Particle Capture Mechanisms Research Articles

MODELLING OF A THREE-DISPERSED SUSPENSION FILTRATION

The injection method of soil stabilization is one of the methods to improve the soil base during the road construction. This method consists in the introduction of special compounds into the ground with the help of special equipment. Such compositions, as a rule, are solutions of polymers or cement, which harden, forming a solid base. The advantages of the injection method of soil stabilization for roads include rapid completion of work, minimal environmental impact, the possibility of application in difficult geological conditions, as well as strengthening the soil base at great depth. Injection solutions penetrate into microcracks and micropores of soils, forming a deposition. The study of liquid filtration in a porous soil system is of great practical importance. The paper considers the filtration of liquid in a porous medium with three types of particles. In the considered problem, each of the three types of suspension particles is characterized by its linear filtration function. It determines the size-exclusion particle capture mechanism, in which particles whose diameter exceeds the size of the pores get stuck in them, the rest pass through them unhindered. Numerical solutions are obtained for the concentrations of suspended particles of three types, as well as the total deposition. Depending on the initial parameters of the problem, the concentrations of suspended particles are either monotonic functions or non-monotonic, reaching the maximum value. In this paper, asymptotic solutions are constructed for the concentrations of suspended and retained particles near the concentration front, which are compared with numerical ones. The solution is obtained at infinity using a traveling wave.

The rangeomorph Pectinifrons abyssalis: Hydrodynamic function at the dawn of animal life

Rangeomorphs are among the oldest putative eumetazoans known from the fossil record. Establishing how they fed is thus key to understanding the structure and function of the earliest animal ecosystems. Here, we use computational fluid dynamics to test hypothesized feeding modes for the fence-like rangeomorph Pectinifrons abyssalis, comparing this to the morphologically similar extant carnivorous sponge Chondrocladia lyra. Our results reveal complex patterns of flow around P.abyssalis unlike those previously reconstructed for any other Ediacaran taxon. Comparisons with C. lyra reveal substantial differences between the two organisms, suggesting they converged on a similar fence-like morphology for different functions. We argue that the flow patterns recovered for P.abyssalis do not support either a suspension feeding or osmotrophic feeding habit. Instead, our results indicate that rangeomorph fronds may represent organs adapted for gas exchange. If correct, this interpretation could require a dramatic reinterpretation of the oldest macroscopic animals.

ANALYSIS OF THE FILTRATION PROBLEM BY BITWISE SEARCH METHOD

During the construction of ground and underground structures, filtration of a liquid grout in loose soil makes it possible to strengthen the foundation and create underground waterproof partitions. A one-dimensional problem of filtering a bidisperse suspension in a homogeneous porous medium with size-exclusion particle capture mechanism is considered. The article is devoted to the calculation of the exact solution of the problem given as the upper limit of the integral with a singularity. The proposed bitwise search method for calculating integrals makes it possible to smooth out fluctuations of the solution near the singularity. Partial and total retention profiles are analyzed.

FILTRATION PROBLEM WITH NONLINEAR FILTRATION AND CONCENTRATION FUNCTIONS

ncient architectural buildings are of great value for all modern humanity. Over time, under the influence of vibrations, water and other man-made and natural factors, the foundations of such buildings are destroyed, the soil structure changes. Currently, one of the most popular methods of strengthening soils and strengthening foundations is the jet grouting technology. When the liquid grout passes through the porous rock, the suspended particles of the grout form a deposit. In this paper, we study a one-dimensional model of suspension deep bed filtration in a porous medium with different particle capture mechanisms. The considered filtration model consists of the balance equation for the masses of suspended and retained particles and the kinetic equation for deposit growth. In this case, the deposit growth rate is determined by the concentration function of suspended particles, which, in turn, depends on the properties of the suspension and the geometry of the porous medium. The solution to the problem is obtained for linear and non-linear concentration functions. An asymptotic solution of the problem is constructed for both types of functions near the concentration front of suspended and retained particles. It is shown that the asymptotic and numerical solutions are close over a long time interval.

Mechanistic study of PM2.5 reduction by kaolin-limestone compound additive in pulverized coal combustion

A novel compound additive prepared from kaolin and limestone shows promising prospects for in-furnace abatement of combustion PM2.5 (particulate matter with aerodynamic diameters equal to or less than 2.5 μm). However, the mechanisms need further clarification. These were investigated by combustion of a low-alkali coal on a high-temperature drop tube furnace (DTF). Combustion experiments with the kaolin-limestone additive were carried out at 1300 °C and in simulated air. Baseline tests of individual additives (i.e., kaolin and limestone) were also performed for comparison. Particulate samples were collected and classified by a Dekati low pressure impactor (DLPI). Heat-treated additive samples were also collected by DLPI and filter. They were characterized by various techniques such as laser diffraction particle sizing, X-ray diffraction (XRD), and field emission scanning electron microscopy equipped with energy dispersive spectrometry (FESEM-EDS). The results show that the addition of kaolin or limestone suppresses the emission of aerosols between 0.3 and 2.5 μm (PM0.3-2.5), but unexpectedly increases that of ultrafine aerosols less than 0.3 μm (PM0.3). The latter is primarily attributed to the carryover of ultrafine additive particles. Due to different effects on the two particle size fractions, the individual additives are found to have overall insignificant effects on PM2.5 emission. In striking contrast, the addition of the kaolin-limestone additive leads to an apparent reduction of both PM0.3 (∼46%) and PM0.3-2.5 (∼37%). As a result, a significantly high reduction of PM2.5 by ∼ 40% is achieved. The superior performance of the compound additive, compared with the individual additives, is accounted for by enhanced interactions between kaolin-limestone, additive-vapor, and additive-ash. These mechanisms, together with the collision-induced particle capture mechanism proposed previously, are believed to play key roles in PM2.5 abatement in real boilers when the compound additive and fuel are premixed.

Simplified model for the calculation of the particle capture process in air filter media

It is difficult to quickly calculate the performance of the air filter media, especially regarding the dynamic particle-capture process. In this study, the geometric and topological features of the existing particle-deposition morphologies based on three different particle-capture mechanisms (diffusion, inertia, interception) were extracted, and a single-fiber particle-deposition model was established. Through a computational fluid dynamics (CFD) simulation, the resistances in different particle-capture stages were calculated, and it was proved that the model can realize rapid calculation of the dynamic particle-capture process. Since no force analysis of particles is required, calculation resources were greatly conserved. Based on this, the study found that for diffusion, the packing density (Sp) of the deposited particles has a large impact on the resistance, subsequently leading to underestimation of the resistance by the two-dimensional (2D) model. Interception needs to be considered with inertia, and the ratio of the two (I/R) is the key factor that affects the resistance.

Free-Standing Ultrafine Nanofiber Papers with High PM0.3 Mechanical Filtration Efficiency by Scalable Blow and Electro-Blow Spinning.

Particulate matter of 0.3 μm in diameter (PM0.3) poses a serious threat to the environment and human beings. Ultrathin and -light nanofibrous filters with excellent filtration properties can significantly prevent the detrimental effects of these particles. Here, we develop free-standing polyamide PA-66 ultrafine nanofiber papers for PM0.3 filtration using effective and scalable blow and electro-blow spinning techniques. The smallest average fiber diameter is 61.7 nm, which is 2-3 orders of magnitude smaller than that of conventional textiles. Poly(ethylene terephthalate) nonwovens are selected to fabricate free-standing nanofiber papers of various polymers, including polyamide, poly(methyl methacrylate), poly(vinylpyrrolidone), and poly(ethylene oxide) owing to the smooth surfaces of the nonwovens. This underlying principle can be used to create similar free-standing nanofiber papers from other commodity polymers in the future. Mechanisms of capturing particulate matter with different nanofiber morphologies are discussed. Salt and oil particulates are used to characterize the filtration properties. PA-66 papers are promising reusable filters owing to their mechanical particle-capture mechanism. The blow-spun PA-66 papers show filtration performance of 98.75% efficiency and a pressure drop of 125.44 Pa owing to the "slip" effect caused by the ultrasmall diameter. In the electro-blow spinning process, a supplementary voltage supply is conducive to separating nanofiber bundles into random-oriented nanofibers. Electro-blown spun papers possess an ultrahigh efficiency of 99.99% with a reduced areal density of 0.9 g m-2. These PA-66 papers can be used in a variety of applications, such as reusable personal protective equipment, industrial waste gas treatment, and central ventilation purification systems.

Modeling of Inclusion Capture in a Steel Slab Caster with Vertical Section and Bending

Particles in molten steel, including argon-gas bubbles, slag droplets, and non-metallic inclusions, are removed into the surface-slag layer or captured by the solidifying steel-shell during continuous steel casting. Captured particles often become serious defects in the final steel product, so understanding particle-capture mechanisms is important for steel quality. Slab casters often have a straight mold and upper-strand prior to a curved lower-strand. The present work investigates particle capture in such a caster using computational modeling with a standard k-ε model for molten-steel flow, a discrete phase model for inclusion transport, and an advanced capture criterion for inclusion entrapment and engulfment into the steel shell. A new postprocessing methodology is presented and applied to predict inclusion-capture rates in commercial cast product. The locations and size distributions of particles captured into the shell, and actual capture rates are quantified. The model predictions are validated with ultrasonic-test plant measurements of the locations of large particles captured in a steel slab. The results reveal how large-inclusion capture accumulates in the beginning of the curved strand, leading to a capture band in the slab inside radius. Finally, the capture fractions and locations due to all capture mechanisms are compared for different inclusion sizes, and the implications are discussed.

DETERMINING THE LENGMUR COEFFICIENT OF THE FILTRATION PROBLEM

Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures. A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration problem - finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution near the concentrations front. The Langmuir coefficient constants are obtained by the least squares method from the condition of best approximation of the asymptotics to exact solution. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the exact solution

Particle movement behavior and capture mechanism in a corrugated cooling channel

The cooling channel can capture both the droplets and particles in the industrial waste gas. The flow field and particle motion in the corrugated cooling channel were numerically simulated and the capture mechanism was investigated. Submicron and micron particles are captured under the actions of thermophoresis and inertia, coupling with turbulence, respectively. The capture probability shows a high distribution for particles near the wall, and a low distribution for particles in the central area. The deposition probability density distribution of particles on the channel wall changes periodically along the flow direction. The overall capture efficiency decreases first and then increases with increasing particle size for submicron particles, in the range of 40% to 50%, and it keeps increasing with particle size for micron particles, reaching 77% for 10 μm particles. A corrugated cooling channel performs well in capturing particulate matter with the help of thermophoresis and inertia coupled with turbulence.

Effect of micropillars with varying geometry and density on the efficiency of impaction-based quartz crystal microbalance aerosol sensors

Inertial impaction is frequently used for the collection and subsequent measurement of aerosol particles in resonator-based airborne particulate matter (PM) sensors. However, particle bounce is known to significantly reduce particle collection efficiency (CE) on surfaces exhibiting low roughness, such as those present in quartz crystal microbalance (QCM) PM sensors. This paper shows that the addition of micropillars to impaction surfaces can significantly enhance their particle collection. Similarities in particle capture mechanisms between fibrous filters and pillar-enhanced surfaces are explained, and we show the adaptability of fibrous filter theory to pillared surface collection efficiency. Experiments confirm that the micropillar cross section and spacing have a significant role in particle capture. Pillars with circular, rectangular, and cross-shaped horizontal cross sections with 15 μm height and 12 μm (dense), 20 μm (nominal), and 27 μm (sparse) center-to-center spacings were printed using two-photon micro stereolithography. The efficiency increased by 35%–52% in the dense case, while the effect of the pillar shape was negligible. At nominal spacing, CE depended heavily on the pillar shape. The cross-shaped and circular pillars improved the CE by 26%–29%, although the rectangular pillars were as efficient as the bare surface. No significant difference between the bare and pillar-enhanced surfaces was visible in sparse spacing. We further show that, upon addition of a nominal distribution of micropillars to the surface of a QCM sensor for real-time mass measurements, the sensor response improved significantly (approximately 2.5 times) compared to a QCM with a bare surface.

Filtration model with multiple particle capture

Grout filtration in porous soil is used in construction industry to create underground waterproof walls. When the suspension flows through the pores, various forces act on the suspended particles, blocking them on the frame of the porous medium. A one-dimensional model of deep bed filtration for a monodisperse suspension in a porous medium with several particle capture mechanisms is considered. The mathematical model includes the equation of mass balance of suspended and retained particles and the kinetic equation of deposit growth with a piecewise-smooth linear-constant filtration function and a nonlinear concentration function. The solution of the nonlinear model is obtained by the finite difference method using an explicit difference scheme with second-order approximation. To construct the asymptotics of a complex model, the solutions of simplified linear and semilinear models and their combination are used. In the zone of a smooth filtration function, the best approximation of the solution of a complex model is determined by a certain linear combination of simple solutions. In another area, solution of a simplified problem with a piecewise-smooth filtration function and a linear concentration function is closest to the solution of a nonlinear model. Calculations show that in the zone of a smooth filtration function, a combination of simple solutions defines a solution approximation with second-order of smallness. In the area where it is necessary to take into account the non-smoothness of the filtration function, the approximation of a solution has a first order of smallness.

Global asymptotics of particle transport in porous medium

Particle transport in a porous medium occurs in environmental, chemical and industrial technologies. The transport of suspended concrete grains in a liquid grout through porous soil is used in construction industry to strengthen foundations. When particles are transported by a fluid flow in a porous medium, some particles are retained in the pores and form a deposit. The aim of the work is the construction and study of a one-dimensional mathematical model of particle transport and retention in the porous medium, taking into account the simultaneous action of several particle capture mechanisms. The model consists of mass balance equation and the kinetic equation of deposit growth. The deposit growth rate is proportional to the filtration function of the retained particles concentration, and the nonlinear concentration function, which depends on the concentration of suspended particles. The use of a new parameter, depending on the distance to the porous medium inlet allows to construct a global asymptotic solution in the entire area of the mathematical model. Asymptotics is obtained as a series in two small parameters. The global asymptotics is close to the numerical solution at all points of the porous medium at any time.

Particle Capture in Porous Medium

Filtration problems in porous media are important for studying the movement of groundwater in porous formations and the spreading of liquid concrete injected into porous soil. Deep bed filtration of a monodisperse suspension in a homogeneous porous medium with two simultaneously acting particle capture mechanisms is considered. A mathematical model of suspension flow through porous medium with pore blocking by size-exclusion and arched bridging is developed. Exact solutions are obtained on the concentration front and at the porous medium inlet. For the linear filtration function, exact and asymptotic solutions are constructed.

Cotransport of Suspended Colloids and Nanoparticles in Porous Media

The objective of this study is to develop a model for cotransport of colloids and nanoparticles (NPs) in porous media under two particle capture mechanisms. The particle capture rate is proportional to the capture probability, which is a function of retained concentration, called the filtration function. Laboratory bench-scale experiments of individual transport of NPs and colloidal-size kaolinite clay particles through packed columns produced breakthrough curves (BTCs) that monotonically increased with time and stabilised at some value lower than the injected concentration. We discuss the filtration function that corresponds to BTCs stabilising at the concentration lower than the injected value. This so-called binary filtration function incorporates two particle capture mechanisms. The analytical transport model with a binary filtration function was capable to fit successfully BTCs obtained from individual transport experiments using kaolinite and NPs conducted by Chrysikopoulos et al. (Transp Porous Med 119(1):181–204, 2017). Assuming that the electrostatic particle–solid matrix interaction and the fraction of the solid matrix surface area occupied by a single attached particle (kaolinite or NP) are the same for individual transport of either kaolinite particles or NPs and for simultaneous cotransport of kaolinite particles and NPs, the proposed binary filtration function was extended for the cotransport case. Although the breakthrough data from cotransport experiments with kaolinite particles and NPs have six degrees of freedom, the developed cotransport model successfully matches the BTCs by tuning two constants only. This validates the developed model for cotransport of two colloidal populations with different attachments and straining rates.

Problem of Deep Bed Filtration in a Porous Medium with the Initial Deposit

The macroscopic model of long-term deep-bed filtration flow of a monodisperse suspension through a porous medium with size-exclusion particle-capture mechanism and without retained-particle mobilization is considered. It is assumed that the pore accessibility and the fractional particle flux depend on the deposit concentration and at the initial time the porous medium contains a nonuniformly distributed deposit. The aim of the study is to find the analytical solution in the neighborhood of a mobile curvilinear boundary, namely, of the suspended-particle concentration front. The property of having fixed sign is proved for the solution. The exact solution of the filtration problem on the curvilinear front is found in explicit form. The sufficient condition of existence of the solution on the concentration front is obtained. An asymptotic solution is constructed in the neighborhood of the front. The time interval of applicability of asymptotics is determined from the numerical solution.

Modeling of particle-capture mechanism of axial magnetic filter in bounded flow field with variable viscosity

The capture mechanism of micron-sized magnetic particles from a surfactant-containing suspension is examined in an axial magnetic filter with a bounded flow field by using the particle trajectory model. The effects of change in the suspension viscosity to the suspension flow velocity are modeled. Analytical and numerical solutions for the particle trajectory model are obtained for a laminar flow regime. It is evaluated that the magnetic particles in the suspension, subjected to a viscosity change, are captured in a gradient magnetic field formed by a magnetized external ferromagnetic wire and the capturing of particles gets harder due to condensation of surfactant layers.

Exact solutions for suspension-colloidal transport with multiple capture mechanisms

We discuss one-dimensional (1D) non-linear problems of suspension-colloidal transport in porous media with two simultaneous particle capture mechanisms. The first mechanism corresponds to low retention concentration and constant filtration function. The second mechanism corresponds to large retention concentration with blocking (Langmuir) filtration function. The 1D flow problems are non-linear; however, they allow for exact solutions. The exact solutions are obtained for the general two-capture case, and also for piecewise-linear approximation of the filtration function. The proposed filtration function describes the breakthrough curves (BTCs) that monotonically increase with time and stabilise at some value lower than the injected concentration; those BTCs are observed for numerous suspension-colloidal flows. The tuning method for determining the model coefficients is developed. Close agreement between the laboratory and modelling data validates the proposed form of filtration function.

Analytical model for deep bed filtration with multiple mechanisms of particle capture

A model for deep bed filtration of a monodisperse suspension in a porous medium with multiple geometric particle capture mechanisms is considered. It is assumed that identical suspended particles can block pores of different sizes. The pores smaller than the particle size are clogged by single particles; if the pore size exceeds the diameter of the particles, it can be blocked by bridging — several particles forming various stable structures.An exact solution is obtained for constant filtration coefficients. Exact solutions for non-constant filtration functions are obtained on the concentrations front of the suspended and retained particles and at the porous medium inlet. Asymptotic solutions are constructed near these lines. For small and close to constant filtration functions, global asymptotic solutions are obtained.A basic model with two mechanisms of particle capture is studied in detail. Asymptotic solutions are compared to the results of numerical simulation. The applicability of various types of asymptotics is analyzed.

Not-so-simple sieving by ascidians: re-examining particle capture at the mesh and organismal scales

The particle capture mechanisms of biological filters determine the particle spectrum that is ingested by filter-feeding animals. Although ascidian feeding has been extensively investigated, the organismal-scale fluid dynamics and mesh-scale particle-filter interactions are not fully characterized. Fluorescein dye visualization of flow through the branchial sac of the ascidian Ciona intestinalis showed organismal-scale flow was laminar and moved both parallel and perpendicular to the mucous mesh. Endoscopic investigations of Herdmania momus revealed the mesh-scale filtration process, including the pre-capture velocities, particle approach angles, and mesh behavior. The mesh speed was variable (range 0–0.4 mm s−1). To determine how particle shape affects hydrosol capture, Styela plicata was fed differently shaped polystyrene particles (ellipsoids and spheres); sampling the inhaled and exhaled water revealed that microellipsoids (0.3 × 0.7 µm) were captured at significantly lower efficiency (32%) than 1 µm microspheres (86%). The capture efficiency of microellipsoids resembled that of microspheres with a diameter similar to the microellipsoids’ minor axis (0.3 µm, 31%) suggesting that the minimum diameter of ellipsoidal particles determines the capture efficiency. Flow near the filter was parallel to the mesh even ~ 10 s of micrometers away, implicating a “crossflow” component to ascidian filtration, where the fluid being filtered is directed along the surface of the filter rather than exclusively perpendicular to it. Collectively, these results suggest that ascidian filtration acts as a hybrid-flow filtration system rather than a classical direct sieve.