Modeling permeability of 3-D nanofiber media in slip flow regime

Over the last few decades, numerous analytical and/or numerical expressions have been developed for predicting the permeability of a fibrous medium. These expressions, however, are not accurate in predicting the permeability of media made up of nanofibers. This is because the previous expressions were mostly developed for coarse fibers, where using the so-called no-slip velocity boundary condition at the fiber surface is quite justified. Removing the no-slip velocity restriction in this work, we study the effect of slip flow on the permeability of fibrous materials made up of nanofibers. This has been accomplished by generating a large series of 3-D virtual geometries that resemble the microstructure of a nanofiber (e.g., electrospun) material. Stokes flow equations are solved numerically in the void space between the nanofibers, with the slip flow boundary condition developed based on the Maxwell first order model. The influence of fiber diameter and solid volume fraction (SVF) on the media's permeability is studied, and used to establish a correction factor for the existing permeability expressions when used for nanofiber media.     

On the importance of fibers' cross-sectional shape for air filters operating in the slip flow regime

In this paper, we investigate the effects of fibers' cross-sectional shape on the performance of a fibrous filter in the slip and no-slip flow regimes. The slip flow regime is expected to prevail when fiber diameter is comparable in size to the mean free path of the gas molecules (about 65 nm at normal temperatures and pressures), whereas the no-slip flow regime describes the aerodynamic condition of flow through media with large fibers. Our numerical simulations conducted for flow around single fibers with different geometries indicate that, while the collection efficiency is only weakly affected by the cross-sectional shape of nanofibers, the fiber drag (i.e., permeability of the media) can be considerably influenced by the fiber's shape. Simulating the flow field around nano- and microfibers with circular, square, trilobal, and elliptical cross-sections, it was found that the more streamlined the fiber geometry, the lower the fiber drag caused by a nanofiber relative to that generated by its micron-sized counterpart.     

A soft-sensor approach to flow regime detection for milling processes

Due to the many industrial applications of rotating drums, a wide range of operating conditions, including different particle flow regimes, are used. Knowledge of the flow regimes inside a drum is beneficial for process optimisation and control. This paper shows how the unique insights provided by a discrete element method (DEM) model of a rotating drum can be used to create soft-sensor models that detect flow regime. Impacts between particles and the drum wall are simulated, from which the feature variables are extracted. A soft-sensor model which links these feature variables to flow regime is constructed using the multivariate statistical technique of Fisher discriminant analysis (FDA). This model is able to successfully classify new testing data, which are not used in soft-sensor model training, as belonging to rolling, cascading and cataracting flow regimes.     

Mobility radius of fractal aggregates growing in the slip regime

A method is presented for the calculation of the mobility radius of fractal aggregates. The connection between the aggregate permeability and the monomer friction factor is derived, which makes it possible to convert the permeability in the continuum regime to that in the slip regime. The method elaborated here estimates the permeability of an aggregate treated either as impermeable sphere of the size equal to mobility radius or a permeable self-similar structure consisting of impermeable monomers. The internal permeability of a fractal aggregate growing in the slip regime is analyzed assuming that the aggregate consists of no more than twelve effective impermeable monomers, the number being a result of hydrodynamic considerations. The method makes it possible to estimate the aggregation number dependence of the mobility radius. A system of carbonaceous flame soot aerosol containing fractal aggregates with D=1.8 is analyzed. The mobility radius-aggregation number relation is found to be very close to that obtained experimentally. For large aggregation numbers this relation tends to that, which is valid for the dynamic radius.     

Duration of tangent-linear regime in sectional multi-component aerosol dynamics

In this article, a tangent-linear multi-component aerosol dynamical box model was studied. In particular, the length of time over which the tangent-linear dynamics dominate the total evolution of a particle number concentration perturbation is determined. In the experiments, three non-linear model initial number concentration distributions, perturbation distributions, and ambient vapour concentrations are used. Results indicate, based on analysis of the evolution of number distribution perturbation, that in pure nucleation events the tangent-linear regime persists for about 1.5 h, and can last for several hours in cases of weak nucleation. Analysis of the perturbation evolution with emphasis on particle surface area or volume indicates that the dynamics is tangent-linear over a much longer period. In conclusion, high ambient sulphuric acid vapour concentration maintains a large number concentration of small particles (below about 10 nm) through nucleation. These particles are the prime source of non-linearity limiting the length of the tangent-linear regime in a box model context. The results have relevance, but are, however, not directly applicable, for instance, in three-dimensional chemical transport and air-quality modelling aiming to incorporate data assimilation techniques, such as four-dimensional variational data assimilation.     

A new drag correlation from fully resolved simulations of flow past monodisperse static arrays of spheres

Fully resolved simulations of flow past fixed assemblies of monodisperse spheres in face‐centered‐cubic array or random configurations, are performed using an iterative immersed boundary method. A methodology has been applied such that the computed gas–solid force is almost independent of the grid resolution. Simulations extend the previously similar studies to a wider range of solids volume fraction ( [0.1, 0.6]) and Reynolds number (Re [50, 1000]). A new drag correlation combining the existed drag correlations for low‐Re flows and single‐sphere flows is proposed, which fits the entire dataset with an average relative deviation of 4%. This correlation is so far the best possible expression for the drag force in monodisperse static arrays of spheres, and is the most accurate basis to introduce the particle mobility for dynamic gas–solid systems, such as in fluidized beds. © 2014 American Institute of Chemical Engineers AIChE J, 61: 688–698, 2015     

Comparison of formulas for drag coefficient and settling velocity of spherical particles

Two formulas are proposed for explicitly evaluating drag coefficient and settling velocity of spherical particles, respectively, in the entire subcritical region. Comparisons with fourteen previously-developed formulas show that the present study gives the best representation of a complete set of historical data reported in the literature for Reynolds numbers up to 2 × 10⁵.     

Preparation of spherical macroporous silica in an aerosol phase

Macroporous silica (MS) and macro/mesoporous silica (MMS) were prepared by spray drying a polystyrene (PS) latex sol containing a silica source, followed by calcination. As a silica source, 3-aminopropyl triethoxysilane (APS) was used for MS while either silica sol (SS) or tetraethoxyothosilicate using P123 templating (P123-TEOS) was used for MMS. Spray drying and calcination could also take place in a once-through aerosol reactor. The transformation of the silicon alkoxides to silica and decomposition of PS occurred at similar temperatures. Therefore, for APS-originated MS, the metal additives such as silver and nickel were required to accelerate the former. In addition, the nickel was well dispersed in the silica matrix during calcination even at 800 °C, in turn to thermally stabilize the porous structures. The wall-preforming additives were unnecessary for PS/SS and PS/P123-TEOS, since the SS drying and P123 templating, respectively, took place at lower temperature than PS decomposition. The porosities of all the porous silica prepared ranged from 0.54 to 0.57, which were close to the volume fraction of PS in the PS-alkoxides mixture solidified right after spray drying.     

A comparison of drag reduction for flows in circular tubes with flow between parallel planes

Drag reduction in the turbulent flow of aqueous solutions of polyacrylamide and poly(ethylene oxide) was studied in tubes and parallel plates. Friction factors were determined at Reynolds numbers up to 20,000 for polymer concentrations of 0.10 to 400g/m³ in glass tubes run in a constant-head, gravity flow system in which the velocity was determined from the horizontal distance traveled by the effluent stream while falling a set vertical distance; and in Plexiglas parallel plates run in a constant-velocity, machine-driven system in which the pressure drop between two points on the plates was measured with a differential pressure transducer. A general method of correlating fraction laminarization or drag reduction effectiveness with polymer concentration for Reynolds numbers above 6000 was developed in which two master curves, one for very low concentrations which was the same for both tubes and parallel plates, and one for higher concentrations which differed for tubes and parallel plates, were found to represent the data very well for both polymers and all conduit sizes and Reynolds numbers. Additionally, relationships were found between conduit size and maximum fraction laminarization and optimum polymer concentration.     

Modeling of flow dynamics in laminar aerosol flow tubes

Flow behaviour in laminar aerosol flow tubes was investigated using a Computational Fluid Dynamics (CFD) model. Since these flow tubes are typically operated at low gas velocity, even small temperature gradients produce convection currents strong enough to interfere with laminar flow. This results in recirculation, causing the residence times of aerosol particles to be poorly defined. The situation is exacerbated when temperature inversions are present, or when the flow direction and temperature are changed simultaneously. We analyzed several characteristic flow tube configurations to define the range of experimental conditions that will ensure a laminar flow profile with minimal recirculation. For a laminar flow situation, we evaluated the extent of diffusion-controlled exchange between aerosol and the flow tube wall.     

Viscosity corrections for concentrated suspension in capillary flow with wall slip

Corrections for viscosity measurements of concentrated suspension with capillary rheometer experiments were investigated. These corrections include end effects, Rabinowitsch effect, and wall slip. The effects of temperature, particle concentration, and contraction ratio on the end effects were studied and their effects were accounted for using an entrance and exit losses model. The non‐Newtonian effect and the nonlinearity of slip velocity against wall shear stress were described using a slip model. The true viscosity of a concentrated suspension with glass powder suspended in a non‐Newtonian binder system was calculated as a function of shear rate and effective particle concentration, taking into consideration particle migration, which is calculated by a diffusive numerical model. Particle size was found to affect significantly the viscosity of the suspension with viscosity decreasing with increasing particle size, which can be reflected by a decrease in the value of the power‐law index in the Krieger model. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Cluster-based drag coefficient model for simulating gas-solid flow in a fast-fluidized bed

Drag coefficient is of essential importance for simulation of heterogeneous gas-solid flows in fast-fluidized beds, which is greatly affected by their clustering nature. In this paper, a cluster-based drag coefficient model is developed using a hydrodynamic equivalent cluster diameter for calculating Reynolds number of the particle phase. Numerical simulation is carried out in a gas-solid fast-fluidized bed with an Eulerian-Lagrangian approach and the gaseous turbulent flow is simulated using large eddy simulation (LES). A Lagrange approach is used to predict the properties of particle phase from the equation of motion. The collisions between particles are taken into account by means of direct simulation Monte Carlo (DSMC) method. Compared with the drag coefficient model proposed by Wen and Yu, results predicted by the cluster-based drag coefficient model are in good agreement with experimental results, indicating that the cluster-based drag coefficient model is suitable to describe various statuses in fast-fluidized beds.     

流体透过颗粒层的全流态流动规律的构建

以Dupuit粉体层假定为基础建立数学物理模型,依据相对运动原理和相似运动规律,将流体透过颗粒层的流动与流体在当量平行细管中的流动及流体绕颗粒的绕流运动相比拟,发现它们之间的相似性与一致性。再从流体力学基本理论出发,通过对现有理论成果归纳与实验数据的重新整理,提炼出新型的流体透过颗粒层的全流态流动规律,从逻辑上统一了流体透过颗粒层流动规律的推理模式,在形式上更新了该流动规律的表现形式,初步完成了对该问题逻辑关联式的重置。     

A new plasma method of synthesizing aerosol particles

A new experimental method of synthesizing aerosol particles is demonstrated. A non-thermal plasma is used to sputter a solid target by energetic ion impact. Sputtered atoms nucleate in the gas phase to form particles, which the plasma levitates particles during several hours of operation. Particle growth can take place at room temperature. The plasma is formed in a vacuum vessel by a pair of parallel electrodes that are powered with a radio-frequency high voltage. Scanning electron micrographs reveal the particle morphology. Particles initially grow with a spherical shape, and their size can be selected by terminating the discharge after they have grown to the desired diameter. By altering the plasma parameters such as gas pressure and voltage, and by allowing particles to grow for a longer period of time, they can coagulate into string-like or fractal-like conglomerates.     

A new splitting wavelet method for solving the general aerosol dynamics equation

In this paper, a new and robust splitting wavelet method has been developed to solve the general aerosol dynamics equation. The considered models are the nonlinear integro-partial differential equations on time, size and space, which describe different processes of atmospheric aerosols including condensation, nucleation, coagulation, deposition, sources as well as turbulent mixing. The proposed method reduces the complex general aerosol dynamic equation to two one-dimensional splitting equations in each time interval, and further the wavelet method and the upstream finite difference method are proposed for solving the particle size directional and the spatial directional splitting equations. By the method, the aerosol size spectrum is represented by a combination of Daubechies’ wavelets and substituted into the size-directional splitting equation at each time step. The class of Daubechies’ wavelets in the wavelet-Galerkin scheme as trial and weight functions has the advantages of both compact support and orthonormality which can efficiently simulate the sharp shape distribution of aerosols along the particle size direction. Numerical experiments are given to show the efficient performance of the method.