Efficiency of inertial deposition of aerosol particles in fibrous filters with regard to particle rebounds from fibers

The inertial deposition of submicron aerosol nanoparticles onto fibers during gas filtration through fine-fiber filters is considered. It is shown that there is critical filtration velocity U* below which the energy loss upon collisions has no influence on the filtration efficiency. Above this critical velocity, the filtration efficiency depends on the mechanism of the inelastic energy loss and can be noticeably lower than the result of its estimation with no allowance for the particle rebound. For a rather dense fibrous medium, when not all particles that have rebounded from a fiber have time to attain the flow velocity before the next collision with another fiber, the filtration efficiency depends on the velocity distribution of the rebounding particles. It is shown that, in this case, the filtration efficiency must increase with the packing density of a filter.     

Pressure Drop and Aerosol-Particle-Collection Efficiency of Polydisperse Fibrous Filters

The effect of the polydispersity of fibrous materials on the viscous drag and the efficiency of gas filtration has been studied. The dependence of the Brinkman constant on parameter β_g, which characterizes the variance of the lognormal function of fiber-length distribution over fiber radii, has been calculated for equations describing the hydrodynamics of a gas in a porous medium. The dependences of the effective aerosol- particle-collection efficiency on the packing density, dispersion of fiber-size scatter, and average fiber radius have been investigated. Quality parameters of filters with different degrees of polydispersity have been compared. Results of calculations have been compared with experimental data.     

The effect of gas slip on pressure drop and deposition of submicron particles in fibrous filters

The effect of gas slip at fibers on the drag to a flow and the deposition of submicron particles in model filters with a tree-dimensional flow field has been considered. The average values of the drag force and the efficiency of diffusion collection of particles with finite sizes in a double hexagonal three-dimensional model filter taken as a standard uniform filter have been calculated as depending on the packing density of fibers and the Knudsen number. It has been shown that, in the region of the sizes of the most penetrating particles, under preset conditions, and at specified filter parameters, the obtained collection efficiency values agree with the results of calculations performed by empirical formulas for a model fan filter. Moreover, formulas derived for a planar flow taking into account the slip effect are applicable to highly porous filters.     

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.     

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.     

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.     

Diffusional deposition of nanoparticles in a 3D model fiber filter

Diffusional particle deposition from a flow on fibers at low Reynolds number Re ≪ 1 is studied in a model filter consisting of equidistant rows of parallel fibers perpendicular to the flow and forming a three-dimensional structure where one hexagonal 2D-dimensional lattice is inserted into another at the right angle. It is shown that under equal low filter packing density fiber collection efficiencies calculated within 3D and 2D models are practically the same.     

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.     

Deposition of aerosol nanoparticles in filters composed of fibers with porous shells

The diffusion deposition of submicron aerosol particles in model filters consisting of fibers covered with permeable porous shells is studied. An ordered system of parallel cylinders arranged perpendicular to the flow is used as a model filter. The results of calculations are given for the dependences of the capture coefficient on the shell radius, the shell permeability, the packing density of the filters, the particle radius, and the flow velocity. Calculations are performed within a wide range of Peclet numbers. It is shown that the capture coefficient and the quality criterion γ of a filter increase with the diffusion mobility of particles and shell permeability, as well as that the dependence of the quality criterion on the radius of permeable shells has a maximum. It is also shown that the capture coefficients for fibers with porous shells, calculated using the cell model and the isolated row of fibers, almost coincide with one another.     

Performance optimization of hollow fiber reverse osmosis membranes. Part II. Comparative study of flow configurations

Sensitivity evaluation of overall performance of hollow fiber membranes was performed to study the effects of such operating parameters as pressure, packing density, and fiber diameter. It is shown that in a wide range of operating conditions, fiber productivity and selectivity as dependent upon hollow fiber length exhibit a similarity property. This is demonstrated in all three flow configurations of concurrent, countercurrent, and flow inside hollow fibers.     

The Effect of Long-Range Fiber Space and Orientation Correlations on the Hydrodynamic Resistance and Diffusion Deposition in Fibrous Filters

On the basis of Brinkman's equation, the problem of hydrodynamic resistance is analyzed for a row of periodically arranged parallel circular fibers placed in a uniform porous medium. The results are applied to the fan model of a filter, for which an equation aimed at determination of Brinkman's constant is derived within the framework of a self-consistent theory. The resistance force acting on a unit length of each fiber is calculated as a function of the geometrical parameters of the model. The capture coefficient is found for diffusion deposition of aerosols on fibers of the model filter. The results obtained agree with the experimental data.     

Nanoparticle deposition in granular filters at Reynolds numbers higher than unity

The influence of the inertia of a viscous incompressible liquid flow on the viscous drag and diffusion deposition of particles in model granular filters at Reynolds numbers higher than unity, Re > 1, has been considered. The granule drag forces and particle-collection efficiencies in isolated layers with square and hexagonal packings of granules have been calculated. The influence on each other of approaching monolayers of granules on pressure drop and nanoparticle deposition has been studied. It has been shown that, at Re > 1, the collection efficiency dramatically increases due to the effect of interception.     

A model of a dust-loaded filter with asymmetric deposit of particles on fibers

Results of numerical simulation have been reported for the flow field and diffusion deposition of nanoparticles in a model dust-loaded fibrous filter, i.e., a row of parallel fibers coated with porous permeable shells shifted toward an incident flow. The flow field and point particle collection efficiency on fibers coated with the shells have been calculated by combining the Stokes, Brinkman, and convective diffusion equations. It has been shown that the pressure drops and efficiencies of nanoparticle deposition in the filters composed by fibers with coaxial and asymmetric porous shells are almost identical.     

Microbore polypropylene capillary channeled polymer (C-CP) fiber columns for rapid reversed-phase HPLC of proteins

The performance of microbore columns with polypropylene (PP) capillary-channeled polymer (C-CP) fibers as the support/stationary phase for separation of macromolecules has been investigated. Polypropylene C-CP fibers (40 μm diameter) were packed in fluorinated ethylene propylene (FEP) tubing of inner diameter 0.8 mm and lengths of 40, 60, 80, and 110 cm. The performance of PP fiber packed microbore columns (peak width, peak capacity, and resolution) was evaluated for separation of a three-protein mixture of ribonuclease A, cytochrome c, and transferrin under reversed-phase gradient conditions. The low backpressure characteristics of C-CP fiber columns enable operation at high linear velocities (up to 75 mm s(-1) at 1.5 mL min(-1)). In contrast with the performance of other phases, such velocities enable enhanced resolution of the three-protein mixture, because peak widths decrease with velocity. Increased column length resulted in increased resolution, because the peak widths remained essentially constant, although retention times increased. In addition, it was found that the peak capacity increased with column length and linear velocity. Radial compression of the microbore tubing enhanced the homogeneity of the packing and, thereby, separation efficiency and resolution. Radial compression of columns resulted in a decrease in the interstitial fraction (~5%), but increased resolution of ~14% between ribonuclease A and cytochrome c. Even so, a linear velocity of 75 mm s(-1) required a backpressure of 9.5 MPa only. It is clear that the fluid and solute-transport properties of the C-CP fiber microbore columns afford far better performance than is obtainable by use of standard format columns. The ability to achieve high separation efficiencies, rapidly and with low volume flow rates, holds promise for high-capacity protein separations in proteomics applications.     

The Influence of Fluctuations on the Efficiency of Aerosol Particle Collection with Fibrous Filters

The influence of fluctuations on the filtration efficiency was studied. In the case of arbitrary random macroscopic inhomogeneities in the packing density and fluctuations in the filter surface form, the expressions were derived for the pressure drop and the penetration of aerosol particle, expressed via the correlation functions of fluctuating parameters. For the high degrees of cleaning, the probabilistic approach was developed, which takes into account the discreteness of the number of aerosol particles deposited on filter fibers.     

Dead-end ultrafiltration in hollow fiber modules: Module design and process simulation

Ultrafiltration in a hollow-fiber module operating with outside-in and dead-end flow at a constant flow rate was simulated using a model that takes into account the longitudinal pressure drops inside the fibers and within the fiber bundle. The model considers both the filtration phase during which the membrane is fouled by the formation of a filter cake and the backwash phase in which it is cleaned, so as to predict the net rate of production of the module during an operating cycle.The results show that there is a combination of packing density and fiber diameter that gives a maximum net flow rate. Furthermore, this model allows the influence of operating conditions and feed properties on the module performance to be estimated. This can be used to determine how operating parameters must be modified when there is a change in the feed properties.     

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.     

Deposition of nanoparticles in filters composed of permeable porous fibers

The diffusion deposition of nanoparticles is studied from a flow at low Reynolds numbers in model filters composed of permeable circular porous fibers. The field of particle concentration is calculated and the capture coefficient is determined for a cell, as well as the isolated row of parallel fibers within a wide range of Peclet numbers (Pe) depending on the fiber permeability. It is shown that at Pe > 1, the diffusion capture coefficient η increases with permeability, while at Pe → ∞, it tends toward the limiting value, which is equal to the gas flow rate through the porous fiber. The capture coefficients calculated from a cell model and for a row of fibers are almost equal to each other. The diffusion deposition of aerosol particles in the highest penetration range is calculated with an allowance for their finite sizes and it is shown that the radii of most penetrable particles decrease with an increase in fiber permeability.     

Structure of the right-handed helical crystal ribbon and multilevel fibrils in a tube fiber from a coir fiber

A coir fiber is composed of many tube fibers with large hollows that align in parallel. SEM observation has shown that the tube fiber existing in a coir fiber is packed by a right-handed helix crystal ribbon, and its length/diameter ratio is lower than that of the crystal ribbon by 1–2 orders of magnitude. Based on the results of TEM, the diameter of protofibrils extracted from coir fibers is 6–10 nm, while that of the microfibrils is 20–40 nm, and the length/diameter ratios of protofibrils and microfibrils are 50–250 and 25–150, respectively. According to these observed results, the packing models of the right-handed helix crystal ribbon and its multilevel fibrils have been derived and further verified through the calculation and comparison of both the crystallinity in volume and whisker sizes obtained by means of X-ray diffraction analysis.     

Inertial deposition of aerosol particles from laminar flows in fibrous filters

The deposition of aerosol particles onto filter fibers under the effect of inertial forces is studied in a wide range of Stokes numbers (St) at Reynolds numbers close to unity (Re ∼ 1). Coefficients η of the capture of inertial particles with finite sizes in model filters composed of parallel rows of identical parallel fibers located normal to the direction of a flow are determined based on the numerical solution of the Navier-Stokes and particle motion equations. It is shown that, at Re < 1 and a constant particle-to-fiber radius ratio, R = r _p/a, number St uniquely characterizes capture coefficients η for particles with different densities, while, at Re ≥ 1, the capture coefficient depends on both St and Re. At constant R and St values, the larger Re the higher the capture coefficient. The influence of the structure of the model filter on pressure drop Δp and η is investigated. A nonuniform arrangement of fibers in rows is shown to increase the Δp/U ratio at lower Re values and to make the η -St dependence more pronounced than that for systems of uniformly ordered fibers. The results of calculations agree with the experimental data.