Numerical simulation of sedimentation of microparticles using the discrete particle method

A mathematical model has been formulated based on the combined continuous and discrete particle method for investigating the sedimentation behaviour of microparticles in aqueous suspensions, by treating the fluid phase as continuous and the particles phase as discrete, thus allowing the behaviour of individual particles to be followed and the evolution of the structure of the particle phase to be investigated as a function of time. The model takes into account most of the prevailing forces acting on individual particles including van der Waals attractive, electrostatic repulsive, gravitational, Brownian, depletion, steric, contact and drag forces. A code has also been developed based on the model. This paper reports some preliminary modelling results of mono-dispersed microparticles settling in aqueous suspensions under various conditions. The results show the short time dynamics of the fluid phase, which has a similar order of magnitude to the particle phase. Such short time dynamics could bear significance to processes such as particle aggregation when their size becomes very small. Preliminary analyses of the results have also been carried out on the evolution of particle settling based on a newly proposed parameter, local normalised volume fraction （LNVF）.     

Frequency response of primary resonance of electrostatically actuated CNT cantilevers

This paper deals with electrostatically actuated carbon nanotube (CNT) cantilever over a parallel ground plate. Three forces act on the CNTs cantilever, namely electrostatic, van der Waals, and damping. The van der Waals force is significant for values of 50 nm or less of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNTs electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The methods of multiple scales and reduced order model (ROM) are used to investigate the system under soft AC near half natural frequency of the CNT and weak nonlinearities. The frequency–amplitude response and damping, voltage, and van der Waals effects on the response are reported. It is showed that only five terms ROM predicts and accurately predicts the pull-in instability and the saddle-node bifurcation, respectively.     

Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates.Three different systems have been considered.In the first system the interaction between particles has been simulated using the JKR (Johnson,Kendall and Roberts) contact theory,while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively.In order to compare the mechanical behaviour of the three systems,the magnitude of the maximum attractive force between particles has been kept the same in all cases.However,the relationship between force and separation distance differs from case to case and thus,the range of the interparticle force.The results clearly indicate that as the range of the interparticle force increases,the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates. Three different systems have been considered. In the first system the interaction between particles has been simulated using the JKR （Johnson, Kendall and Roberts） contact theory, while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively. In order to compare the mechanical behaviour of the three systems, the magnitude of the maximum attractive force between particles has been kept the same in all cases. However, the relationship between force and separation distance differs from case to case and thus, the range of the interparticle force. The results clearly indicate that as the range of the interparticle force increases, the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

Effects of van der Waals force on nonlinear vibration of electromechanical integrated electrostatic harmonic actuator

An electromechanical integrated electrostatic harmonic actuator is promising for the miniaturization of electromechanical devices. As the dimensions of the actuator decrease, the effects of the van der Waals force become obvious. In this study, by considering the nonlinearity of electrostatic and van der Waals forces, nonlinear vibration equations of the flexible ring of an electrostatic harmonic actuator are deduced. Using these equations, the nonlinear free vibration and nonlinear forced response of the actuator are investigated. The effects of the van der Waals force on the nonlinear vibration of the flexible ring are analyzed. Results show that these effects of the van der Waals force are relatively obvious under some conditions and should be considered.     

Bifurcation and pull-in voltages of primary resonance of electrostatically actuated SWCNT cantilevers to include van der Waals effect

In this work the voltage response of primary resonance of electrostatically actuated single wall carbon nano tubes (SWCNT) cantilevers over a parallel ground plate is investigated. Three forces act on the SWCNT cantilever, namely electrostatic, van der Waals and damping. While the damping is linear, the electrostatic and van der Waals forces are nonlinear. Moreover, the electrostatic force is also parametric since it is given by AC voltage. Under these forces the dynamics of the SWCNT is nonlinear parametric. The van der Waals force is significant for values less than 50 nm of the gap between the SWCNT and the ground substrate. Reduced order model method (ROM) is used to investigate the system under soft excitation and weak nonlinearities. The voltage-amplitude response and influences of parameters are reported for primary resonance (AC near half natural frequency).     

A cell model theory of the shear viscosity of a concentrated suspension of interacting spheres in a non-Newtonian fluid

A theoretical approach to the shear viscosity of concentrated suspensions of small particles in a non-Newtonian fluid has been developed using a cell theory model involving particle-particle interaction. The cell theory of Frankel and Acrivos was first generalized to power-law fluid matrices without particle interaction. Particle-particle interaction was then taken into consideration. The theory suggests that the flow behavior of such systems at low shear rates is chiefly dependent upon non-hydrodynamics interparticle interaction such as van der Waals—London and electrostatic forces which induce flocculation and yield stresses. The flow properties at high shear rates are determined by hydrodynamics interaction essentially dependent upon particle concentration and shape.     

尼龙粉末在SLS预热温度下的离散元模型参数确定及其流动特性分析

尼龙粉末是增材制造中常用的粉体材料,温度对其流动性有重要影响. 探索尼龙粉末增材制造预热温度下的流动性是研究选择性激光烧结(selective laser sintering, SLS)工艺中粉体铺展成形的基础. 选取SLS技术中的尼龙粉末为原材料,采用离散元数值方法,研究尼龙粉末的流动行为,是增材制造工艺数值模拟和铺粉工艺优化的研究热点. 以Hertz-Mindlin模型为基础,基于Hamaker理论模型和库伦定律,在尼龙粉末的接触动力学模型中引入范德华力和静电力,建立预热温度下尼龙粉末流动的离散元模型(discrete element method, DEM),通过对比相应实验结果,标定了该模型的参数. 对加热旋转圆筒中尼龙粉末流动过程进行了DEM数值模拟,校核了所建模型的正确性,并研究了粉体粒径分布对尼龙粉末流动特性的影响规律. 研究表明,尼龙粉末黏附力是静电力与范德华力的共同作用结果;随着粉体粒径的增大,尼龙粉末崩塌角增大,流动性增强;相对于高斯粒径分布,粒径均匀分布的尼龙粉末颗粒流动性更强. 研究结果可指导SLS中铺粉工艺的优化.      

MEASUREMENT OF ADHESION FORCES IN AIR WITH THE VIBRATION METHOD

The vibration method represents a practical method for the measurement of adhesion forces and adhesion force distributions. This method causes sinusoidally altemating stresses and yields detachment and contact forces between particles and substrate of the same order of magnitude. Alternating contact forces of the vibration method can cause an adhesion force intensification through flattening of asperities. The measuring principle of the vibration method and the analysis of experimental results are described in the article. Normal adhesion forces (pull-off forces) are measured using the vibration method and the colloidal probe technique. The results of both methods show good agreement for small particle sizes. The influence of the detachment force direction is shown by comparing tangential and normal adhesion forces measured using particle reentrainment in a turbulent air flow and the vibration method, respectively. The surface roughness of the substrate and the relative humidity are shown to significantly influence the measured adhesion forces. For the calculation of the adhesion forces, an approach by Rabinovich was combined with approximations of plastic micro asperity flattening. The Rabinovich approach accounts for roughness effects on the van der Waals force by incorporating the rms roughness of the interacting surfaces. rms-values of the particles and substrates were measured with atomic force microscopy at different scanning areas.     

Linear instability of ultra-thin liquid films flowing down cylindrical fibre

The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fibre are investigated by a linear theory. The film with the thickness less than 100 nm is driven by an external force and under the influence of the van der Waals forces. The results show that, when the relative film thickness decreases, the curvature of the fibre depresses the development of the linear perturbations, whereas the van der Waals forces promote the instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from the absolute instability to the convective instability, indicating that the van der Waals forces can enlarge the absolutely unstable region. Furthermore, the surface tension can cause the development of the absolute instability, whereas the external force has an opposite effect.     

Linear instability of ultra-thin liquid films flowing down cylindrical fibre

The stability characteristics of an ultra-thin layer of a viscous liquid flowing down a cylindrical fibre are investigated by a linear theory. The film with the thickness less than 100 nm is driven by an external force and under the influence of the van der Waals forces. The results show that, when the relative film thickness decreases, the curvature of the fibre depresses the development of the linear perturbations, whereas the van der Waals forces promote the instabilities. This competition results in a non-monotonous dependence of the growth rate on the relative film thickness. The critical curves are also obtained to describe the transition from the absolute instability to the convective instability, indicating that the van der Waals forces can enlarge the absolutely unstable region. Furthermore, the surface tension can cause the development of the absolute instability, whereas the external force has an opposite effect.     

INVESTIGATION OF THE DYNAMIC BUCKLING OF DOUBLEWALLED CARBON NANOTUBE SUBJECTED TO AXIAL PERIODIC DISTURBING FORCES

IntroductionThediscoveryofthefirstcarbonnanotubes[1]hasattractedwideattentionandstimulatedextensivestudies[2 - 5 ].Thestudiesshowedthatthecarbonnanotubesexhibitsuperiormechanical,electronicandchemicalproperties.Onthemechanicalbehavior,thecarbonnanotubespossessexceptionallyhighstrength ,stiffnessandelasticmodulus.Theestimatemodulusofthecarbonnanotubemayreachashighas 1TPa.Itisthelargestofallknownmaterials.Thestrengthorstiffnessishigherthananyknownfiber[3].Thecarbonnanotubeareusedascompositemat…     

Nonlinear analysis of a SWCNT over a bundle of nanotubes

The deformation of a single wall carbon nanotube (SWCNT) interacting with a curved bundle of nanotubes is analyzed. The SWCNT is modeled as a straight elastic inextensible beam based on small deformation. The bundle of nanotubes is assumed rigid and the interaction is due to the van der Waals forces. An analytical solution is obtained using a bilinear approximation to the van der Waals forces. The analytical results are in good agreement with the results of two numerical methods. The results indicate that the SWCNT remains near the curved bundle provided that its curvature is below a critical value. For curvatures above this critical value the SWCNT breaks contact with the curved bundle and nearly returns to its straight position. A parameter study shows that the critical curvature depends on the stiffness of the SWCNT and the absolute minimum energy associated with the van der Waals forces but it is independent of the SWCNT's length in general. An analytical estimate of the critical curvature is developed. The results of this study may be applicable to composites of nanotubes where separation phenomena are suspected to occur.     

NUMERICAL CALCULATION OF LONDON-VAN DER WAALS ADHESION FORCE DISTRIBUTIONS FOR DIFFERENT SHAPED PARTICLES

A basic method to calculate van der Waals dispersion force distributions for submicron superquadric particles in particle-wall systems is presented. The force distribution is achieved by rotating particles through a large number of arbitrary spatial orientations, each time keeping constant the contact distance to the wall surface while calculating the dispersion force. To accomplish this, the use of 2D particle shape suffices, that is, through using an inter-dimensional function, which has been determined previously. A further development of the method within digital image analysis may lead to possible applications to forecasting the macroscopic properties of particle systems, for example, flowability, agglomeration behavior or dispersibility. For small ranges of superquadric particle shapes, each with a different size, the way from determining the inter-dimensional function up to applying image analysis is shown in an example.     

ELECTROSTATICALLY SUPPORTED MIXING OF FINE GRAINED PARTICLES

The processing of fine-grained particles with diameters between 1 and 10 microns is difficult due to strong van-der-Waals attraction forces. In order to improve the handling properties, the fine-grained particles, i.e. host-particles,are coated with various nanoparticles, i.e. guest-particles. The mixing of fine-grained powders is influenced by particle-particle interactions. If these forces are distinctively used, both interactive and ordered mixtures can be produced.These particle mixtures consist of composite-particles that have new physical properties. These modified properties d epend strongly on the coating process, the diameter- and mass-relationship of the guest- and the host-particles. The properties of the composite-particles can systematically be adjusted to the requirements of industrial applications. For example, a laboratory bubbling fluidized bed can be used to describe the conveying behavior of the functionalized host-particles. Applications for the functionalized particles are in the pharmaceutical and the powder coating industries,e.g. enhanced dry powder inhalers and thin lacquer films. The present research compares three different mixing/coating processes. The composite-particles are characterized by TEM, SEM and with their fluidization characteristics. The coating process itself is monitored by the electrostatic charge of the particles.     

Analysis of humidity-dependent adhesion between a probe tip and a surface

Adhesive forces commonly exhibit a monotonic increase or a maximum with increasing relative humidity. However, anomalous behavior has been reported. Here, a numerical model of adhesive forces, comprised mainly of capillary and van der Waals forces, between a tip and a surface is established. It is described by a power law that considers the geometry, the liquid bridge wetting radius, the contact angle, and the separation distance. Capillary forces (sum of surface tension and Laplace pressure) and van der Waals forces are calculated. The latter cannot be neglected in the adhesion even at high humidity. Decrease in adhesion with increasing relative humidity can be attributed to a blunt tip shape, which is validated by experimental data. Specifically, the decrease in adhesion is attributed primarily to a transition from a rounded to a blunt tip shape. Structuring objects at the micro- or nanoscale can either increase or decrease adhesion as a function of relative humidity. This has a wide range of applications in robotic manipulation and can provide a better understanding of adhesion mechanisms in atomic force microscopy in ambient air.     

Correlation of powder flow properties to interparticle interactions at ambient and high temperatures

A combination of a continuum approach and a particle–particle approach to describe the multi-scale nature of the mechanical properties of bulk solids may be beneficial to scientific and engineering applications. In this paper, a procedure is proposed to estimate the interparticle forces beginning with the bulk flow properties as measured with standardized techniques. In particular, the relationship between interparticle forces and bulk solid tensile strength is adopted based on the microscale approaches of Rumpf (1970) and Molerus (1975). The flow properties of fluid cracking catalyst (FCC), corundum and glass bead powders were all characterized with a modified Schulze ring shear cell capable of operating at temperatures up to 500 °C. The powder test conditions were selected such that the van der Waals forces were the most significant particle–particle interactions. The model equations describe two cases, in which either elastic or plastic deformation of the contact points is assumed. The results indicate that the model provides the correct order of magnitude for the values of the tensile strength when proper values for the mean curvature radius at the contact points are taken into account. A sensitivity analysis for the main parameters in the model was performed. This analysis indicated that the assumption of plastic deformation at contact surfaces coupled with a decrease in porosity justified an increase of the tensile strength with consolidation stress. Furthermore, the effect of temperature on the measured flow behavior can be explained as a change in the strength of the material.     

Surface instability of a semi-infinite anisotropic elastic body under surface van der Waals forces

We investigate the surface instability of an anisotropic elastic half-plane subjected to surface van der Waals forces due to the influence of another rigid contactor by means of the Stroh formalism. It is observed that the surface of a generally anisotropic elastic half-plane subjected to van der Waals forces from another rigid flat is always unstable. The wave number of the surface wrinkling is only reliant on the positive M₂₂ component of the 3 × 3 surface admittance tensor M, the van der Waals interaction coefficient β and the surface energy γ of the elastic half-plane. The decay rate of surface perturbation along the direction normal to the surface of the anisotropic half-plane is different from the wave number, a phenomenon different from that observed for an isotropic half-plane.     

Application of Lattice-Boltzmann Method for Analysing Detachment of Micron-Sized Particles from Carrier Particles in Turbulent Flows

Numerical calculations based on the Lattice-Boltzmann method were performed for a particle cluster consisting of a large spherical carrier particle covered with hundreds of small spherical drug particles. This cluster, fixed in space within a cubic computational domain, was exposed to turbulent plug airflow with predefined intensity. Such a situation is found in dry powder inhalers where carrier particles blended with fine drug powder are dispersed in a highly turbulent flow with the objective of detaching the drug powder for pulmonary delivery. Turbulence was generated by a digital filtering technique applied to the inflow velocity boundary condition. This technique was first validated by analysing the turbulence intensity at 15 fluid nodes along the stream-wise direction of the computational domain. The size ratio between the drug and carrier particle was 5 μ m/100 μ m, and the coverage degree of the carrier by the small particles was 50%, which is a typical value for carrier particle blending. The range of carrier particle Reynolds numbers considered was between 80 and 200, typical values found in inhaler devices. Exemplarily, at Re = 200 turbulence intensity was varied from 0.3% to 9.0%. The systematic increase of the mean flow (i.e. 80 < Re <200) resulted in varying turbulence intensities from 20 to 9%. These simulations provided the temporal evolution of the fluid dynamic forces on the drug particles in dependence of their angular position on the carrier in order to estimate the possibility of drug particle detachment. For turbulent conditions (i.e. Re = 200 and I = 9.0%) the maximum fluid forces on the drug particles were found to be about 10-times larger than found in laminar flow. The fluctuations in the forces were found to be higher than the flow velocity fluctuations due to the modification of the boundary layer around the cluster and instabilities triggered by the turbulent flow. There are three possibilities for detaching the drug powder, namely, through lift-off and sliding or rolling. Lift-off was found to be of minor importance due to the observed small normal fluid forces even at Re = 200 and I = 9.0%. The probability of sliding and rolling detachment in dependence of the angular position was estimated based on measured adhesion properties, i.e. van der Waals force, adhesion surface energy and friction coefficient. The remarkable rise of detachment probability for both effects due to the action of turbulence is an important finding of this study. In accordance with laminar flow, rolling detachment occurs before sliding, however in turbulent conditions over the entire carrier particle. The present studies improve the understanding of drug particle detachment from carrier particles in an inhaler device. The results will be the basis for developing Lagrangian detachment models that eventually should allow the optimisation of dry powder inhalators through computational fluid dynamics.