette flow. The outer cylinder rotates at a constant angular velocity, and the inner one is at rest. The Knudsen number, calculated from the average gas density, is much less than one. To find the fluid dynamic variables and fluxes, the direct simulation Monte Carlo method (DSMC) is used. We find the effect of a very sharp decrease in shear stress and energy fluxes transferred to the cylinders if the Knudsen number is sufficiently low and the rotation speed of the outer cylinder is sufficiently high. We show that when the average Knudsen number is sufficiently low, if the velocity is initially high and increases slightly further, the weakly rarefied flow regime near the inner cylinder transitions abruptly to a free molecular flow regime. Thus, the flow abruptly separates from the inner cylinder. We compare the fluxes obtained by solving the Navier–Stokes equations and by the DSMC method. It turns out that the solutions of the Navier–Stokes equations with slip boundary conditions also change abruptly at certain critical values, and these critical values are close to the appropriate DSMC values.

Comprehensive modeling of ignition and combustion of multiscale aluminum particles under various pressure conditions

The ignition and combustion of aluminum particles are crucial to achieve optimal energy release in propulsion and power systems within a limited residence time. This study seeks to develop theoretical ignition and combustion models for aluminum particles ranging from 10 nm to 1000 μm under wide pressure ranges of normal to beyond 10 MPa. Firstly, a parametric analysis illustrates that the convective heat transfer and heterogeneous surface reaction are strongly influenced by pressure, which directly affects the ignition process. Accordingly, the ignition delay time can be correlated with pressure through the pb relationship, with b increasing from –1 to –0.1 as the system transitions from the free molecular regime to the continuum regime. Then, the circuit comparison analysis method was used to interpret an empirical formula capable of predicting the ignition delay time of aluminum particles over a wide range of pressures in N2, O2, H2O, and CO2 atmospheres. Secondly, an analysis of experimental data indicates that the exponents of pressure dependence in the combustion time of large micron-sized particles and nanoparticles are –0.15 and –0.65, respectively. Further, the dominant combustion mechanism of multiscale aluminum particles was quantitatively demonstrated through the Damköhler number (Da) concept. Results have shown that aluminum combustion is mainly controlled by diffusion as Da > 10, by chemical kinetics when Da ≤ 0.1, and codetermined by both diffusion and chemical kinetics when 0.1 < Da ≤ 10. Finally, an empirical formula was proposed to predict the combustion time of multiscale aluminum particles under high pressure, which showed good agreement with available experimental data.

Forces acting on near-wall spherical particles in shear flows of diluted gases

In the present paper, we studied the forces on a spherical particle of radius R moving in the vicinity of the plane wall in a shear flow of free molecular regime. We consider that the distance ratio between the plane wall and the particle (L) and the particle radius (R) is large (e.g., L/R > 5), and the gas molecular mean free path (λ) is much higher than the particle size (λ/R ≫1). An analytical formula for the forces is obtained based on gas kinetic theory and certain simplifying assumptions, and is verified by using Direct Simulation Monte Carlo Method. It is found that the forces acting on the particle can be affected by the momentum accommodation coefficients (σ) of the wall and particle surfaces, the wall/gas temperature ratios (Tw/T), and the velocity gradient (G) of the gas flow. In the cases of specular reflections (σ = 0), the near-wall effect can be neglected. With the increase of the momentum accommodation coefficients, the near-wall effect can be enhanced. When near-wall particles move in the direction parallel to the plane wall, there is a lift force which is perpendicular to the wall due to the near-wall effect and the shear flow. For Tw/T < 1, the lift force for the near-wall particles is in the direction against the wall. While for Tw/T > 1, the force is in the direction away from the plane wall. The findings presented in this paper can provide theoretical guidance for the application of near-wall particles in shear flows.

Numerical modeling of the non-equilibrium condensation in multi-component flows through the high expansion ratio nozzles

Excessive flow expansion in the thruster nozzles reduces the flow temperature and pressure. This provides conditions for the condensation phenomena in the nozzle, which can affect the thrust performance of thrusters. In this paper, the condensation effect of water components in the decomposition products of hydrogen peroxide in a typical thruster nozzle is modeled. To describe the state and properties of the real gas mixture, the Peng-Robinson equation of state is used. Moreover, the effects of H2O2 concentration and nozzle profile on the condensation and nozzle performance parameters are studied. The results show that by more flow expansion and crossing the saturated state of condensable components, the thrust coefficient improves up to 6%. This improvement decreases by increasing the H2O2 concentration in the reaction chamber for a fixed nozzle expansion ratio. Due to the small growth of droplets during the free molecular regime of the droplet growth in the high-speed flow, the non-equilibrium condensation continues until the nozzle outflow. In addition, although all the profiles have the same expansion ratio for nucleation start, increasing the nozzle length results in larger nano-droplets, more liquid mass fraction formation up to 4%, and moving the Wilson point to the further upstream sections in the nozzle.

Damping separation of finite open systems in gravity-related experiments in the free molecular flow regime

Damping separation of finite open systems in gravity-related experiments in the free molecular flow regime

Modeling of dual-skin asymmetric hollow fiber microporous membranes for predicting the skins parameters separately using gas permeation test

This study presented a comprehensive gas permeation model to predict the skin parameters of a complex system, specifically a hollow fiber membrane with an asymmetric structure consisting of two external and internal skin layers. According to the work of Haefer for n segments of pores connected in series as in hollow fiber membranes, applying the Wakao et al. model, a comprehensive model for the transition regime was derived. The model was examined against the various fabricated PES and PEI hollow fiber membranes. Unlike conventional models, the proposed method predicted the mean pore size and mean pore length independent of surface porosity for each skin layer. The study revealed valuable insights into i) the middle pressure, ii) the difference between the skin parameters of the two membrane skins, and iii) the impact of the feeding direction on gas permeation behavior. It was shown that the dependency of permeation behavior on the feeding direction is linked to the influence of middle pressure on viscous flow, which is closely related to surface porosities of each side. It is evident that even the slightest variations in the fabrication parameters can result in different structures. Furthermore, it is evident that the assumption of neglecting slip flow was reasonable within the experienced Knudsen number range. The model also highlighted that the skin parameters of the two skin layers may not be identical, a distinction not captured by the current models. The traditional approach of setting the middle pressure as the average of the upstream and downstream pressures has been improved by expressing it as a linear function of both pressures. In the feed side, higher pressures led to dominant viscous flow, whilst the permeate side was more influenced by the free molecular regime due to lower pressures. There existed a competition between the Knudsen flow and the viscous flow at a specific Knudsen number for the feeding side pores, whether it was the inner or outer surface. The finding emphasized the significance of porosity values on each side in determining the proximity of middle pressure to feed and permeate side pressures, underscoring the importance of accurate knowledge of surface porosities, mean pore sizes, and pore lengths for both skin layers in understanding processes involving porous dual-skin hollow fiber membranes.

Topography formation driven by sublimation of pure species on icy airless worlds

Sublimation can drive morphologic changes on the surfaces of icy, airless worlds; the magnitude of these changes depends sensitively on their surface shape, subsurface geology, and volatility of the ice species present. To predict the steady-state and stability of the surface, we examine the molecular transport conditions and their constraints for several pure species sublimating from irregular surfaces in a free-molecular regime subject to variations in thermal conditions at or near the surface. We find that the temperature difference, ΔT∗ between the high and low points on the surface required for morphological instability changes of a given surface geometry increases as the volatility of the ice species increases. From Figure 4, for k=1 and Ts=150K, ΔT∗ is about 3K for H2O and 5K for CO2. Furthermore, we developed an analytical relationship between the saturation vapor pressure of a pure species, its surface geometry and temperature profile, and the required molecular transport conditions.

Simulation of Rarefied Gas Flow in a Channel Applying Artificial Neuron Network

The purpose of the present paper is to confirm numerically applying our ANN algorithm for transitional gas flow between continuum and free-molecular flow. The main advantage of this approach is substantial computing time economy compared to usual DSMC procedure. The learning of ANN is based on well known rarefied gas flow examples, analytic solutions in limit cases, calculations by lattice Boltzmann method (LBM), and on quite few Monte Carlo simulations. Our previous results obtained for large Knudsen numbers have been applied near the free-molecular regime. In this region the flow has demonstrated the properties of unstable nonlinear dynamic system. The flow of nitrogen in a microchannel with aspect ratio L/h = 20 and by pressure ratio P between 1.84 and 4.14 is simulated by ANN. This example has shown a good coincidence of ANN and DSMC calculations even in the case when only a small part of original DSMC computation has been applied for learning ANN. Thus, computing time is reduced up to 10 times in this case.

A variant of improved discrete velocity method for efficient simulation of flows in entire Knudsen number regimes

In this paper, a variant of the improved discrete velocity method (VIDVM) is proposed for flows in the whole Knudsen number regimes. This method retains the advantage of the improved discrete velocity method (IDVM), which calculates numerical fluxes through a self-adaptive strategy by combining the microscopic reconstruction and the macroscopic reconstruction. Like the IDVM, the microscopic reconstruction for VIDVM is also based on the collisionless Boltzmann solver. However, different from IDVM, the macroscopic reconstruction for VIDVM is established on the Euler solver instead of the Navier–Stokes solver. Considering that the Euler solver merely computes the inviscid fluxes while the Navier–Stokes solver additionally calculates the viscous fluxes, the present method could be more efficient than IDVM. To validate the accuracy and efficiency of the present scheme, some benchmark cases from the continuum regime to the free molecular regime are conducted. Results reveal that the present scheme can predict the flow as well as IDVM, but the present solver is more efficient than IDVM.

Size distributions in irreversible particle aggregation

The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to derive a linear partial differential equation which is solved to show that the size distributions are close to log-normal asymptotically in time.

Simulation study of drag force characteristics of nanoparticles in transition regime

Transport properties of nanoparticles in gases have many practical applications, such as aerosol science, combustion, and micro- and nano-scale fabrication. A nanoparticle moving in a fluid is expected to experience a drag force, which determines the transport property of the particle. According to the Einstein relationship, the diffusion coefficient of a particle is inversely proportional to the drag force coefficient. However, in the transition regime, it is usually difficult to evaluate the drag force of suspended particles. A typical method is to extend the asymptotic solution of the free molecular or continuum limit to the transition regime. According to the gas kinetic theory, Li and Wang proposed a theoretical expression for drag force on nanoparticles in the free molecular regime, which is then extended to the entire range of Knudsen number following a semi-empirical approach [Li Z G, Wang H 2003 &lt;i&gt;Phys. Rev. E&lt;/i&gt; &lt;b&gt;68&lt;/b&gt; 061207]. For nanoparticles, it is necessary to verify the theoretical predictions since the gas-particle non-rigid-body interactions must be taken into account. In this work, the drag force on nanoparticle in the transition regime is investigated by using molecular dynamics (MD) simulation. To evaluate the drag force, a harmonic potential is used to the nanoparticle to constrain its Brownian motion in our MD simulation. In the steady state, the drag force can be obtained by the balance between the drag force and harmonic force. It is found that the gas-particle non-rigid-body interaction has a significant influence on the drag force of nanoparticle. For weak gas-solid coupling, the MD simulation results can be in good agreement with the prediction of Li-Wang theory. However, for strong coupling, there exists significant discrepancy between the MD simulation results and the theoretical results. Due to the gas-solid intermolecular interactions, gas molecules can be adsorbed on the nanoparticle surface, and after a time period, they may be re-emitted from the surface when they gain sufficient kinetic energy. Therefore, an adsorption-desorption equilibrium and an adsorption layer can be established on the particle surface. The adsorption layer enlarges the collision cross-sectional area and enhances the momentum transfer between gas molecules and the particle, and thus the drag force increases. This can explain the inconsistencies between the theoretical results and MD simulations. In this work, we introduce an adsorption ratio to evaluate the thickness of the adsorption layer. Then, the effective particle radius can be defined by the sum of particle radius and the thickness of the adsorption layer. By using the effective particle radius, the simulation values are in very good agreement with the theoretical predictions. The results of this work provide insights into the applications of nanoparticles in aerosol science.

Investigating the temperature distribution behavior and flow parameters of argon fluid in a nanochannel with changing dimensions of the obstacle using the molecular dynamics (MD) method

This article, examines the flow of argon inside a nanochannel with respect to the molecular dynamics (MD) in the free molecular flow regime using LAMMPS software. The nanochannel is made of copper featuring a square cross-section and obstacles of varying dimensions and values. In this study, the flow of argon fluid is three-dimensional. To gain a deeper understanding of the effect of solid walls within the nanochannel and their influence on flow behavior, the research is simulated in a nanochannel with all side walls for the 3D model and without side walls for the 2D model. This research assesses the effect of the obstacles’ dimensions and values on the nanochannel wall surface and areas above the wall surface. The total dimensions of all simulated two- and three-dimensional atomic structures with a square cross-section are assumed to be 60 × 60 × 100 Å3. and the presence of square obstacles (with dimensions of 8 × 8 × 8 Å3) and rectangular obstacles (with dimensions of 8 × 18 × 8 Å3) is examined. This study seeks to understand the influence on flow behavior, temperature distribution, density, heat flux, velocity, and thermal conductivity coefficient. This study is simulated using a time step of 1 fs for 10,000 time steps, involving approximately 10,000–15,000 argon and copper atoms. The results of this research indicate that obstacles with structures of P and R and larger dimensions increase the number of solid atoms exhibiting stronger attractive forces. Compared to a smooth nanochannel, the thermal exchange between fluid and solid atoms results in a density increase of 17.5 % and 17.3 %, respectively. On the other hand, in the 3D nanochannel, the sidewalls of the nanochannel have reduced the effect of the presence of R and P obstacles with larger dimensions, which comparing to a smooth nanochannel, have increased the density by 8.21 % and 7.53 %, respectively. The obstacles with different spatial positions (P and R structures) in the two-dimensional nanochannel cause a rise in the thermal conductivity coefficient. The P structure obstacles have a better effect on the thermal conductivity coefficient in the 2D nanochannel compared to the R structure. In the three-dimensional nanochannel, utilizing smaller obstacles proves to be more effective because it results in better atom distribution or temperature distribution due to increased atomic collisions in the central region compared to the wall regions.

Continuous gas-phase synthesis of iron nanoparticles at ambient conditions with controllable size and polydispersity

HypothesisBy altering aerosol growth dynamics with unipolar charges, one can obtain aerosols with narrow particles size distributions, a highly desirable feature in applications of functional nanoparticles. ExperimentsUnlike liquid colloid systems, aerosol particles in the free molecular regime undergo coarsening due to Brownian coagulation and will eventually attain a self-preserving size distribution with a typical geometric standard deviation of 1.46 - 1.48. We developed a novel continuous one-step aerosol synthesis reactor that produces iron nanoparticles from ferrocene at ambient conditions, which confines the site of precursor breakdown and particle formation in the downstream vicinity of a positive corona discharge. FindingsWe demonstrated that the particle size could be controlled within 3 - 10 nm with a suppressed geometric standard deviation (1.15 - 1.35). The as-produced iron nanoparticles were successfully used as catalyst for the growth of single-walled carbon nanotubes with a narrow diameter range. With a transient aerosol dynamics model, we showed that a fraction (as small as 0.1%) of unipolar-charged particles could have a significant impact on the aerosol growth dynamics, which eventually results in a narrower particle size distribution with smaller size and higher number concentrations.