Molecular dynamics simulation of polymer nanoparticle collisions: orbital angular momentum effects

The collisional dynamics of polymer nanoparticles is investigated using molecular dynamics, with a particular focus on angular momentum effects. Unlike zero impact parameter collisions discussed elsewhere, which are greatly weighted toward sticking collisions, the outcome of collisions with non-zero angular momentum show much greater variability, showing both reactive (where polymer chains are exchanged between particles) and purely scattering trajectories. In the case of inelastic scattering trajectories, the profile for translation to vibration energy transfer is calculated.     

Eulerian-Lagrangian simulation of aeolian sand transport

A numerical investigation of aeolian sand transport is performed with an Eulerian-Lagrangian model. In this model, the gas phase is described by the volume-averaged Navier-Stokes equations of two-phase flow. The particle motion is obtained by solving Newton's second law of motion taking into account the inter-particle collisions, where a soft sphere model is used to describe inter-particle collisions. The dynamic process of aeolian sand transport is simulated. The simulation results show that the variation of mean horizontal velocity of the particles with height can be expressed by a logarithmical function or a power function at h > 0.02 m, and the power function can be described below 0.02 m. The sand mass flux decreases exponentially with height for h > 0.02 m, but there is a deviation from the exponential decay due to the creep grains in the near-bed region. It is also shown that the inter-particle collisions play an important role in sand saltation. Therefore the present numerical model is capable of being applied to the study of windblown sand movement.     

Poly(ionic liquid)-derived nanoporous carbon analyzed by combination of gas physisorption and small-angle neutron scattering

The preparation of nanoporous carbon materials and their characterization combining small-angle neutron scattering (SANS) with gas physisorption is presented. Carbon with a porous structure and tunable form is obtained here by a salt-templating approach using poly(ionic liquid) as precursor. SANS in combination with contrast matching by deuterated p-xylene was used for a separation of the scattering component deriving from the density fluctuations of the carbon matrix and the inaccessible porosity. The resulting scattering curves could be used for an unambiguous characterization of the pore structure of the materials. SANS curves measured at different partial pressure of the matching agent p-xylene were used for a differential filling of the micro- and mesopores. The analysis using the chord length distribution (CLD) was employed to determine the specific surface area and the pore size at different adsorption steps. The SANS results were in good agreement with the quenched solid density functional theory (QSDFT) analysis of the nitrogen physisorption. By the comparison of both characterization methods the pore shape could be determined. The combination of both SANS and gas physisorption is thus shown to provide a comprehensive characterization of the pore structure of the carbon monoliths throughout the entire pertinent length scale.     

Numerical modeling of gas-particle flow using a comprehensive kinetic theory with turbulence modulation

In most fluidized beds, both solids flux and gas phase Reynolds number are high and the flow are usually turbulent. It is therefore necessary to consider both the effects of particle-particle collisions and particle phase turbulence in any mathematical model for simulating gas-particle flows. A comprehensive model is developed in the present work in which a two-equation (k-?) turbulence model is used for calculating the gas phase. In addition, a transport equation of particle phase turbulent kinetic energy is proposed and used for modeling the particle phase turbulence (k_p model). Similar to that of the single gas phase, effective viscosity of the particle phase is the sum of the laminar viscosity caused by particle-particle collisions described by kinetic theory and the turbulent viscosity caused by collections of particles described by the k_p model. The proposed model is used to predict gas-particle flows in a vertical pipe. Results obtained using this model compare well with experimental data.     

基于颗粒流运动论的喷动流化床气固流动行为三维模拟

1 INTRODUCTION Spout-fluid beds have been of increasing interest in the petrochemical, chemical and metallurgic indus-tries since spout-fluid beds can reduce some of the limitations of both spouting and fluidization by su-perimposing the two type of systems[1―4]. In recent years, spout-fluid beds have become an alternative for gas/solid contactors in coal gasification. Spout-fluid bed coal gasifiers have been adopted for APFBC-CC (advanced pressurized fluidized bed combus-tion-combined…     

Size- and structure-independence of the thermophoretic transport of an aerosol particle for specular boundary conditions in the free molecule regime

Early conjectures and recent numerical simulations indicate that the motion of aerosol particles, including multispherule fractal aggregates, established as the result of temperature inhomogeneities in the prevailing gas are, to within a few percent, insensitive to particle size and morphology, especially in the free-molecule limit. Extending these results, we show here that in the limiting case of specular boundary conditions and free-molecular flow, particle thermophoretic velocity is exactly independent of size and structure (shape), and equal to the well-known analytical expression of Waldmann for an isolated, spherical particle in the same local environment. Our result, which applies to particles of any morphology, constitutes perhaps the only available analytical solution of a free molecular transport property for particles which can be locally concave and, more importantly, provides additional rational justification for the principal assumption underlying the widely used technique of thermophoretic sampling. Beyond the theoretical interest of the result as the limiting behavior of Maxwell's model of partial diffusive-specular scattering, our finding is of practical relevance for particles smaller than a few nanometers, for which there is now conclusive evidence that specular scattering adequately describes gas molecules–particle interactions. The result additionally provides a good test case to validate numerical algorithms dealing with complex geometries.     

A model for collisional exchange in gas/liquid/solid fluidized beds

A new model is presented for numerical simulations of collisional transfer of mass, momentum and energy in gas/liquid/solid fluidized beds. The mathematical formulation uses a collision model similar to that of Bhatnagar, Gross, and Krook (BGK), in a particle distribution function transport equation, in order to approximate the rates at which collisions bring about local equilibration of particle velocities and the masses, compositions, and temperatures of liquid films on bed particles. The model is implemented in the framework of the computational-particle fluid dynamics (CPFD) numerical methodology, in which the particle phase is represented with computational parcels and the continuous phase is calculated on Eulerian finite-difference grid. Computational examples using the Barracuda^® code, a commercial CFD code owned by CPFD Software, LLC, show the ability of the model to calculate spray injection and subsequent liquid spreading in gas/solid flows.     

Gas-particle interactions in dense gas-fluidized beds

The occurrence of heterogeneous flow structures in gas-particle flows seriously affects gas–solid contacting and transport processes in dense gas-fluidized beds. A computational study, using a discrete particle method based on Molecular Dynamics techniques, has been carried out to explore the mechanisms underlying the formation of heterogeneous flow structures. Based on energy budget analyses, the impact of non-linear drag force on the flow structure formation in gas-fluidized beds has been examined for both ideal particles (elastic collision, without inter-particle friction) and non-ideal particles (inelastic collision, with inter-particle friction). Meanwhile, the separate role of inter-particle inelastic collisions, accounted for in the model via the restitution coefficient (e) and friction coefficient (μ), has also been studied.It is demonstrated that heterogeneous flow structures exist in systems with both non-ideal particle-particle interaction and ideal particle-particle interaction. The heterogeneous structure in an ideal system, featured with looser packing, is purely caused by the non-linearity of the gas drag: the stronger the non-linearity of the gas drag force with respect to the voidage, the more heterogeneous flow structures develop. A weak dependence of drag on the voidage produces a homogenous flow structure. Collisional dissipation dramatically intensifies the formation of heterogeneous flow structures after the system equilibrium breaks. Quantitative comparisons of flow structures obtained by using various drag correlations in literature will also be reported.     

A structural study of polyelectrolyte gels in a unidirectionally swollen state

We investigated the structures of polyelectrolyte gels, poly(N-isopropylacrylamide-co-2-acrylamido-2-methylpropane sulfonic acid) (NIPA/AMPS) hydrogels in a unidirectionally swollen state by using small-angle X-ray scattering (SAXS). The SAXS results show that the structure of the NIPA/AMPS gels strongly depends upon the composition of NIPA/AMPS. Increase in composition of AMPS causes suppression of concentration fluctuations in the long wavelength. As a consequence, a NIPA/AMPS hydrogel with a low composition of AMPS macroscopically phase-separated at high temperatures, while microphase separation occurred for a NIPA/AMPS gel with a higher composition of AMPS. The instability in the microphase separation initially occurred in the direction perpendicular to the swelling for the latter gel. In the disordered state near the microphase separation region, an elliptic scattering pattern was observed, and the scattering intensity around the peak position in the direction perpendicular to the unidirectionally swelling was larger than that in the direction parallel to it. The behavior became more remarkable, as the interaction parameter χ became larger. These behaviors are consistent with the prediction from the Rabin-Panukov theory. The scattering vector at the scattering maximum in the perpendicular direction q_m,⊥ significantly shifted to smaller q, where q represents the magnitude of the scattering vector, when the microphase separation occurred. It is shown that the periodicity of the microphase-separated structure ranged from 300 to 400 Å.     

On the origin of heterogeneous structure in dense gas-solid flows

The formation and evolution of flow structures in dense gas-fluidized beds with ideal collisional particles (elastic and frictionless) are investigated numerically by employing the discrete particle method, with special focus on the effect of gas-particle interaction.It is clarified that heterogeneous flow structures still exist in systems with elastic and frictionless particle collisions, even though the particles in the emulsion phase are more loosely packed. The flow structures in various flow regimes, including uniform, bubbling and turbulent fluidization, can be reproduced from these simulations. Systems with strong particle fluctuating motion but weak gas suspension display an emulsion-bubble structure. On the contrary, systems with weak particle fluctuation motion tend to produce uniform structures. If these two interactions are equally important, the system features complex flow patterns resembling those displayed in the turbulent fluidization.Energy analysis has revealed that the fluctuating motion of particles corresponds to the existence of heterogeneity in ideal collisional systems. The flow regime transition is actually the macro-scale expression of the altering degree of dominance of particle-particle and particle-fluid interactions.Particularly, it is also found that non-linear drag has the “phase separation” function by accelerating particles in the dense phase and decelerating particles in the dilute phase producing the fluctuating motion and thereby triggering non-homogeneous flow structure formation.     

Knudsen diffusion in powders. Part I Critical examination of a gas diffusion relationship used in Knudsen flow permeametry

B. V. Derjaguin's treatment of gas diffusion in a porous medium under conditions of Knudsen flow is discussed. A semi-theoretical value obtained for the constant β in the general equation is tested experimentally. In opposition to previous conclusions, molecular diffusion seems best interpreted in terms of elastic collisions against the pore walls. The structure of the pore system is shown to be the controlling parameter of the gas flow, and the novelty of the present treatment consists in ways to take the pore structure into account.     

Small-angle neutron scattering characterization of the structure of nanoporous carbons for energy-related applications

We used small-angle neutron scattering (SANS) and neutron contrast variation to study the structure of four nanoporous carbons prepared by thermo-chemical etching of titanium carbide TiC in chlorine at 300, 400, 600, and 800 °C with pore diameters ranging between ∼4 and ∼11 Å. SANS patterns were obtained from dry samples and samples saturated with deuterium oxide (D₂O) in order to delineate origin of the power law scattering in the low Q domain as well as to evaluate pore accessibility for D₂O molecules. SANS cross section of all samples was fitted to Debye-Anderson-Brumberger (DAB), DAB-Kirste-Porod models as well as to the Guinier and modified Guinier formulae for cylindrical objects, which allowed for evaluating the radii of gyration as well as the radii and lengths of the pores under cylindrical shape approximation. SANS data from D₂O-saturated samples indicate that strong upturn in the low Q limit usually observed in the scattering patterns from microporous carbon powders is due to the scattering from outer surface of the powder particles. Micropores are only partially filled with D₂O molecules due to geometrical constraints and or partial hydrophobicity of the carbon matrix. Structural parameters of the dry carbons obtained using SANS are compared with the results of the gas sorption measurements and the values agree for carbide-derived carbons (CDCs) obtained at high chlorination temperatures (>600 °C). For lower chlorination temperatures, pore radii obtained from gas sorption overestimate the actual pore size as calculated from SANS for two reasons: inaccessible small pores are present and the model-dependent fitting based on density functional theory models assumes non-spherical pores, whereas SANS clearly indicates that the pore shape in microporous CDC obtained at low chlorination temperatures is nearly spherical.     

Correlation between gas transport properties and the morphology/dynamics of crystalline fluorinated copolymer membranes

The crystalline structure, dynamics, and gas transport properties (i.e., the gas permeability, gas diffusion coefficient, and gas solubility coefficient) of poly(tetrafluoroethylene‐co‐perfluoroethylvinylether) (PFA) membranes were systematically investigated via differential scanning calorimetry, wide/small/ultra‐small‐angle X‐ray scattering, and quasielastic neutron scattering measurements. We evaluated the gas transport properties using a constant‐volume/variable‐pressure method. The gas permeability and the gas diffusion coefficient decreased with increasing crystallinity of the PFA membranes at crystallinities below 32%. However, in membranes with a crystallinity of 32% or greater, these parameters depended on the characteristics of the gas molecules, such as their kinetic diameter. The so‐called long spacing period and the thickness of the crystalline/amorphous regions increased with crystallinity according to the small/ultra‐small‐angle X‐ray scattering results. Furthermore, the quasielastic neutron scattering measurements indicated that the scattering law was well fitted to a sum of narrow and broad Lorentzian components. In particular, the narrow components, that is, the local motion of amorphous components and side chains, increased with crystallinity. These results suggest that large gas molecules could pass through the PFA membranes, assisted by the motion in the amorphous region. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45665.     

Probing surface structure via time-of-escape analysis of gas in Knudsen regime

Continuing the study begun in [Feres, R., Yablonsky, G., 2004. Knudsen's cosine law and random billiards. Chemical Engineering Science 59, 1541-1556], we consider transport in the Knudsen regime of inert gases through straight channels and investigate how small-scale surface geometry of a macroscopically flat channel affects the diffusion characteristics of the gas. We show that the diffusivity constant contains information about the surface micro-geometry.Our investigation is carried out partly by analytical means and also through numerical simulation of what we call time-of-escape experiment. This is a type of multi-scattering experiment that measures the mean residence time in channels of varying lengths, allowing for an analysis of the transport process at various stages of development.We focus attention on the smoothness constantξ=D/D₀, defined as the ratio of diffusivity for a given micro-geometry, D, and diffusivity D₀ under “ideal roughness,” i.e., under the assumption that the Knudsen cosine law holds at each collision. The dependence of ξ on small-scale surface morphology is investigated using a variety of parametrized families of micro-geometries. We show that ξ can tell the presence of certain geometric features, such as curvature or sharp angles at the microscopic level. For example, for a simple two-dimensional model of atomically smooth surface made of a linear packing of spheres of radius R probed by gas molecules of radius A (Fig. 6), we obtain the approximate relation ξ∝1+A/R, with a proportionality constant of roughly 1.3. (See Section 2 for the range of parameters considered.) This relates to rapid diffusion phenomena recently observed by [Holt, J.K., Park, H.G., Wang, Y., Stadermann, M., Artyukhin, A.B., Grigoropoulos, C.P., Noy, A., Bakajin, O., 2006. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312, (1034)]. In the classical collision model of Maxwell-Smoluchowski, with no detailed regard of surface geometry, one always has ξ?1, but we observe that ξ can sometimes be less than 1 (Section 2.5). We obtain exact values for the mean number and duration of collisions as function of the micro-geometry (Section 3). This is needed to determine the relative importance of these quantities on diffusivity. We also extend the analysis of the scattering operator of random billiards of [Feres, R., Yablonsky, G., 2004. Knudsen's cosine law and random billiards. Chemical Engineering Science 59, 1541-1556] by giving a general criterion for the validity of Knudsen's cosine law, and describe some of the spectral properties of this operator.     

Characterization of enzymatically synthesized amylopectin analogs via asymmetrical flow field flow fractionation

Asymmetrical flow field flow fractionation (AF4), when coupled with multi-angle laser light scattering (MALLS), is a very powerful technique for determination of the macromolecular structure of high molar mass (branched) polysaccharides. AF4 is a size fractionation technique just as size exclusion chromatography (SEC), nevertheless can overcome some crucial problems found in SEC analysis especially in starch like structures. This paper describes a detailed investigation of the macromolecular structure of two groups of well-defined synthetic amylopectin analogs – synthesized via an in vitro enzyme-catalyzed reaction using the enzymes phosphorylase b from rabbit muscle and Deinococcus geothermalis glycogen branching enzyme (Dg GBE). Size, molar mass distributions and structural data were studied by AF4 coupled with online quasi-elastic light scattering (QELS) and multi-angle light scattering (MALLS).     

Molecular-dynamics simulations of thermal accommodation of helium gas on a nanoparticle

Thermal accommodation of inert He gas atoms colliding on a nanometer-sized Ar or N₂ particle was analyzed using molecular dynamics simulations. The instantaneous values of apparent thermal accommodation coefficient (α_th) showed a distribution close to the normal distribution but with a longer tail toward lower values. The mean and standard deviation of α_th for Ar particle were about 0.39 and 0.54, respectively, and 0.44 and 0.56 for a N₂ particle. Those values were almost independent of gas temperature or pressure, with less than 10% variation over a three- or four-fold variation of the gas conditions. The thermal accommodation coefficient per collision (α₀), which was calculated from the apparent α_th and the average number of collisions on the particle surface, was about 0.18 on the Ar particle and 0.20 on the N₂ particle, both of which are in good agreement with theoretical predictions based on single interactions between free molecules.     

Physical properties of poly(n-alkyl acrylate) copolymers. Part 1. Crystalline/crystalline combinations

The physical properties of n-alkyl acrylate copolymers containing two crystallizeable monomers, including thermal characteristics, structure as determined by small angle X-ray scattering, and gas permeability as a function of temperature, were examined in detail and compared to the corresponding homopolymers. The copolymers exhibit co-crystallization and, thus, for a given average side-chain length have comparable melting temperatures as the corresponding homopolymers. For a given side-chain length, the copolymers have somewhat lower heats of fusion than the corresponding homopolymers because of a reduction in crystallite size as revealed by SAXS. This depression in crystallinity is reflected in the permeability data for the copolymers. Poly(n-alkyl acrylates) exhibit a ‘jump’ in their gas permeability at the T_m of the side-chain lengths that is mainly caused by a switch in the side-chain morphology from crystalline to amorphous upon melting. The depression in crystallinity for the copolymers results in a smaller permeation jump. The jump breadth correlates with the melting endotherms for these polymers as determined by DSC. Ultimately, the melting endotherms for these copolymer systems provide an excellent tool for predicting permeability changes across the melting region.     

Modeling of propagation of shock and detonation waves in dusty media with allowance for particle collisions

Shock-wave and detonation flows in a two-phase medium consisting of a gas and incompressible particles are studied by methods of numerical simulation with allowance for the random motion and collisions of particles. Steady solutions corresponding to two previously predicted wave types are obtained for the problem of interaction of a plane shock wave with a cloud of particles. The influence of the mixture parameters on the corresponding solutions is determined. In considering the problem of propagation of cellular heterogeneous detonation in a mixture of reacting particles, oxidizer, and inert particles, it is found that the detonation flow structure and the cell size are retained in the mixture with particle collisions. However, smearing (dispersion) of the layers and inert phase structures formed in the far zone of cellular detonation occurs because of particle collisions.