arXiv subjects

Philip Pearce

Publications and source records attributed to Philip Pearce.

12 recordsLinked to original sources

arXiv2026

Bacterial adhesion to curved surfaces in fluid flow

Minimising bacterial surface adhesion and subsequent biofilm formation in industrial and medical settings requires understanding how bacteria are transported and adhere to complex surface geometries in the presence of non-uniform flow. In this paper, we consider the transport of a dilute suspension of motile bacteria through a corrugated two-dimensional channel with perfectly adhesive walls. We asymptotically analyse the diffusive boundary layer that forms in high velocity flows using a curvilinear coordinate system based on the fluid streamfunction, presenting a similarity solution to the diffusivity-varying diffusion-type equation that arises. From this solution, we derive an analytical expression for the bacterial adhesion rate as a function of surface arclength and the spatially varying wall shear rate. Our model predicts that bacterial adhesion becomes localised on curved surfaces, with bacteria showing preferential adhesion to wall `peaks' at lower shear rates and preferential adhesion to wall `valleys' at higher shear rates. More broadly, our results highlight how spatially varying flows generated by complex geometries can lead to localised bacterial adhesion, with potential implications for both enhancing and minimising biofilm formation.

cond-mat.soft↗

arXiv2026

Chemotaxis of cell aggregates: morphology and dynamics of migrating active droplets

Biological tissues have been observed to display emergent fluid-like properties, owing to physical interactions between cells. However, it remains unclear in general how these fluid-like properties affect tissue structure and function. Here, we are motivated by recent experiments in which cell aggregates were observed to behave as active droplets during collective migration along chemical gradients, or chemotaxis. To understand this process, we develop a minimal model of a growing thin active droplet driven by a self-generated chemical gradient. In broad agreement with the experiments, dynamic simulations reveal that chemotacting droplets exhibit proliferation-driven morphological transitions. To fully characterise these transitions, we perform a multiple scales analysis to show that the droplet dynamics follow a sequence of travelling wave solutions defined by a nonlinear eigenvalue problem parametrised by the slowly increasing droplet volume. Our analysis reveals that morphological transitions can occur continuously or through a discontinuous bifurcation. Further asymptotic analysis of the travelling wave problem reveals that these morphological transitions arise from exponentially small ("beyond-all-orders") asymptotic terms that originate from the rear and front contact lines. Moreover, we show that the nature of the transitions is fully determined by two key dimensionless parameters, which quantify the internal stress balance within the droplet and the strength of the coupling between the droplet migration dynamics and the external chemical field. Overall, our results provide a complete characterisation of the morphodynamics of a class of migrating active thin droplets, with implications in a range of biological systems where cell aggregates exhibit fluid-like behaviour.

cond-mat.soft↗

arXiv2025

A Weakly Nonlinear Theory for Pattern Formation in Structured Models with Localized Solutions

Structured models, such as PDEs structured by age or phenotype, provide a setting to study pattern formation in heterogeneous populations. Classical tools to quantify the emergence of patterns, such as linear and weakly nonlinear analyses, pose significant mathematical challenges for these models due to sharply peaked or singular steady states. Here, we present a weakly nonlinear framework that extends classical tools to structured PDE models in settings where the base state is spatially uniform, but exponentially localized in the structured variable. Our approach utilizes WKBJ asymptotics and an analysis of the Stokes phenomenon to systematically resolve the solution structure in the limit where the steady state tends to a Dirac-delta function. To demonstrate our method, we consider a chemically structured (nonlocal) model of motile bacteria that interact through quorum sensing. For this example, our analysis yields an amplitude equation that governs the solution dynamics near a linear instability, and predicts a pitchfork bifurcation. From the amplitude equation, we deduce an effective parameter grouping whose sign determines whether the pitchfork bifurcation is subcritical or supercritical. Although we demonstrate our framework for a specific example, our techniques are broadly applicable.

math.AP↗

arXiv2025

Effective permeability conditions for diffusive transport through impermeable membranes with gaps

Membranes regulate transport in a wide variety of industrial and biological applications. The microscale geometry of the membrane can significantly affect overall transport through the membrane, but the precise nature of this multiscale coupling is not well characterised in general. Motivated by the application of transport across a bacterial membrane, in this paper we use formal multiscale analysis to derive explicit effective coupling conditions for macroscale transport across a two-dimensional impermeable membrane with periodically spaced gaps, and validate these with numerical simulations. We derive analytic expressions for effective macroscale quantities associated with the membrane, such as the permeability, in terms of the microscale geometry. Our results generalise the classic constitutive membrane coupling conditions to a wider range of membrane geometries and time-varying scenarios. Specifically, we demonstrate that if the exterior concentration varies in time, for membranes with long channels, the transport gains a memory property where the coupling conditions depend on the system history. By applying our effective conditions in the context of small molecule transport through gaps in bacterial membranes called porins, we predict that bacterial membrane permeability is primarily dominated by the thickness of the membrane. Furthermore, we predict how alterations to membrane microstructure, for example via changes to porin expression, might affect overall transport, including when external concentrations vary in time. These results will apply to a broad range of physical applications with similar membrane structures, from medical and industrial filtration to carbon capture.

cond-mat.soft↗

arXiv2025

A shear-induced limit on bacterial surface adhesion in fluid flow

Controlling bacterial surface adhesion and subsequent biofilm formation in fluid systems is crucial for the safety and efficacy of medical and industrial processes. Here, we theoretically examine the transport of bacteria close to surfaces, isolating how the key processes of bacterial motility and fluid flow interact and alter surface adhesion. We exploit the disparity between the fluid velocity and the swimming velocity of common motile bacteria and, using a hybrid asymptotic-computational approach, we systematically derive the coarse-grained bacterial diffusivity close to surfaces as a function of swimming speed, rotational diffusivity, and shape. We calculate an analytical upper bound for the bacterial adhesion rate by considering the scenario in which bacteria adhere irreversibly to the surface on first contact. Our theory predicts that maximal adhesion occurs at intermediate flow rates: at low flow rates, increasing flow increases surface adhesion, while at higher flow rates, adhesion is decreased by shear-induced cell reorientation.

cond-mat.soft↗

arXiv2025

Mesoscopic heterogeneity in biomolecular condensates from sequence patterning

Biomolecular condensates composed of intrinsically disordered proteins (IDPs) are vital for proper cellular function, and their dysfunction is associated with diseases including neurodegeneration and cancer. Despite their biological importance, the precise physical mechanisms underlying condensate (dys)function are unclear, in part owing to the difficulties in understanding how biomolecular sequence patterns influence emergent condensate behaviours across relevant length and timescales. Here, through minimal physical modelling, we explain how IDP sequence patterning gives rise to nano-scale organisational heterogeneities in condensates. By applying our coarse-grained molecular-dynamics polymer model, which accounts for steric, attractive, and electrostatic interactions, we systematically quantify and map out the emergent morphological phases resulting from a wide range of sequence patterns. We demonstrate how sequences that enable local coil-to-globule transitions within regions of single polymers - driven by a competition between the preferred crowding densities of different regions in the sequence - also exhibit cluster formation in condensates. Overall, our work provides a conceptual framework to understand how sequence properties determine mesoscopic organisation within biomolecular condensates.

cond-mat.soft↗

arXiv2025

Emergent clogging of continuum particle suspensions in constricted channels

Particle suspensions in confined geometries can become clogged, which can have a catastrophic effect on function in biological and industrial systems. Here, we investigate the macroscopic dynamics of suspensions in constricted geometries. We develop a minimal continuum two-phase model that allows for variation in particle volume fraction. The model comprises a ``wet solid'' phase with material properties dependent on the particle volume fraction, and a seepage Darcy flow of fluid through the particles. We find that spatially varying geometry (or material properties) can induce emergent heterogeneity in the particle fraction and trigger the abrupt transition to a high-particle-fraction ``clogged'' state.

physics.flu-dyn↗

arXiv2023

An agent-based modelling framework to study growth mechanisms in EGFR-L858R mutant alveolar type II cells

Mutations in the epidermal growth factor receptor (EGFR) are common in non-small cell lung cancer (NSCLC), particularly in never-smoker patients. However, these mutations are not always carcinogenic, and have recently been reported in histologically normal lung tissue from patients with and without lung cancer. To investigate the outcome of EGFR mutation in healthy lung stem cells, we grew murine alveolar type-II organoids monoclonally in a 3D Matrigel. Our experiments showed that the \textit{EGFR-L858R} mutation induced a change in organoid structure: mutated organoids displayed more `budding', in comparison to non-mutant controls, which were nearly spherical. We perform on-lattice computational simulations, which suggest that this can be explained by the concentration of division amongst a small number of cells on the surface of the organoid, which may arise from several possible biological mechanisms. These results suggest that the L858R mutation produces structures which expand quickly from surface protrusions. We are currently unable to distinguish the cell-based mechanisms that lead to this spatial heterogeneity in growth, but suggest a number of future experiments which could be used to do so. We suggest that the likelihood of L858R-fuelled tumorigenesis is affected not just by random fluctuations in cell fitness, but by whether the mutation arises in a spatial environment that allows mutant cells to reproduce without being forced to encounter each other. These data may have implications for cancer prevention strategies and for understanding NSCLC progression.

q-bio.CB↗

arXiv2019

Physical and geometric determinants of transport in feto-placental microvascular networks

Across mammalian species, solute exchange takes place in complex microvascular networks. In the human placenta, the primary exchange units are terminal villi that contain disordered networks of fetal capillaries and are surrounded externally by maternal blood. Here we show how the irregular internal structure of a terminal villus determines its exchange capacity for a wide range of solutes. Distilling geometric features into three scalar parameters, obtained from image analysis and computational fluid dynamics, we capture archetypal features of the the structure-function relationship of terminal villi using a simple algebraic approximation, revealing transitions between flow- and diffusion-limited transport at vessel and network levels. Our theory accommodates countercurrent effects, incorporates nonlinear blood rheology and offers an efficient method for testing network robustness. Our results show how physical estimates of solute transport, based on carefully defined geometrical statistics, provide a viable method for linking placental structure and function, and offer a framework for assessing transport in other microvascular systems.

physics.bio-ph↗

arXiv2018

Propagation and stability of flames in inhomogeneous mixtures

We investigate the effect of thermal expansion and gravity on the propagation and stability of flames in inhomogeneous mixtures. We focus on laminar flames in the simple configuration of an infinitely long channel with rigid porous walls in order to understand the effect of inhomogeneities on these fundamental structures.

physics.flu-dyn↗

arXiv2016

Image-Based Modeling of Blood Flow and Oxygen Transfer in Feto-Placental Capillaries

During pregnancy, oxygen diffuses from maternal to fetal blood through villous trees in the placenta. In this paper, we simulate blood flow and oxygen transfer in feto-placental capillaries by converting three-dimensional representations of villous and capillary surfaces, reconstructed from confocal laser scanning microscopy, to finite-element meshes, and calculating values of vascular flow resistance and total oxygen transfer. The relationship between the total oxygen transfer rate and the pressure drop through the capillary is shown to be captured across a wide range of pressure drops by physical scaling laws and an upper bound on the oxygen transfer rate. A regression equation is introduced that can be used to estimate the oxygen transfer in a capillary using the vascular resistance. Two techniques for quantifying the effects of statistical variability, experimental uncertainty and pathological placental structure on the calculated properties are then introduced. First, scaling arguments are used to quantify the sensitivity of the model to uncertainties in the geometry and the parameters. Second, the effects of localized dilations in fetal capillaries are investigated using an idealized axisymmetric model, to quantify the possible effect of pathological placental structure on oxygen transfer. The model predicts how, for a fixed pressure drop through a capillary, oxygen transfer is maximized by an optimal width of the dilation. The results could explain the prevalence of fetal hypoxia in cases of delayed villous maturation, a pathology characterized by a lack of the vasculo-syncytial membranes often seen in conjunction with localized capillary dilations.

q-bio.TO↗

arXiv2016

Maths in Medicine: How to Survive a Science Fair

When talking to secondary school students, first impressions are crucial. Accidentally say something that sounds boring and you'll lose them in seconds. A physical demonstration can be an eye-catching way to begin an activity or spark off a conversation about mathematics. This is especially true in the context of an event like a science fair where there are hundreds of other exhibitors and stands, possibly involving loud music and/or dancing robots! In this article we describe three devices that were built to illustrate specific physical phenomena that occur in the human body. Each device corresponds to a simple mathematical model which contains both elements that are accessible to pupils in the early years of secondary education and more challenging mathematical concepts that might appeal to A-level students. Two of the devices relate to the Windkessel effect, a physical phenomenon that regulates blood flow, and the third demonstrates the elastic properties of ligaments and tendons.

physics.ed-ph↗