Defining critical flux in submerged membranes: Influence of length-distributed flux

Flux can vary along the fiber length in submerged hollow-fiber membranes depending upon the axial gradients of both pressure and foulant layer build-up. However, the measurement of flux is necessarily length-averaged because it is determined by the flow rate exiting the end of the fiber. The length-averaged flux below which no foulant accumulates in a specified filtration time is defined as the critical flux. Critical flux is shown in this work to be a relative rather than absolute value. It depends on the fiber length, observation time, aeration rate and the compressibility of the particles. Fouling will occur in full-scale if the critical flux test is established in tests with fibers that are much shorter than in full-scale and/or with a filtration time that is shorter than in full-scale.     

Nanoaerosol Filtration with Fine-Fiber Polydisperse Filters

The self-consistent theory of nanoaerosol filtration has been considered at small Peclet numbers. It has been shown that, at Pe < 1, it is necessary to consider the deposition of particles simultaneously on thePe < entire ensemble of fibers. Only at can the filtration efficiency be found from the collection efficiencies calculated separately for each fiber. The self-consistent theory has been used to estimate the efficiencies of filtration with polydisperse fibrous filters. The penetrations of particles through filters with different variances of the functions of fiber length distribution over fiber radii have been compared at a constant packing density or a constant total length of all fibers. It has been shown that, at a constant packing density, a rise in the variance leads to a decrease in the filtration efficiency, while, at a constant total fiber length, the efficiency is almost independent of the width of the distribution function.     

The effect of diffusion on nanoaerosol filtration through porous materials with allowance for desorption processes

The effects of the finite residence time of aerosol particles in the bound state and their detachment due to thermal fluctuations on the filtration efficiency of porous and fibrous materials have been investigated with allowance for longitudinal diffusion in a flow. It has been shown that the desorption of particles affects the filtration efficiency even at times shorter than residence time τ_d of the particles in the bound state, while, at t ? τ_d, filtration stops. Allowance for the diffusion of aerosol particles in the flow leads to a decrease in the filtration efficiency as compared with the calculations performed without taking into account the longitudinal diffusion.     

Filtration of nanoaerosols through porous materials with allowance for desorption processes

The effects of finite residence time of aerosol particles in a bound state and their detachment due to thermal fluctuations on the filtration efficiency of porous and fibrous filters have been studied. It has been shown that, when desorption processes are taken into account, nanoparticle filtration efficiency decreases with time already at times that are short compared with the residence time of particles in the bound state.     

Nanoparticle‐enhanced bamboo‐like tubular nanofibers for active capture of particulate matter

We proposed a thought of active capture of particles by improving the interaction force between fibers and particles. Nanoparticle‐enhanced tubular nanofibers (Ag‐SPNTs) were prepared by template‐free cationic polymerization followed by surface modification. Ag‐SPNTs have coarse surface and bamboo‐like tubular structure with a diameter of approximately 80‐150 nm. Ag nanoparticles were embedded on the nanofibers surface, and the content of Ag nanoparticles in the nanofibers could be tuned by changing the concentration of [Ag(NH₃)₂]⁺ in the preparation process. f‐d curve measured by AFM showed that increasing the content of Ag nanoparticles in the nanofibers resulted in the enhanced interaction force between the nanofiber surface and particles. Particle matter capture test showed that the number of captured microscaled/naonoscaled particles on the fiber surface increased obviously for the nanoparticle‐enhanced tubular nanofibers (Ag‐SPNTs) compared to the nanofibers without nanoparticle (SPNTs), probably due to the increased interaction force and adhesion energy between fiber surface and particles. Filtration property test showed that the Ag‐SPNTs fiber films had a better filtration performance with a higher filter efficiency and QF value than that of SPNTs. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019     

Special features of filtration of heavy particles with fine-fiber materials

The excitation of elastic vibrations of fibers upon inertial deposition of submicron aerosol particles in the course of gas filtration through fine-fiber filters has been considered. Equations describing the dynamics of the interaction of several aerosol particles with a fiber have been derived. It has been shown that, in the case of heavy particles and long fibers, particles that have been previously deposited onto the fibers can be knocked-out upon an impact of a fast particle. Moreover, it has been demonstrated that fast particles can penetrate through traps consisting of several fibers due to the deformation of the latter. All these processes may have a substantial effect on the filtration performance in the inertial regime.     

Deposition efficiency of fractal-like aggregates in fibrous filters calculated using Brownian dynamics method

Nonspherical particles, such as fractal-like aggregates emitted by diesel engines, are commonly met in the ambient air. Some of them are believed to be carcinogenic to humans, thus their efficient removal is of crucial practical importance. A fibrous filter is the device commonly used for aerosol purification but the literature lacks experimental data concerning aggregates filtration. Effect of aggregates' parameters (fractal dimension, primary particle radius) as well as fiber diameter and air velocity on the filtration efficiency is investigated theoretically using the modified Brownian dynamics method. Three different expressions for the friction coefficient evaluation for the aggregates were examined. The results obtained indicate that structure of an aggregate, filter structure and process conditions strongly influence the aggregates deposition efficiency, which significantly differs from the values determined for mass-equivalent spherical particles. The results determined using the Brownian dynamics approach were compared with the values calculated using classical single fiber theory and noticeable discrepancy was observed for the most penetrating particles, while both approaches agree for the limiting cases of small or large particles. Peclet number based on the mobility radius and the interception parameter based on the outer radius are the proper criteria to describe diffusional and deterministic deposition of aggregates.     

Some Aspects of Magnetic Filtration Theory for Removal of Fine Particles from Aqueous Suspensions

The magnetic filtration theory was evaluated to intensify the filtration of industrial fluids by magnetic filters. Effects of filtration velocity and external magnetic field intensity on filter performance were investigated and the dependence of the logarithmic efficiency coefficient on filtration velocity was questioned. It was concluded that change in the magnetic susceptibility of the dispersion particles, caused by external magnetic field, and change in the flow rate properties of the liquid alongside the filter pores are the most essential factors to be considered in the design, development, and modeling of magnetic filtration systems in various industrial areas.     

Inertial Hydrodynamic Effects in Electrophoresis of Particles in an Alternating Electric Field

The influence of the effects associated with the inertia of particles and the surrounding fluid on the electrophoresis in an alternating electric field has been theoretically investigated. From solving the hydrodynamic equations the electrophoretic velocity of a spherical particle was found to depend on the frequency of the external electric field and on the particle-to-fluid-density ratio. It is shown that, due to inertial effects, the liquid flow around particles with a thin electrical double layer (EDL) is no longer potential. A mechanism of the formation of steady-state flow in the vicinity of oscillating particles with a thin EDL is proposed. Using numerical methods, a picture of the fluid streamlines in such a flow is obtained. The spatial distribution of the fluid velocity in the vicinity of a particle is also found. It was established that with an increasing frequency of the electric field the steady-state flow velocity passes through a maximum. The flow direction depends on the ratio between the densities of a particle and the surrounding fluid. The reversal of direction takes place when this ratio is about 0.7. The case of a thick EDL has also been considered, and a comparative analysis of the flow distributions around the particles with a thin and those with a thick EDL has been carried out.     

Hyperbranched Polymer Induced Antibacterial Tree-Like Nanofibrous Membrane for High Effective Air Filtration

The air filtration materials with high efficiency, low resistance, and extra antibacterial property are crucial for personal health protection. Herein, a tree-like polyvinylidene fluoride (PVDF) nanofibrous membrane with hierarchical structure (trunk fiber of 447 nm, branched fiber of 24.7 nm) and high filtration capacity is demonstrated. Specifically, 2-hydroxypropyl trimethyl ammonium chloride terminated hyperbranched polymer (HBP-HTC) with near-spherical three-dimensional molecular structure and adjustable terminal positive groups is synthesized as an additive for PVDF electrospinning to enhance the jet splitting and promote the formation of branched ultrafine nanofibers, achieving a coverage rate of branched nanofibers over 90% that is superior than small molecular quaternary ammonium salts. The branched nanofibers network enhances mechanical properties and filtration efficiency (99.995% for 0.26 µm sodium chloride particles) of the PVDF/HBP-HTC membrane, which demonstrates reduced pressure drop (122.4 Pa) and a quality factor up to 0.083 Pa⁻¹ on a 40 µm-thick sample. More importantly, the numerous quaternary ammonium salt groups of HBP-HTC deliver excellent antibacterial properties to the PVDF membranes. Bacterial inhibitive rate of 99.9% against both S. aureus and E. coli is demonstrated in a membrane with 3.0 wt% HBP-HTC. This work provides a new strategy for development of high-efficiency and antibacterial protection products.     

Characterization of macromolecules in liquid solutions by thermal diffusion. I. Dependence of the soret coefficient on the nature of the dispersing medium

Experiments have been carried out on thermal diffusion of macromolecular particles dispersed in various liquids, with the object of checking some predictions of the radiation-pressure theory of Soret effect in liquids and of establishing a method of physical characterization of macromolecules in liquid solutions. The experimental results confirm the importance of the ratio G between thermal conductivity K and (phase) velocity v of high-frequency elastic waves of the materials composing the mixture in determining the thermodiffusive behavior of a liquid solution. We have shown that the migration of the macromolecular component takes place in the same direction in which thermal energy is flowing or opposite to it, depending on whether G of the dispersed particles is smaller or larger relative to the G of the liquid. Another aspect of the same phenomenon may be observed when macroscopic pieces of nonmetallic materials are suspended in a liquid, and heat is made to flow through this solid plunger and the surrounding liquid. The experiments performed with molecular solutions and with macroscopic plungers mutually complement and confirm each other. Anomalous results obtained in the case of solutions of polyvinylpyrrolidone in methanol are also discussed, and the possibility that this might be the consequence of the existence of a marked velocity dispersion in the high-frequency region of the spectrum of thermal waves in both water and methyl alcohol is indicated. Finally the possibility is hinted that thermal diffusion might have been responsible for the phenomena of molecular selection and evolution which ultimately led to the origin of life on our planet.     

A second-order phase transition in a monolayer of rectangle particles

Summary To describe the surface pressure-area isotherms of monolayers of amphiphilic molecules a two-dimensional gas of rectangular particles is proposed. Using theZwanzig's simplication of theOnsager's virial expansion analysis we found a second-order transition. Then introducing attractive potentials of different shapes, surrounding the hard core we may change the position of the critical points. The calculated isotherms have similar profiles than those obtained experimentally. With the more refined potential well, this depending on the area overlap of the wells, the interaction parameters have the same order of magnitude than those given in the literature. It is shown that this orientational transition is obtained only with particles which are asymmetrical enough.On leave from UER Pluridisciplinaire de Luminy Université d'Aix-Marseille II.     

Stokes flow and deposition of aerosol nanoparticles in model filters composed of elliptic fibers

The calculation is implemented for the fiber collection efficiencies due to diffusion of nanoparticles in model filters, i.e., separate rows of fibers with an elliptic cross section located normal to the flow at different orientations of the ellipse axes with respect to the flow. The Stokes flow field in the system of the fibers is found by the method of fundamental solutions. The concentration field of Brownian particles and the efficiency of their deposition onto the fibers are determined from the numerical solution of the equation for the convective diffusion. The dependence of the capture coefficient on the Peclet number for elliptic fibers is shown to have the form η = APe^−m, where exponent m changes from 2/3 to 3/4 at the parallel and normal orientation of the major axes of the ellipses with respect to the flow, respectively. It is shown that, from the viewpoint of aerosol nanoparticle capture, the best filters are those in which the fibers have a maximum midsection at the same cross-sectional area.     

Flow-through particles for the high-performance liquid chromatographic separation of biomolecules: perfusion chromatography

This paper reports a new technique for reducing resistance to stagnant mobile phase mass transfer without sacrificing high adsorbent capacity or necessitating extremely high pressure operation. The technique involves the flow of liquid through a porous chromatographic particle, and has thus been termed "perfusion chromatography". This is accomplished with 6000-8000 A pores which transect the particle. Data from electron microscopy, column efficiency, frontal analysis and theoretical modelling all suggest that mobile phase will flow through these large pores. In this manner, solutes enter the interior of the particles through a combination of convective and diffusional transport, with convection dominating for Peclet numbers greater than one. The implications of flow through particles on bandspreading, resolution and dynamic loading capacity are examined. It is shown that the rate of solute transport is strongly coupled to mobile phase velocity such that bandspreading, resolution of proteins and dynamic loading capacity are unaffected by increases in mobile phase velocity up to several thousand centimeters per hour. The surface area of this very large-pore diameter material is enhanced by using a network of smaller, 500-1500 A interconnecting pores between the throughpores. Scanning electron micrographs show that the pore network is continuous and that no point in the matrix is more than 5000-10,000 A from a through-pore. As a consequence, diffusional path lengths are minimized and the large porous particles take on the transport characteristics of much smaller particles but with a fraction of the pressure drop. Capacity and resolution studies show that these materials bind and separate an amount of protein equivalent to that of conventional high-performance liquid chromatography as well as low performance agarose-based media at greater than 10-100 times higher mobile phase velocity with no loss in resolution.     

Analysis of constant permeate flow filtration using dead-end hollow fiber membranes

Dead-end filtration of colloids using hollow fibers has been analysed theoretically and experimentally. A mathematical model for constant flux filtration using dead-end hollow fiber membranes has been developed by combining the Hagen–Poiseuille equation, the (standard) filtration equation, and cake filtration theory of Petsev et al. [D.N. Petsev, V.M. Starov, I.B. Ivanov, Concentrated dispersions of charged colloidal particles: sedimentation, ultrafiltration and diffusion, Colloid Surf. A: Physicochem. Eng. Aspects, 81 (1993) 65–81.] to describe the time dependence of the filtration behavior of hollow fiber membranes experiencing particle deposition on their surface. Instead of using traditional constitutive equations, the resistance of the cake layer formed by the deposited colloids has been directly correlated to the cake structure. This structure is determined by application of a force balance on a particle in the cake layer combined with the assumption that an electrostatically stable cake layer of mono-sized particles would be ordered in a regular packing geometry of minimum energy. The developed model has been used to identify the relationship between the filtration behavior of the hollow fiber membrane and the particle properties, fiber size, and imposed average flux. Filtration experiments using polystyrene latex particles of relatively narrow size distribution with a single dead-end hollow fiber membrane demonstrate good consistency between experimental results and model prediction. The developed model has been used to simulate the distribution of the cake resistance, transmembrane pressure, and flux along the hollow fiber membrane and used to assess the effect of fiber size, particle size, zeta potential, and the average imposed flux on the suction pressure-time profiles, flux, and cake resistance distributions. These results provide new insights into the filtration behavior of the hollow fiber membrane under constant flux conditions.     

Influence of contact electrification on the collision of elastic particles with a rigid surface

The influence of the contact formation of an electrical double layer (EDL) on the collision of uncharged, perfectly elastic particles with a dry rigid surface is theoretically investigated. The kinetics of the formation of an EDL in the elastic collision of a particle, the work of the nonequilibrium separation of the plates of the EDL when it rebounds, and the magnitude of a charge gained by the particle on its collision are calculated.

It is shown that the nonequilibrium forces associated with the EDL can considerably reduce the rebound velocity of particles, in the case of their elastic collision, and even cause their sticking to the surface, when impinging against it at a velocity lower than the critical one.

The dependence of the critical collision velocity on the geometrical, mechanical, and electrosurface parameters of particles and the substrate is established.

Some known experimental data are well described by the expression for the rebound impingement velocity ratio, obtained from consideration of the energy balance.     

Effect of electrostatic, hydrodynamic, and Brownian forces on particle trajectories and sieving in normal flow filtration

Particle deposition and fouling are critical factors governing the performance of microfiltration and ultrafiltration systems. Particle trajectories were evaluated by numerical integration of the Langevin equation, accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, and Brownian diffusion. In the absence of Brownian forces, particles are unable to enter the membrane pores unless the drag associated with the filtration velocity can overcome the electrostatic repulsion. Brownian forces significantly alter this behavior, allowing some particles to enter the pore even at low filtration velocities. The average particle transmission, evaluated from the probability of having a particle enter the pore, increases with increasing filtration velocity due to the greater hydrodynamic drag force on the particle. These results provide important insights into particle behavior in membrane systems.     

Effects of pre-oxidation temperature on coal secondary spontaneous combustion

The hydrodynamic force (drag) on spherical and irregularly shaped particles significantly increases when the particles move close to solid and permeable boundaries. The overall effect of the increased hydrodynamic drag is to hinder the particle movement in the vicinity of boundaries and this includes the Brownian movement and electrophoresis. The Monte Carlo simulation method is used to model the Brownian movement, the resulting diffusion, and the electrophoresis of spherical particles in narrow, cylindrical pores, filled with Newtonian fluids. It is observed that the effect of the pore walls is a significant reduction of the space-averaged electrophoretic velocity of the particles, which implies reduced particle flux through the pores. The hindered electrophoresis is primarily a geometric phenomenon, caused by the increased drag and depends on the size of the particles and the pore-to-particle diameter ratio. The temperature of the fluid slightly affects the hindered electrophoresis through its effect on the viscosity, which is a determinant of the Brownian force, the diffusivity and the electrophoretic velocity. The hindered electrophoresis is almost independent of the other fluid and particle properties, such as density. Based on the simulation results a non-linear correlation for the flux of particles is derived, valid in the ranges 5?<?R/α?<?120, 5 nm?<?α?<?100 nm and 273 K?<?T?<?355 K.

     

Hydrodynamic impact of particle shape in slurry packed liquid chromatography columns

We report on a series of flow velocity and efficiency profiles, which were measured across the cross section of preparative chromatographic columns packed with different stationary phase materials using computed tomography. It is shown that this non-invasive technique is very useful for visualization of the inner part of a packed column and measurement of the spatial resolved column packing properties. For evaluation of the influence of the particle shape on the velocity distribution and column performance, irregular and spherical reversed phases were studied in detail. The results showed a decreasing velocity towards the column wall most certainly due to a lower permeability. This effect was much less pronounced in the case of spherical particles, indicating a more homogenous packing structure. The influence of the column packing pressure, as a possible measure for improvement of the packing homogeneity was also studied. It was shown that under the same packing conditions spherical particles always lead to a more homogeneous packing. The overall results of this work contribute to the origin of the fact that spherical material is superior to irregular one from the hydrodynamic point of view.