Filters that act by adsorbing contaminant onto their pore walls will experience a decrease in porosity over time, and may eventually block. As adsorption will generally be greater towards the ...entrance of a filter, where the concentration of contaminant particles is higher, these effects can also result in a spatially varying porosity. We investigate this dynamic process using an extension of homogenization theory that accounts for a macroscale variation in microstructure. We formulate and homogenize the coupled problems of flow through a filter with a near-periodic time-dependent microstructure, solute transport due to advection, diffusion and filter adsorption, and filter structure evolution due to the adsorption of contaminant. We use the homogenized equations to investigate how the contaminant removal and filter lifespan depend on the initial porosity distribution for a unidirectional flow. We confirm a conjecture made by Dalwadi et al. (Proc. R. Soc. Lond. A, vol. 471 (2182), 2015, 20150464) that filters with an initially negative porosity gradient have a longer lifespan and remove more contaminant than filters with an initially constant porosity, or worse, an initially positive porosity gradient. In addition, we determine which initial porosity distributions result in a filter that will block everywhere at once by exploiting an asymptotic reduction of the homogenized equations. We show that these filters remove more contaminant than other filters with the same initial average porosity, but that filters which block everywhere at once are limited by how large their initial average porosity can be.
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•Membrane fouling leads to a decline in the flux with time.•The rate of flux decline also commonly decreases with time.•However, in many experiments the rate of flux decline can ...increase with time.•This is observed only when multiple fouling mechanisms interact with one another.•A network model accounts for these interactions to capture the system behaviour.
Membrane fouling during particle filtration occurs through a variety of mechanisms, including internal pore clogging by contaminants, coverage of pore entrances, and deposition on the membrane surface. Each of these fouling mechanisms results in a decline in the observed flow rate over time, and the decrease in filtration efficiency can be characterized by a unique signature formed by plotting the volumetric flux, Q^, as a function of the total volume of fluid processed, V^. When membrane fouling takes place via any one of these mechanisms independently the Q^V^ signature is always convex downwards for filtration under a constant transmembrane pressure. However, in many such filtration scenarios, the fouling mechanisms are inherently coupled and the resulting signature is more difficult to interpret. For instance, blocking of a pore entrance will be exacerbated by the internal clogging of a pore, while the deposition of a layer of contaminants is more likely once the pores have been covered by particulates. As a result, the experimentally observed Q^V^ signature can vary dramatically from the canonical convex-downwards graph, revealing features that are not captured by existing continuum models. In a range of industrially relevant cases we observe a concave-downwardsQ^V^ signature, indicative of a fouling rate that becomes more severe with time. We derive a network model for membrane fouling that accounts for the inter-relation between fouling mechanisms and demonstrate the impact on the Q^V^ signature. Our formulation recovers the behaviour of existing models when the mechanisms are treated independently, but also elucidates the concave-downward Q^V^ signature for multiple interactive fouling mechanisms. The resulting model enables post-experiment analysis to identify the dominant fouling modality at each stage, and is able to provide insight into selecting appropriate operating regimes.
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The tortuosity of the track taken by an animal searching for food profoundly affects search efficiency, which should be optimised to maximise net energy gain. Models examining this generally describe ...movement as a series of straight steps interspaced by turns, and implicitly assume no turn costs. We used both empirical‐ and modelling‐based approaches to show that the energetic costs for turns in both terrestrial and aerial locomotion are substantial, which calls into question the value of conventional movement models such as correlated random walk or Lévy walk for assessing optimum path types. We show how, because straight‐line travel is energetically most efficient, search strategies should favour constrained turn angles, with uninformed foragers continuing in straight lines unless the potential benefits of turning offset the cost.
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We investigate how a filter-medium microstructure influences filtration performance. We derive a theory that generalizes classical multiscale models for regular structures to account for filter media ...with more realistic microstructures, comprising random microstructures with polydisperse unidirectional fibres. Our multiscale model accounts for the fluid flow and contaminant transport at the microscale (over which the medium structure is fully resolved) and allows us to obtain macroscopic properties such as the effective permeability, diffusivity and fibre surface area. As the fibres grow due to contaminant adsorption, this leads to contact of neighbouring fibres. We propose an agglomeration algorithm that describes the resulting behaviour of the fibres upon contact, allowing us to explore the subsequent time evolution of the filter medium in a simple and robust way. We perform a comprehensive investigation of the influence of the filter-medium microstructure on filter performance in a spectrum of possible filtration scenarios.
The molecular mechanisms underlying the muscle atrophy of intensive care unit-acquired weakness (ICUAW) are poorly understood. We hypothesised that increased circulating and muscle growth and ...differentiation factor-15 (GDF-15) causes atrophy in ICUAW by changing expression of key microRNAs.
To investigate GDF-15 and microRNA expression in patients with ICUAW and to elucidate possible mechanisms by which they cause muscle atrophy in vivo and in vitro.
In an observational study, 20 patients with ICUAW and seven elective surgical patients (controls) underwent rectus femoris muscle biopsy and blood sampling. mRNA and microRNA expression of target genes were examined in muscle specimens and GDF-15 protein concentration quantified in plasma. The effects of GDF-15 on C2C12 myotubes in vitro were examined.
Compared with controls, GDF-15 protein was elevated in plasma (median 7239 vs 2454 pg/mL, p=0.001) and GDF-15 mRNA in the muscle (median twofold increase p=0.006) of patients with ICUAW. The expression of microRNAs involved in muscle homeostasis was significantly lower in the muscle of patients with ICUAW. GDF-15 treatment of C2C12 myotubes significantly elevated expression of muscle atrophy-related genes and down-regulated the expression of muscle microRNAs. miR-181a suppressed transforming growth factor-β (TGF-β) responses in C2C12 cells, suggesting increased sensitivity to TGF-β in ICUAW muscle. Consistent with this suggestion, nuclear phospho-small mothers against decapentaplegic (SMAD) 2/3 was increased in ICUAW muscle.
GDF-15 may increase sensitivity to TGF-β signalling by suppressing the expression of muscle microRNAs, thereby promoting muscle atrophy in ICUAW. This study identifies both GDF-15 and associated microRNA as potential therapeutic targets.
We develop a mathematical model for the cumulative erosion of a micro-particle in a channel system. At 90∘ bends in the system, a particle may deviate from the flow, impact the wall, and erode ...material. We highlight the case of the eroded material adhering to the particle, growing in size, and thus demonstrate how the damage accumulates exponentially with time. We describe and quantify the statistical nature of the evolution of particle growth and erosion (mass and location). We perform this analysis according to a number of realistic particle concentration distributions: uniform, Gaussian, and bimodal. A bimodal distribution, corresponding to the tubular pinch effect in suspension flows, results in unequal peak zones of erosion due to the flow characteristics.
•Model of erosion by particle impact in a Poiseuille fluid flow in a channel bend.•Statistical description of cumulative erosion by particle inlet distributions.•Study of evolution of size and impact site distribution due to adhesion of eroded material to impacting particle.
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We derive reduced models for extrusion problems where it is necessary to account for fluid compressibility. We consider the two-dimensional extensional flow of a compressible viscous fluid and ...discuss two specific applications: weakly compressible fluids and bubbly liquid–gas mixtures that behave as a single compressible fluid. The mathematical model we present consists of equations for conservation of mass, conservation of momentum and a closure relationship between the pressure and density. The most substantial differences between compressible extrusion problems is in the closure relationship. By integrating the conservation equations across the fluid cross-section and exploiting a slender aspect ratio, we derive reduced equations for conservation of mass and conservation of momentum in the direction of flow. The reduced system of equations relating cross-sectionally averaged quantities is closed by a relationship between the averaged pressure and density, which will differ substantially depending on the application. We demonstrate the utility of a reduced model for both the weakly compressible fluid and bubbly mixture applications; namely, in providing valuable quantitative insights without needing to solve a complicated free-boundary problem.
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to ...develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary conditions, and interfaces to third party tools such as ParaView, METIS and ARPACK. As in the previous editions, a wide variety of problem solving capabilities are presented including structural analysis, elasticity and plasticity, construction processes in geomechanics, uncoupled and coupled steady and transient fluid flow and linear and nonlinear solid dynamics. Key features: Updated to take into account advances in parallel computing as well as new material on thermal stress analysis Programs use an updated version of Fortran 2003 Includes exercises for students Accompanied by website hosting software Programming the Finite Element Method, Fifth Edition is an ideal textbook for undergraduate and postgraduate students in civil and mechanical engineering, applied mathematics and numerical analysis, and is also a comprehensive reference for researchers and practitioners. Further information and source codes described in this text can be accessed at the following web sites: www.inside.mines.edu/~vgriffit /PFEM5 for the serial programs from Chapters 4-11 www.parafem.org.uk for the parallel programs from Chapter 12.
A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of ...homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.
Transcription factors specialized to limit the destructive potential of inflammatory immune cells remain ill-defined. We discovered loss-of-function variants in the X-linked ETS transcription factor ...gene ELF4 in multiple unrelated male patients with early onset mucosal autoinflammation and inflammatory bowel disease (IBD) characteristics, including fevers and ulcers that responded to interleukin-1 (IL-1), tumor necrosis factor or IL-12p40 blockade. Using cells from patients and newly generated mouse models, we uncovered ELF4-mutant macrophages having hyperinflammatory responses to a range of innate stimuli. In mouse macrophages, Elf4 both sustained the expression of anti-inflammatory genes, such as Il1rn, and limited the upregulation of inflammation amplifiers, including S100A8, Lcn2, Trem1 and neutrophil chemoattractants. Blockade of Trem1 reversed inflammation and intestine pathology after in vivo lipopolysaccharide challenge in mice carrying patient-derived variants in Elf4. Thus, ELF4 restrains inflammation and protects against mucosal disease, a discovery with broad translational relevance for human inflammatory disorders such as IBD.
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