Modeling instantaneous pressure drop of pleated thin filter media during dust loading

In this paper, we present a modeling methodology for studying the effects of dust loading on the pressure drop across pleated filters. Our simulations demonstrate that there exists an optimum pleat count for clean filters at which pressure drop reaches a minimum regardless of the in-plane or through-plane orientation of the fibers. With the particle deposition included in the analysis, our results indicated that the rate of increase in pressure drop decreases with increase in the pleat count. We demonstrated that a higher pleat count results in a higher flow velocity inside the pleat channels causing more non-uniformity in the dust deposition across the pleat. Especially when particles are sufficiently large, the dust cake tends to form deeper inside the pleated channel when the pleat count is high. This effect is observed to be less pronounced when the pleats have a triangular shape. We also showed that if the dust cake permeability is higher than that of the filters fibrous media, the rate of increase in pressure drop does not always decrease with increase in the pleat count. Finally, by comparing filters having 15 pleats per inch, we observed that rectangular pleats are preferred over the triangular pleats when the particles are highly inertial, i.e., filtering high-speed large particles. When particle's inertia is small, our results indicate that triangular pleats cause less pressure drop, and so are recommended.     

Agglomerates and granules of nanoparticles as filter media for submicron particles

An experimental study on filtration of submicron solid and liquid aerosol particles by using a filter media composed of agglomerates or granules of nanoparticles is described. Fumed silica nanoagglomerates, carbon black granules, silica shells, activated carbon granules, glass beads and nanoporous hydrophobic aerogel were among the granular filter media tested and compared to a commercially available HEPA fiber-based filter. Other than the glass beads which were used for comparison purposes, the primary particle size of the agglomerates/granules is of nanometer scale, but they agglomerate to form porous structures of about several hundreds of microns which were customized as packed (deep bed) or fluidized bed filters and challenged against submicron solid and liquid aerosols. For packed bed filters, the size of the granules has been optimized to a range of 150-500 µm with a filter thickness of about 1-3 in. and superficial gas velocities of less than 4 cm/s. Fluidized beds required granules smaller than 150 µm and the height of the bed was in the range of 15-40 cm.The customized filters and a HEPA fiber-based filter were challenged simultaneously against the same aerosol at the same superficial gas velocities. When using carbon black or aerogel granules as filter media, collection efficiencies comparable or even higher than HEPA fiber-based filters are obtained, but with the advantage of extra filtration capacity due to the deep bed configuration and the absorption of liquids into the porosity of the media. A fluidized bed filter of aerogel granules not only provides higher collection efficiency and larger capacity than a HEPA fiber-based filter when challenged against both oil mist and solid aerosols but also has an extremely low pressure drop compared to a packed bed filter and can be operated continuously with respect to removing saturated granules and adding fresh ones.     

Application of nanofibers to improve the filtration efficiency of the most penetrating aerosol particles in fibrous filters

Conventional, mechanical fibrous filters made of microfibers exhibit a local minimum of fractional collection efficiency in the aerosol particle size-range between 100 and 500 nm, which is called the most penetrating particle size (MPPS). Simple theoretical calculations predict that this efficiency may be significantly increased using nanofibrous media. The main objective of this paper is an experimental verification of these expectations and simultaneously checking whether this anticipated gain in the filtration efficiency is not overpaid with an excessive pressure drop. For this purpose we developed a modified melt-blown technology, which allowed us to produce filters composed of micrometer as well as nanometer sized fibers. One conventional microfibrous filter and five nanofibrous filters were examined. The complete structural characteristics, pressure drop and efficiency of removal of aerosol particles with diameters 10-500 nm were determined for all media. The results of the experiments confirmed that using nanofibrous filters a significant growth of filtration efficiency for the MPPS range can be achieved and the pressure drop rises moderately. Simultaneously, we noticed a shift of the MPPS towards smaller particles. Consequently, the quality factor for bilayer systems composed of a microfibrous support and a nanofibrous facial layer was considerably higher than this one for a conventional microfibrous filter alone. Additionally, it was found that utilization of many-layer nanofibrous filters combined with a single microfibrous backing layer is even more profitable from the quality factor standpoint. Comparing experimental results with theoretical calculations based on the single-fiber theory we concluded that for microfibrous filters a fairly good agreement can be obtained if the resistance-equivalent fiber diameter is used in calculations instead of the mean count diameter determined from the SEM images analysis; in the latter case, filtration efficiency computed theoretically is slightly overestimated. This is even more evident for nanofibrous media, suggesting that in such case a structural filter inhomogeneity has a strong influence on the filter efficiency and its resistance and one should strive for minimization of this effect manufacturing nanofibrous filters as homogeneous as possible. We can finally conclude that fibrous filters containing nanofibers, which are produced using the melt-blown technique, are very promising and economic tools to enhance filtration of the most penetrating aerosol particles.     

A numerical investigation of aerosol dynamics in a wall-less reactor

This paper describes a numerical investigation of aerosol formation during silane decomposition in a wall-less reactor. The wall-less reactor is amenable to numerical investigation because the homogeneous chemical reactions leading to the formation of solid particles are isolated from heterogeneous effects, such as occur at the walls of a laminar flow aerosol reactor. The flow/heat transfer and gas-phase chemical kinetics are simulated utilizing separate one-way coupled models. The aerosol dynamics model is based on a simplified sectional model originally developed by Okuyama et al. This model is modified to allow for the simulation of particle growth via condensation. Simulations have been performed which indicate that particle growth via condensation may be an important process. Additionally, the effects of total reactor pressure, temperature and inlet silane concentration on the dynamics of the aerosol population have been investigated. Conditions which result in the formation of larger and more numerous particles have been identified.     

Contribution of synchrotron X-ray holotomography to the understanding of liquid distribution in a medium during liquid aerosol filtration

The three-dimensional structure of a fibrous filter determines its behaviour during filtration, such as the obtained pressure drop, the fractional efficiency and the filter lifetime. Therefore, suitable parameters describing the inner structure (the local packing density) are key inputs for modelling filter performance accurately. The synchrotron X-ray holotomography, carried out at the European Synchrotron Radiation Facility, was performed in this study to provide information on the three-dimensional structure of a fibrous filter. Moreover, this non-invasive technique was used to determine the liquid distribution in a filter clogged with a liquid aerosol of di-ethyl-hexyl-sebacate. These samples were imaged at a voxel size of 0.7 μm, which allows the quantification of the different phases within the filter (liquid, fibres and void space). The results complete the two-dimensional studies obtained by scanning electron microscopic and highlight the formation of liquid menisci not only on the filter surface but also in the filter depth. Image analyses of synchrotron X-ray holotomography radiographs also highlight a heterogeneous liquid distribution along the thickness of the clogged filter.     

Granular-bed filtration assisted by filter cake formation 3. Penetration of filter cakes by a monodisperse aerosol

For several types of granular solids (sands, silicon carbide and copper shot), penetrations have been measured for a monodisperse aerosol (1.1 μm Dow microspheres) passing through fly ash deposited upon horizontal surfaces of the solids. Fractional penetrations can run as low as 10⁻⁵. Pressure drop data for dust cake/granular medium combinations are also given. The data illustrate significance of dust autohesivitiy and dust/granular solid adhesivity for granular-bed filtration assisted by dust cake formation.     

Development of a qualitative test method for the cleanability of polymer woven filter media

In this paper a new method for cleaning of filter media is presented, and the cleanability with different textures and surface finishes is compared. With the method described, it is possible to evaluate the quality of the cleaning process. According to the German VDMA standard cleaning test, riboflavin and malt extract are applied as model contaminants for evaluation of the cleaning results. To compare the cleanability of filter media with different properties and geometries the results are adapted to the law of mass transfer and to the Sherwood number, a dimensionless parameter describing the quality of a cleaning process.     

Derivation of filtration equations incorporating the effect of pressure redistribution on the cake-medium interface: A constant pressure filtration

This study presents a simplified model of cake filtration that incorporates the effect of pressure redistribution on the cake-filter medium interface. The analytical solutions arrived at allow for improved prediction of the cake growth process (including cake thickness and filtration velocity as functions of time) compared with conventional theory. The pressure and void ratio profiles calculated from the present study are compared with results obtained from the use of conventional theory and the numerical solution of dynamic filtration equations.     

Clogging of fibrous filters by liquid aerosol particles: Experimental and phenomenological modelling study

Fibrous filters are the most common means used to separate liquid aerosol particles from an industrial gas stream. The pressure drop and penetration (=1-efficiency) are the most important performance criteria of the filter. In this study, experimental and modelling results describing the pressure drop and penetration evolution of a glass microfibre HEPA filter are presented. For the experimental part, the pressure drop and penetration evolutions of a HEPA filter are described as well as the influence of the filtration velocity on those evolutions. For the modelling part, the physical collection mechanisms taken into account and their mathematical expressions which are the basis of the phenomenological model are described in a first step. After that the experimental values are compared to their modelled counterparts. Different efficiency models from the literature have been tested in order to determine the one closest to the experimental values. The influence of the filtration velocity on the model is studied in the last part. The model presented here is capable of describing the pressure drop and penetration evolution of a HEPA filter over the whole filtration period.     

Investigation of different crystal habits without chemical additives in a three-phase reactor

A lot of powders with fine particle sizes and specific crystal habits are produced by precipitation processes, in which growth and morphology of the particles are controlled by a wide range of chemical agents. This study investigates alternative ways to limit crystal growth and influence crystal morphology. Experiments are carried out in an ultrasound levitator, where a single droplet can be suspended against gravity by an acoustic levitation force. The ultrasound leviator is a three-phase reactor, which allows the investigation of precipitation with applying specific shear forces at growing crystals within the droplet. The investigated system is calcium carbonate. By variation of physical reaction parameters as temperature and level of applied shear forces it is possible to obtain different crystal habits and morphologies. The morphology of calcium carbonate produced in the leviator can vary between prismatic, shell-like and spherical shape. Also the particle size distribution of the precipitated product is influenced. Increasing mechanical stress leads to a shift of the particle size distribution to smaller sizes.     

Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of CSTR

The role of scission reactions in low-density polyethylene (ldPE) polymerization has recently been the subject of various modeling studies. The linear scission approximation leading to a uniform fragment length distribution, seems to describe the scission mechanism well. For linear scission the predicted bimodal molecular weight distribution (MWD) in the case of a CSTR agrees with that found by size exclusion chromatography (SEC). However, scission of branched polymers does not follow the linear scission model, since it leads to predominately long and short fragments. Therefore, we systematically compared the linear scission model with the newly proposed ‘topological scission’ model. We found a pronounced difference in MWD between linear scission, yielding a bimodality and topological scission, leading to a long tail in MWD. In addition we examined mechanical scission that could occur in stirred autoclave reactors due to mechanical action. Mechanical scission also turns out to generate bimodality in MWD. The molecular architecture of ldPE is also discussed in connection with scission kinetics and the topological scission model.     

Molecular weight distribution in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor

It has been shown that scission kinetics strongly affects the molecular weight distribution (MWD) of low-density polyethylene (ldPE) in a continuous stirred tank reactor (CSTR). The present paper focuses on the effects of different chemical scission mechanisms, linear and topological scission, as well as mechanical scission on MWD in batch and tubular reactors. In contrast to the CSTR, a batch reactor MWD does not show bimodalities or long tails. The tubular reactor was modeled as an industrially representative system with four initiator injection points and a proper ‘cocktail’ of different initiators. Calculated MWD was compared to one experimentally determined with SEC-MALLS for a commercial tubular product and fair agreement was found. Typically, these MWDs are broad, but not bimodal. Sensitivity studies were performed as to scission kinetics and the effect of chain transfer agent (CTA). Both batch and tubular reactor were observed to be less sensitive to scission kinetics than a CSTR. In addition, alternative CTA injection strategies (downstream positions) were tested. These showed interesting behavior leading to very broad and bimodal MWD. The model allows following the MWD broadening along the tube. We conclude that batch and tubular ldPE reactors lead to completely different MWD behavior than a CSTR and that it is possible to manipulate it to a great extent.     

复杂混合液的动态膜滤装置及其膜滤速率研究

本文从阻力理论出发，分析了旋叶式动态膜滤装置在对复杂混合液膜滤过程中的各种膜滤阻力的形成，影响因素及其变化规律，通过对多种复杂混合液的膜滤实验总结，建立了适于描述复杂混合液膜滤速率的数学模型，为工业复杂混合液的分离纯化和浓缩提供了一条新的途径。     

A parametric study of direct gravure coating

An experimental investigation of direct gravure coating, focusing on roll-to-web fluid transfer over a wide range of conditions is presented. The results highlight that the pickout of fluid from the gravure cells (i.e. the fraction of the cell volume transferred to the web) is affected significantly by the ratio of the web-to-roll speed, the fluid properties and the shape and size of the gravure cells. The stability of the operability window is also explored. At high web-to-roll speed ratios the pickout from the gravure cells approaches one and an instability, caused by starvation, results in streaking on the web.     

钛硅分子筛TS-1动态过滤的研究

对钛硅分子筛TS 1微粉催化剂应用动态过滤技术 ,在动态旋叶压滤机上进行了过滤性能的研究 ,得到了过滤速率随时间的变化规律 ,并分析了操作压力对过滤速率的影响。为了结合实际工业生产的要求 ,对过滤介质进行了再生实验。该研究为TS 1微粉催化剂的过滤分离提供了一个可行的方法 ,为确定适宜的操作条件及工业应用提供了实验依据     

Mechanism of mixing enhancement with baffles in impeller-agitated vessel, part I: A case study based on cross-sections of streak sheet

Enhancement mechanism of mixing with baffle in agitated vessel using rotated two-bladed paddle impeller was investigated under a laminar condition. In mixing pattern, the toroidal isolated mixing region in the baffled vessel becomes distortive and much smaller than that of unbaffled vessel. From the visualization of streak cross-sections in the baffled vessel, interestingly, the renewed streak folds (streak lobes) are generated at the vicinity of baffles in both the vertical and horizontal cross-sections. These behaviors of streak are unlike the unbaffled case that the streak stretches straightforwardly. The streak lobe is known as the mixing template that its number and size are key factor for laminar mixing in agitated vessel. The results suggest that baffles can effectively transform the circumferential flow to vertical and/or radial flows. Consequently, in the baffled vessels, not only the vicinity of vessel wall but also the tip of baffles can become the origination of streak lobe formation, and folds of streak in the vertical and circumferential directions are further enhanced with baffles.     

A methodology for simultaneous process and product design in the formulated consumer products industry: The case study of the detergent business

In this work we present a mathematical optimization based methodology for simultaneous formulae and process design in the consumer product business applied to the case of the laundry detergent. The design of a new detergent is formulated as a modified pooling problem including process, performance, processability and environmental constraints. This new features add a number of nonlinearities related to the modeling of the different aspects of the process and customer acceptance. The problem becomes a multiobjective optimization problem that is solved using the ?-constraint method with global optimization techniques to minimize of the environmental impact while minimizing the production cost for a couple of case studies. As future work, further process, product and legal constraints can be added to make the problem more realistic.     

A two-scale modeling of motion-induced fluid release from thin fibrous porous media

In this work, a two-scale two-phase modeling methodology is presented for studying fluid release from saturated/unsaturated thin fibrous media when brought in contact with a moving solid surface. Our macroscale model is based on the Richards’ equation for two-phase fluid transport in porous media. The required constitutive relationships, capillary pressure and relative permeability as functions of medium's saturation, are obtained through microscale modeling. At microscales, a 3-D model based on fiber diameter, fiber orientation, and medium's solid volume fraction (SVF), is generated to resemble the internal structure of the fibrous sheets and be used in full-morphology analysis as well as microscale permeability simulation. A mass convection boundary condition is considered here to model the fluid transport at the boundary in contact with the target surface. It was shown that the mass convection coefficient, k_f, plays a significant role in determining the release rate and is expected to be in the range of 10^-6<k_f<10^-9, depending on the properties of the fluid, fibrous sheet, the target surface as well as the speed of the relative motion, and remains to be determined experimentally.     

A numerical study of stir mixing of liquids with particle method

The process of stir mixing of two viscous liquids is simulated using the moving particle semi-implicit (MPS) method. A mixing rate is defined within the particle method to characterize the level of mixing, as the number, position, period, and rotating speed of the stirring stick(s) and liquid viscosity are changed. The motions of liquid particles are tracked to reveal the flow field and mixing mechanisms. The variation of the mixing rate shows that the mixing rate is higher when the sticks are rotating monotonically at high speed, and an optimum position of the stick can be identified. The mixing rate does not enhance significantly when three or more sticks are employed, and the liquid viscosity has minor influences on the mixing rate. These results give useful qualitative suggestions on controlling the mixing rate during chemical reactions.