Microplastics as vectors for virus transport in saturated quartz sand: Reduced PRD1 bacteriophage infectivity and enhanced mobility.

Bacterial transport is the critical initial step for biofilm formation and microbial functions in porous media. Various physicochemical properties determine the interaction between bacterial cells and matrix. There is, hence, interest to evaluate the Hamaker constant as a comprehensive indicator to quickly predict bacterial deposition in porous media. In this study, percolation column experiments were conducted using four model bacterial strains with distinct hydrophobicity and surface charge properties. Deposition efficiencies were quantified using clean-bed filtration theory and interpreted based on the extended Derjaguin–Landau–Verwey–Overbeek (XDLVO) interaction energy. Research found that hydrophobicity determines the surface energy and, hence, varies the Hamaker constant, posing significant effects on the XDLVO energy to dominant deposition efficiency. The positive correlation between the Hamaker constant and deposition efficiency was mechanistically explained by variations of the XDLVO interaction energy at the secondary minimum distance, which governs reversible deposition. This correlation was validated at both the initial and final stages of bacterial deposition in porous media. These findings indicate that the Hamaker constant provides a simplified yet effective theoretical tool for the prediction of bacterial transport.

In this communication we describe a new scheme to process the data from stimulated echo protein diffusion experiments. For a series of gradient-encoded proton spectra [Formula: see text] considered over the selected spectral region [Formula: see text], we build a model to approximate the unique (protein-dependent) shape of the spectrum. Taking a cue from the optimal filtration theory, [Formula: see text] is constructed as the intensity-weighted combination of [Formula: see text]. The so obtained [Formula: see text] is then used to fit the individual spectra [Formula: see text], thus providing highly accurate estimates for the integral signal intensities that are subsequently used for Stejskal-Tanner-type analyses. This algorithm has been implemented as a part of a new web server, named DDfit ( https://ddfit.org , mirror at https://ddfit.bio-nmr.spbu.ru/ ). The server accepts spectrometer data from the standard stimulated and double-stimulated echo experiments by Bruker, as well as custom-designed experiments. The server is easy to use, with data processing taking no more than several seconds. Our tests using simulated as well as experimental data found that DDfit determines protein diffusion coefficients with both accuracy and precision, offering several-fold improvement in precision compared to other processing schemes.

Abstract For any power q of the positive ground field characteristic, a smooth q -bic threefold—the Fermat threefold of degree $q+1$ , for example—has a smooth surface S of lines which behaves like the Fano surface of a smooth cubic threefold. I develop projective, moduli-theoretic, and degeneration techniques to study the geometry of S . Using, in addition, the modular representation theory of the finite unitary group and the geometric theory of filtrations, I compute the cohomology of the structure sheaf of S when q is prime.

Natural colloids can alter the bacterial surface biomolecules and interfacial energies affecting the transport of bacteria in unsaturated porous media.

Magnetic filters are effectively used for the removal of low-concentration and submicron-sized magnetic particles from industrial liquids and gases. The matrices of magnetic filters are composed of ferromagnetic fillers (balls, rods, plates, metal shavings, etc.) that can be easily magnetized in an external magnetic field and have various geometries. Calculating the high-gradient magnetic fields formed in the pores of the filled beds and determining the force effect are crucial for the theory and practice of magnetic filtration and separation. Due to the tiny size of the pores, direct measurement and evaluation of magnetic field intensity in these regions are challenging. Therefore, various approximate methods are employed to model magnetized filled beds. This study primarily investigates the magnetization characteristics of filled beds composed of ferromagnetic balls. The analytical expressions of the main magnetization curves of this type of filled bed have been obtained. These expressions have been formulated in a way that can be easily used in engineering practice calculations. The theoretical calculations obtained have been compared with some experimental results from the literature, and recommendations have been made for the use of these formulas in the design, control, and optimization of magnetic filters.

Introduction. Construction of underground facilities such as pipelines, tunnels and subways in low-permeable wa­ter-saturated mobile soils is labor-intensive, expensive and dangerous. Construction dewatering systems remove a significant portion of water from such soils, turning them into stable rocks suitable for efficient excavation works. The development of mobile drainage and construction dewatering systems for pipelines, tunnels and subways can be carried out using the methodology of water and air filtration theory in urban construction, the method of computer modeling of fluid filtration and operations based on using spreadsheets, with the involvement of new artificial intel­ligence technologies and machine learning. Methods and materials. The working hypothesis of the research is the idea of creating a comprehensive approach to effectively solve the problem of groundwater flooding during the construction of linear projects, underground pipelines, tunnels and subways in low-permeable water-saturated soils. The methods of filtration theory used in the work are divided into analytical and numerical. The analytical operator method is used to solve the problems of non-stationary filtration of groundwater in construction dewatering systems. Modeling with spreadsheets applies to several processes of construction operations arrangement. The finite difference method in spreadsheets is used to solve filtration models of dewatering systems that cannot be solved analytically. In addition, a new feature is the use of spreadsheets to model organization and technology of construction drainage and dewatering. The possibility of using self-learning recursive computer programs is considered. Discussion. A review of domestic and foreign studies has shown that there are no publications related to the topic of the article. Certain issues relevant to this paper and referred in particular to the construction of underground pipelines, tunnels and subways have been studied. At the same time, the features of drainage of low-permeable water-saturated mobile soils are analyzed. Mobile sections of construction drainage and dewatering systems are proposed for consideration as an example, their installation and dismantling time being comparable with that of building the trench during open cut construction or the shield speed during tunneling, for example, a subway. Conclusion. Thus, it is proposed to develop systems for mobile sections of construction drainage and dewater­ing for underground pipelines, tunnels and subways based on the new integrated approach with the use of the methodology of the theory of water and air filtration in urban construction, methods of computer modeling of fluid filtration and construction operations based on spreadsheets, as well as new technologies of artificial intelligence and machine learning.

In this work, we develop an asymptotic theory for axe-filtrations within the broader framework of semi-modules, aiming to generalize the classical theory of filtrations from rings to these algebraic structures where addition is not necessarily invertible. This extension is crucial as semi-modules and semirings appear naturally in fields like geometry and computer science. Our first contribution is the introduction of the concept of an axe-filtration on a semi-module, which adapts the notion of a sequence of powers of an ideal in a ring. We then define a generalized Samuel number, denoted <i>v̅</i><sub>φ</sub>(θ), designed to measure the relative asymptotic growth between two distinct axe-filtrations, φ and θ. The main result of this paper establishes a fundamental theorem: the existence of this Samuel number is guaranteed under the condition that one axe-filtration, φ, is a valuative reduction of the other, θ. This key finding extends the classical results of D. Rees by connecting the asymptotic behavior of these generalized filtrations to the well-established theory of discrete valuations. By doing so, we lay the groundwork for a robust asymptotic theory applicable to semi-modules. This work provides new analytical tools for studying non-symmetrizable algebraic structures and opens avenues for further research into the geometric and algebraic properties of systems described by semirings.

An instantaneous trans-membrane pressure (P(t)) predictive model based on traditional cake filtration theory in the constant flow-rate backwash process

Abstract We show that submultiplicative norms on section rings of polarised projective manifolds are asymptotically equivalent to sup‐norms associated with metrics on the polarisation. We then discuss some applications to the spectral theory of submultiplicative filtrations, the asymptotic study of the Narasimhan–Simha pseudonorms and holomorphic extension theorem. As an unexpected byproduct, we show that injective and projective tensor norms on symmetric algebras of finite‐dimensional complex normed vector spaces are asymptotically equivalent.

Introduction. Flooding of built-up and developing city areas with groundwater is an unfavorable process in our country and around the world. The groundwater level (GWL) rises to the surface of the earth. The consequences of increasing the groundwater level are dangerous for humans and the environment. Drainage of urban areas leads to a decrease in groundwater level. Drainage systems are an active protection against flooding with groundwater. Climate affects the processes of flooding and drainage in urban construction. This influence is taken into account too little in the current building codes and calculation methods for designers, builders and employees of urban services. A lot of materials have been accumulated that require scientific publication due to their relevance for further improvement ways to withstand flooding of urban and populated areas with groundwater with climate considering. Ineffective situations of extensive protection against sudden onset flooding are observed all over the world every year. It is necessary to strengthen the role of scientific approaches in making the choice of appropriate measures to keep save against flooding. Paying attention to the climate influence on flooding and drainage processes in urban construction can make a significant contribution in this direction.Methods and materials. The urban man-made environment differs considerably from the natural before construction, most of all in flooding and drainage of territories, buildings and structures. Therefore, the theory of filtration in urban construction requires improvement of the methodology of forecasting, calculating and modeling flooding and drainage, especially paining attention to the climate of cities, which is still almost not taken into account in the development of protective measures. This paper presents new ideas and their implementation on the stated research theme. This opens a new direction of scientific methodology related to flood protection in urban construction with the consideration of climate influence. New ideas cannot be implemented in one article, since the problem is very extensive. Therefore, in the future, it is expected that other scientific studies will be published on this current theme, planned as a direction of promising and relevant scientific research.Discussion. In the course of the study, the characteristics of the city climate that can affect the processes of flooding and drainage of groundwater in built-up and developing city areas has been considered.The impact of the Sun is very significant. Sun rays, passing through the atmosphere, affect the groundwater regime. The share of solar energy is several times of magnitude greater than the influence of the temperature gradient coming from the depths of the Earth to the earth's surface. The impact of sunlight is expressed in the form of solar radiation. In this case, the albedo of the irradiated surfaces has an effect. Urban development creates significant shading of the soil surface with a subsequent decrease in evaporation and an increase in moisture infiltration to groundwater. The wind regime of the development changes. This has been taken into account in the presented methodology of the article, the necessary dependencies and examples of calculating the reduction of water evaporation from the soils of the foundations of buildings and structures are given. New experimental measurements on the theme of the study, as well as author’s innovative devices and instruments have been considered.Conclusion. Thus, a new direction of scientific methodology related to protection from flooding in urban construction has been discovered, taking into account the climate change of the technogenic environment of the built-up and developing city areas. The presented work should be considered as a pioneering article, giving in the first approximation a new methodology for the considering the influence of climate on the processes of flooding and drainage in urban construction. Therefore, in the future, it is expected that other scientific works will be published on this acute topic, planned in the direction of promising and relevant scientific research.

Increasing the duration of rapid filter operation between washings is an effective way to reduce the amount of washing water and operating costs at water treatment stations for domestic and drinking needs when drawing from surface sources. The level of pollution of surface water supply sources in Ukraine is steadily increasing. During military operations, the load on treatment facilities may rise significantly. Moreover, operating conditions can change abruptly and unpredictably. This article presents the results of a study comparing the performance of rapid filters in two filtration modes: with constant and time-varying filtration rates. The theory of low-concentration suspension filtration developed by D.M. Mints applies to the mode with a constant filtration rate. Calculations for alternative filtration modes require more general theoretical frameworks. The studies were conducted using a mathematical model. The presented mathematical model includes: the filtration equation for a low-concentration suspension, the equations of mass transfer and mass transmission of the suspended solids from the liquid phase to the solid (grains of the filter media), the formulations for determining the resistance of clean (unclogged) media and the influence of clogging on the resistance and porosity of the granular media, the expressions for calculating the adhesion (and detachment) coefficients of suspension particles on the filter media grains. The adequacy of the mathematical model at a constant filtration speed was validated by comparing the calculated results with the data obtained using the filtration theory of D.M. Mints. As a result of numerical experiments for two filtration modes, the impact of influent water turbidity on the efficiency of the rapid filter was investigated. The filter operating time between washings used as the efficiency criterion. The comparison of the two modes was conducted under the condition that the average productivity and filtration area in both cases were the same. The influence of the granular media parameters (grain size and layer thickness) was investigated. Studies have shown the advantages of operating a rapid filter in a variable filtration rate mode compared to a constant rate mode. However, the disadvantage of the variable filtration rate mode is the increased likelihood of filtrate quality deterioration at the beginning of the filtration cycle.

• Nanoparticle tracer optimization by DLVO, XDLVO and filtration theory. • Material-dependent Hamaker constant and ζ-potential are crucial parameters. • Silica nanoparticles behave superior to metallic nanoparticles. • Diffusion-dominated retention is the main filtration mechanism for nanoparticles. • Surface modifications are powerful tools to improve nanoparticle tracer performance. Functional nanoparticles emerged as potential new tracers for geoscientific applications, such as geothermal reservoir exploration. In this study, optimization strategies based on DLVO, extended DLVO (XDLVO) and filtration theory are presented. Our results show that nanoparticle material should have a low Hamaker constant, making metallic nanoparticles unfavorable. To ensure dispersion stability and minimize sorption on commonly negatively charged reservoir minerals, the nanoparticles should exhibit ζ-potentials below -30 mV. Decreasing the size of nanoparticles increases the diffusion-driven collisions with minerals grains and the probability of deposition while keeping the particle-to-grain size ratio below 0.008 prevents size exclusion effects. The impact of gravity on particle deposition is negligible for nanoparticles, making higher-density nanoparticle tracers viable. Experimental findings and XDLVO theory confirm the applicability of surface modifications to form a steric barrier that lowers attachment efficiencies while increasing colloidal dispersion stability. The impact of temperature cannot be assessed in a straightforward manner as it depends on multiple factors that can have contradicting effects. The presented study can serve as a guideline for the design of stable nanoparticle tracers with predictable transport properties in reservoirs. It shows that selecting appropriate materials, adapting ζ-potentials or employing effective surface modifications are key strategies to improve the performance of engineered nanoparticle tracers for geothermal exploration.

ABSTRACTVacuum preloading combined with prefabricated vertical drains is commonly used for enhancing the high water content slurry. However, the process of slurry dewatering, which is inherently a filtration problem, is difficult to describe using consolidation theories. This study presents a new vacuum filtration theory for slurry based on the elliptical cylinder model, where the radial and vertical deformations are governed by the equal settlement assumption. To describe the permeability and compressibility of slurry, the extended power function equations are adopted. The governing equations associated with the influenced zone and the moving boundary are essential components of the vacuum filtration theory, which are solved by the finite difference method. The applicability of the theory is confirmed by comparing the results of it with the laboratory tests and the radial filtration theory. Depending on the properties of the slurry used in the laboratory tests, the filtration behaviour are analysed. Finally, parametric analysis is carried out to investigate the effect of vacuum pressure on the filtration behaviour of the slurry.

This study introduces a novel theoretical model for upscaling colloid transport from the grain scale to the Darcy scale under both favorable and unfavorable conditions. The model integrates colloid interception history, where an interception occurs when colloids enter the near-surface zone within 200 nm of a collector, to capture the traditional exponential retention profile, as well as the anomalous, non-exponential behaviors observed under unfavorable conditions. The development of this theoretical model is based on a two-stage framework: first, upscaling from the grain scale to the single-interception scale, followed by upscaling from the single-interception scale to the Darcy scale. The initial stage addresses the distribution of colloids corresponding to a given interception order. The second stage focuses on the distribution of colloids across multiple interception orders. The key innovation of this work is the inclusion of the colloid removal process, where a fraction, denoted by $\alpha$, is removed at each encountered interception, rather than with each grain passed, as specified by classical colloid filtration theory. Our model accounts for scenarios under unfavorable conditions wherein if $\alpha$ remains constant, the distribution is exponential, albeit shallower relative to favorable conditions. Additionally, the model considers cases where $\alpha$ varies with interceptions, leading to multi-exponential and nonmonotonic retention profile shapes. In both scenarios, the proposed theoretical model offers a mathematical representation of colloid retention profiles under favorable and unfavorable conditions, including those exhibiting anomalous shapes.

For pathogens, engineered nanomaterials, micro- and nanoplastics, and other colloids, variance from expectations of Colloid Filtration Theory is well-demonstrated under unfavorable conditions where a repulsive barrier exists in colloid-surface interactions. Specifically, their retention profiles (RPs) are nonexponential. We present experiments demonstrating that nonexponential RPs arise from variations in interception history among attached colloids wherein the fraction of the colloid population that attaches after multiple interceptions is negligible under favorable conditions and is significant to dominant under unfavorable conditions. We show that RPs were exponential only for colloids that attached under favorable conditions, whereas RPs were nonmonotonic for colloids that attached under unfavorable conditions, with RPs for multiple intercepting attachers assuming γ distributions having maxima at transport distances that increased with interception order. We show that in our experiments the value of attachment efficiency (α) was greater for multiple than single interception attachers, and we speculate on the origin of this change in α. We emphasize that such variance from overall exponential RP reflects a fundamental aspect of colloid transport under unfavorable conditions, as they arise without significant variations in colloid size, surface properties, and density, and without straining and detachment.

Dual-porosity model for centrifugal filtration and washing dynamics of absorbent materials

Integral equations are encountered in various sections of physics — in acoustics, filtration theory, in electrophysics, in mechanics of solid deformable bodies. Fredholm integral equations can be used for mathematical description of processes of radiation and scattering of sound waves. Often finding an exact analytical solution to integral equations seems difficult, in connection with which numerical methods are used to solve such equations. This work is devoted to the analysis of algorithms for the numerical solution of the Fredholm integral equation of the second kind. The paper presents the results of the implementation of some algorithms for the numerical quadrature method for solving integral equations. The quadrature method reduces the solution of the integral equation to the solution of a system of linear algebraic equations, which can be implemented in various ways. The choice of the quadrature formula is assumed to be arbitrary; in the study under consideration, the trapezoid formula was used as a quadrature formula. When reducing an integral equation to a system of linear algebraic equations, there is also arbitrariness in the choice of the method for solving linear equations. To solve the system of linear equations, the Gauss method, the method of simple iterations and the iterative Jacobi method were used. The study of the properties of the integral equation shows that the kernel of the integral operator satisfies the properties under which the integral operator is a contracting operator and, therefore, the integral equation has a unique solution. Comparison of numerical calculations for various methods of solving a system of linear equations demonstrates that the Jacobi method for solving a system of linear algebraic equations converges to an exact solution significantly faster than the method of simple iterations. The results obtained can be used in developing algorithms for solving integral equations.

In order to solve the high energy consumption and other problems of the post-pump filter, an efficient pre-pump filter, pontoon mesh rotary filter, has been developed. In this study, the physical full test under the factors of flow rate, sand content, flushing flow rate, and filtration time was carried out using filtration efficiency as an index. The results were analyzed using quantile analysis, PPR, MLP, and Sobol index, and a prediction model was established, in which the MLP-based prediction model was more effective. The influence ranking of single and double factors were determined and the optimum working conditions were proposed. The results of the study provide a reference for filters, enrich the theory of micro-pressure filtration, and provide operational parameters for filter applications.

In this paper one mathematical model of filtration theory with phase transitions is investigated. When using surface-active substances (surfactants) for the development of oil and gas fields in the reservoir occur sorption processes at the interfaces of individual phases (surfactants and oil, or surfactants and soil). In real processes a finite time is required for achievement equilibrium. Therefore considering the mathematical model was called the mathematical model with phase relaxation. The solvability of the mathematical model, the limiting transition in relaxation time are investigated. It is proved that in the limiting case, the original problem is a problem of Stefan type.