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.     

Turbulence structure for plane Poiseuille–Couette flow and implications for drag reduction over surfaces with slip

Direct numerical simulations were used to simulate plane channel and plane Poiseuille–Couette flows. For Poiseuille–Couette flow, the walls of the channel were moving with a specified velocity. This is equivalent to forcing a slip velocity at the wall of the channel, and such flow behaviour can be viewed as the effect due to an ultra‐hydrophobic wall. It was found that the location of the zero Reynolds stress value shifted towards the wall moving in the streamwise direction. The near‐wall eddies were found to be longer and weaker than for the plane‐Poiseuille channel flow. It appears that such an eddy structure can lead to turbulence drag reduction.     

Hydrothermal performance analysis of various surface roughness configurations in trapezoidal microchannels at slip flow regime

The effects of various surface roughness geometrical properties including roughness height (5%, 10%, 15%), number (3, 6), and shape (rectangular and triangular) on the flow and heat transfer of slip-flow in trapezoidal microchannels were investigated. The effects of mentioned parameters on the heat transfer coefficient through the microchannel, average Nusselt number and pressure drop for Reynolds number of 5, 10, 15 and 20 were examined. The obtained results showed that increasing the roughness height and number increases the pressure drop due to higher stagnation effects before and after roughness elements and decreases the Nusselt number due to higher recirculation zones effects than obstruction effects. The most reduction in Nusselt number and the most increment in pressure drop occur at the roughness height of 15%, roughness number of 6 and Reynolds number of 20 by about 10.6% and 52.8% than the smooth microchannel respectively.     

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.     

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     

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.     

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.     

Pipeline scale-up in drag reducing turbulent flow

Models available in literature for predicting drag reduction scale-up are inadequate as they have been successful only over a narrow range of diameters. A new scale-up model is presented which equates dampening of turbulent velocity fluctuations by drag reducing additives to a reduction in the Prandtl mixing length. Flow and pressure drop data from a laboratory scale pipe along with shear viscosity measurements are sufficient to predict drag reduction scale-up in bigger diameter pipes. Using this approach, scale-up was successfully predicted over a diameter range of 7 to 154 mm for a surfactant-water system and 26.6 to 1194 mm for a polymer-oil system.     

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.     

Experimental measurements of aspiration efficiency for idealized spherical aerosol samplers in calm air

In a recent previous paper (Su & Vincent, J. Aerosol Sci. 33 (2002) 103) we described a new method by which to investigate the relationships between aspiration efficiency, particle inertia, gravitational effect and sampling orientation for aerosol sampling in perfectly calm air. All previous experimental work to elucidate the basic nature of aerosol sampling in calm air described has been carried out for thin-walled tubes, and none has yet been reported in relation to blunt samplers. To begin to fill this important gap, the present paper describes the application of our new method towards acquiring new measurements of aspiration efficiency for simple blunt samplers.Experiments were carried out to determine the aspiration efficiencies of simple, idealized, spherical blunt samplers for a range of sampling scenarios, for two sizes of blunt samplers and different sampling inlet diameters, and for upwards and downwards sampling scenarios (and hence a range of governing dimensionless physical quantities). It was shown that aspiration efficiency decreased both with increasing inertia (as represented by the Stokes’ number) and with increasing gravitational effect (as represented by the ratio of particle settling velocity to the air velocity at the sampler inlet). The results enabled qualitative physical explanation of the difference between what was observed for upwards and downwards-facing sampling, respectively, in terms of (a) the role of the sampler body in deflecting the air flow in the region close to the body of the sampler (in turn influencing the performance of the sampler), and (b) the interception of particles in the downwards-facing scenario falling within the ‘shadow’ projected upwards by the sampler body.The significant contribution of this work has been the acquisition of a definitive set of new experimental data. These data will be valuable in the future development of understanding of the physics underlying aerosol sampler performance. Such knowledge will be of practical value because (a) blunt samplers are generally the most representative of the types of instruments used in practical occupational, and (b) calm or slowly moving air is characteristic of many indoor situations.     

A theoretical study of aerosol sampling by an idealized spherical sampler in calm air

The performance of an idealized spherical sampler operating in calm air for an inlet arbitrarily oriented relative to the gravity force is studied theoretically. Under potential flow assumption the air velocity field is obtained by using a model of a finite-size sink on a sphere. The particle motion equations are solved to find the limiting trajectory surface and to calculate the aspiration efficiency. The singular points of the motion equations as a function of settling velocity of particles and the sampler orientation angle are investigated. The connection between the pattern of typical zones of particle trajectories around the sampler and the location of the singular points is illustrated. The effects of partial sampling from zones without particles and of particle screening are discussed. The results of parametrical investigations of the dependence of the aspiration efficiency on the Stokes number and their analysis are presented. In the case of vertically upwards orientation of the sampler the proposed mathematical model gives fair agreement with experimental data from the work by Su and Vincent (Abstracts of sixth international aerosol conference, Taipei, Taiwan, 2002a, pp. 639–640).     

Water slip flow in superhydrophobic microtubes within laminar flow region

The fabrication of superhydrophobic surfaces and the studies on water flow characteristics therein are of great significance to many industrial areas as wel as to science and technology development. Experiments were car-ried out to investigate slip characteristics of water flowing in circular superhydrophobic microtubes within lam-inar flow region. The superhydrophobic microtubes of stainless steel were fabricated with chemical etching–fluorination treatment. An experimental setup was designed to measure the pressure drop as function of water flow rate. For comparison, superhydrophilic tubes were also tested. Poiseuille number Po was found to be smaller for the superhydrophobic microtubes than that for superhydrophilic ones. The pressure drop reduc-tion ranges from 8%to 31%. It decreases with increasing Reynolds number when Re b 900, owing to the transition from Cassie state to Wenzel state. However, it is almost unchanged with further increasing Re after Re N 900. The slip length in superhydrophobic microtubes also exhibits a Reynolds number dependence similarly to the pressure drop reduction. The relation between slip length and Darcy friction factor is theoretically analyzed with consideration of surface roughness effect, which was testified with the experimental results.     

A consolidated flow regime map of upward gas fluidization

A new flow regime map, resulting from more fundamental studies on the hydrodynamics and new flow regimes, is proposed in response to more practical reclassifications of the existing regimes with the development of upward gas-solids fluidization systems. The previously reported flow regime maps and flow structures of some widely used fluidized beds are carefully examined. To better reflect the industrial applications, the fast fluidization regime is reclassified as high-density and low-density circulating fluidization regimes. A consolidated flow regime map is then proposed where the flow regimes of upward fluidization expand to include new types of fluidized beds such as circulating turbulent fluidized bed and high-density circulating fluidized bed. The proposed flow regime map consists of six flow regimes: bubbling, turbulent, circulating turbulent, high-density circulating and low-density circulating fluidization, and pneumatic transport. The transitions between the regimes are discussed with new correlations proposed for fluid catalytic cracking type particles. Analysis on the dominating phase in the different types of fluidized beds reveals the dynamic changeover from solids phase continuous in conventional low-velocity batch/“fixed” fluidization operations to gas phase continuous in high-velocity continuous/“moving” fluidization operations and provides more insights to the transitions between the flow regimes for industrial design and practice.     

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