Filters whose porosity decreases with depth are often more efficient at removing solute from a fluid than filters uniform porosity. We investigate this phenomenon via an extension of homogenization theory that accounts for macroscale variation in microstructure. In the first stage paper, we homogenize problems flow through filter near-periodic microstructure and transport due to advection, diffusion, adsorption. second stage, use computationally homogenized equations quantify why gradients...

Abstract In this work we analytically investigate the alignment mechanism of self-propelled ellipse-shaped cells in two spatial dimensions interacting via overlap avoidance. By considering a two-cell system and imposing certain symmetries, obtain an tractable dynamical system, which mathematically analyse detail. We find that for elongated there is half-stable steady state corresponding to perfect between cells. Whether move towards (i.e., become perfectly aligned) or not determined by where...

Significance Bacteria control multicellular behaviors through a process called quorum sensing (QS). Because QS signaling molecules diffuse between cells, they are susceptible to removal by external fluid flow, which is ubiquitous feature of bacterial habitats ranging from the lungs, gut, and nasal passage rivers, lakes, oceans. It therefore vital account for realistic flow conditions when assessing functional role genetic networks. By systematically connecting cell- population-level...

The observed behaviour of passive objects in simple flows can be surprisingly intricate, and is complicated further by object activity. Inspired the motility bacterial swimmers, this two-part study we examine three-dimensional motion rigid active particles shear Stokes flow, focusing on bodies that induce rapid rotation as part their In Part 1 develop a multiscale framework to investigate these emergent dynamics apply it spheroidal objects. 2 (Dalwadi et al. , J. Fluid Mech. vol. 979, 2024,...

In this two-part study, we investigate the motion of rigid, active objects in shear Stokes flow, focusing on bodies that induce rapid rotation as part their activity. Part 2, derive and analyse governing equations for rapidly spinning complex-shaped particles – general helicoidal with chirality. Using multiscale framework develop 1 (Dalwadi et al. , J. Fluid Mech. vol. 979, 2024, A1), systematically emergent angular translational dynamics these chiral objects. We show due to can be described...

Filters that act by adsorbing contaminant onto their pore walls will experience a decrease in porosity over time, and may eventually block. As adsorption generally be larger towards the entrance of filter, where concentration particles is higher, these effects can also result spatially varying porosity. We investigate this dynamic process using an extension homogenization theory accounts for macroscale variation microstructure. formulate homogenize coupled problems flow through filter with...

A simple model for the motion of shape-changing swimmers in Poiseuille flow was recently proposed and numerically explored by Omori et al. (2022). These explorations hinted that a small number interacting mechanics can drive long-time behaviours this model, cast context well-studied alga Chlamydomonas its rheotactic such flows. Here, we explore analytically via multiple-scale asymptotic analysis, seeking to formally identify causal factors shape behaviour these flow. By capturing evolution...

We study motility-induced phase separation (MIPS) in living active matter, which cells interact through chemical signaling, or quorum sensing. In contrast to previous theories of MIPS, our multiscale continuum model accounts explicitly for genetic regulation signal production and motility. Through analysis simulations, we derive a new criterion the onset MIPS that depends on features network. Furthermore, identify characterize type oscillatory instability occurs when gene inside promotes...

When cooling cells to preserve them during cryopreservation, too quickly results in the formation of lethal intracellular ice, while slowly amplifies toxic effects cryoprotective agents (CPAs) added slow down ice formation. We derive a mathematical model for cell cryopreservation understand and quantify these observations. assume that system has spherical geometry three different regions: extracellular liquid medium, cell. The two interfacial boundaries separating regions can move must be...

Classically, the rotation of ellipsoids in shear Stokes flow is captured by Jeffery's orbits. Here, we demonstrate that orbits also describe high-frequency shape-deforming swimmers moving plane a flow. In doing so, support use these simple models for capturing shape-changing swimmer dynamics studies active matter and highlight ubiquity ellipsoid-like complex systems.

In mathematical models that include nutrient delivery to bacteria, it is prohibitively expensive a pointwise uptake within small bacterial regions over bioreactor lengthscales, and so such often impose an effective instead. this paper, we systematically investigate how the should scale with size other microscale properties under first-order kinetics. We homogenize unsteady problem of diffusing through locally periodic array spherical which absorbed. introduce general model could also be...

When a hazardous chemical agent has soaked into porous medium, such as concrete, it can be difficult to neutralize. One removal method is decontamination, where cleanser applied react with and neutralize the agent, forming less harmful reaction products. There are often several cleansers that could used same so important identify features associated fast effective decontamination. As many aqueous solutions while agents immiscible water, decontamination takes place at interface between two...

The method of matched asymptotic expansions is used to study the canonical problem steady laminar flow through a narrow two-dimensional channel blocked by tight-fitting finite-length highly permeable porous obstacle. We investigate behaviour local close interface between single-phase and regions (governed incompressible Navier–Stokes Darcy equations, respectively). solve for in these inner limits low high Reynolds number, facilitating an understanding nature transition from Poiseuille plug...

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale transport. For idealised microstructures, mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional comprising an array obstacles smooth but arbitrary shape, size spacing which vary along length medium. We use via method multiple scales systematically upscale novel problem involving cells varying area obtain effective...

Many swimmers oscillate rapidly as they move, though the details of this fast motion are often neglected in their study. Here, we explore long-term effects that these oscillations can have on swimmer motion, identifying intuitive conditions rapid preclude accumulation biases self-propelling objects. We also highlight how combination and external flow lead to significant unexpected changes behavior, which consider context classical Jeffery's orbit.

In biological systems, chemical signals termed morphogens self-organize into patterns that are vital for many physiological processes. As observed by Turing in 1952, these a state of continual development, and usually transitioning from one pattern another. How do cells robustly decode spatio-temporal the presence confounding effects caused unpredictable or heterogeneous environments? Here, we answer this question developing general theory formation variations ‘pre-pattern’ morphogens, which...

Organoids are three-dimensional multicellular tissue constructs. When cultured

The mevalonate pathway is normally found in eukaryotes, and allows for the production of isoprenoids, a useful class organic compounds. This has been successfully introduced to Escherichia coli, enabling biosynthetic route many isoprenoids. In this paper, we develop solve mathematical model concentration metabolites over time, accounting loss acetyl-CoA other metabolic pathways. Additionally, test our theoretical predictions experimentally by introducing part into Cupriavidus necator. model,...

The exact geometry of the thin glycocalyx layer that coats interior blood vessels is unknown. A mathematical model developed to predict how differences in affect hydraulic flow through glycocalyx, and could be inferred experiments.

When modeling transport of a chemical species to colony bacteria in biofilm, it is computationally expensive treat each bacterium even as point sink, let alone capture the finite nature bacterium. Instead, models tend bacterial and extracellular matrix domains single phase, over which an effective bulk uptake imposed. In this paper, we systematically derive equations that should govern such system, starting from microscale problem diffusing through finite-sized bacteria, within can also...

The UK Government Decontamination Service (UKGDS) advise on the national capability for decontamination of buildings, infrastructure, transport and open environment. Additionally, UKGDS are a source expertise in event chemical, biological, radiological or nuclear (CBRN) incidents, major release hazardous materials. In first part report, study group derive solve mathematical models to investigate depth which toxic chemicals may seep into dry porous substrates. This involved applying Darcy's...

One method to grow artificial body tissue is place a porous scaffold seeded with cells, known as construct, into rotating bioreactor filled nutrient-rich fluid. The flow within the affected by movement of construct relative which, in turn, hydrodynamical and gravitational forces experiences. motion thus coupled bioreactor. Over time scale few hours, appears move periodic orbit but, over tens drifts from periodicity. In biological literature, this effect often attributed change density that...

A biosustainable production route for 3-hydroxypropionic acid (3HP), an important platform chemical, would allow 3HP to be produced without using fossil fuels. We are interested in investigating a potential biochemical from pyruvate through $$\beta $$ -alanine and, this paper, we develop and solve mathematical model the reaction kinetics of metabolites involved pathway. consider two limiting cases, one where levels never replenished, other continuously replenished thus kept constant. exploit...

Abstract In biological systems, chemical signals termed morphogens self-organise into patterns that are vital for many physiological processes. As observed by Turing in 1952, these a state of continual development, and usually transitioning from one pattern another. How do cells robustly decode spatio-temporal the presence confounding effects caused unpredictable or heterogeneous environments? Here, we answer this question developing general theory formation variations ‘pre-pattern’...