arXiv subjects

Ian M. Griffiths

Publications and source records attributed to Ian M. Griffiths.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Snap-Fit: Optimizing the Lifting Capabilities of a Partial Cylindrical Shell

The cylindrical snap-fit is a ubiquitous fastening method that is both simple to manufacture and assemble, and yet secure. It consists of a partial cylindrical shell that `snaps' onto a cylindrical object. We build on previous work to describe the mechanics of the cylindrical snap-fit as a naturally curved thin elastic shell placed atop a rigid cylinder; we investigate the shell's behaviour when subject to a point force pushing it onto or pulling it off the cylinder. We classify the possible contact regimes according to whether the shell has a nonzero lifting capacity. We term situations with lifting capacity `grip-fits' and show that this includes both the snap-fit and a `stick-fit' regime, which allows lifting despite not having the characteristic `snap'. Regimes without lifting capacity are also characterized for completeness. We show that the different regimes may be characterized entirely by the shell/cylinder geometry and the coefficient of friction. We then consider different metrics for the lifting performance in the grip-fit regime. Our analysis reveals the trade-offs between assembly force, disassembly force, lifting force, and clamping force, providing design principles for secure lifting, easy detachment, and safe handling of fragile objects.

cond-mat.soft↗

arXiv2026

Modelling Intermediate-Current Transitions in Asymmetric-Valence Binary Electrolytes

Asymmetric valences in a binary electrolyte can significantly affect the performance of systems such as reverse electrodialysis cells, batteries, and supercapacitors. To generate a theoretical understanding of this effect, we consider a steady one-dimensional Poisson-Nernst-Planck model of an electrolytic cell with imposed constant ionic fluxes, focusing on varying ion valences in a general asymmetric binary electrolyte. Numerical simulations reveal a smooth transition between the qualitatively distinct near-equilibrium and strongly non-equilibrium steady-state regimes. These regimes are distinguished by a valence-dependent transition point at an intermediate current where the classical Debye-scale boundary layer vanishes. We characterise this transition using asymptotic analysis, recovering the Gouy-Chapman and limiting-current results in the appropriate limits, and determining the correct transition results when neither is appropriate. We provide implicit solutions for the potential and ion concentrations of general asymmetric binary electrolytes and, notably, we provide explicit analytic expressions for the asymptotic composite solutions for 2z:z, z:2z, and z:z electrolytes. We show how the results can be presented in a collapsed phase diagram that can be used to predict qualitative intermediate-current steady-state behaviour in terms of ion valences and fluxes.

physics.chem-ph↗

arXiv2025

Mathematical Modelling of Face Coverings for Virus Protection

Traditional face masks used extensively, for example, during the COVID-19 pandemic, are relatively impermeable, forcing aerosol-containing breath to flow into the surrounding atmosphere by ``leaking" out from the lateral edges of the mask. This protects close-proximity persons but results in a high viral load being delivered into the air. An alternative face covering, the Virustatic Shield, developed by Virustatic, involves a much more permeable material coated in an active agent, with the goal of increasing the transmission through the mask and thus reducing the viral load released. In this paper, we build and solve a model that describes the air flow and aerosol transport through a porous face mask. Our model for air flow is based on a low-Reynolds-number approximation to the Navier--Stokes equations, and reduces to a two-dimensional scalar partial differential equation for the local flux through the mask. We use the model to explore the interplay between leakage from the mask sides and flow directly through. We compare and contrast the leakage for traditional face masks and for neck gaiters, and find that neck gaiters have a lower leakage. We utilise a simple model for aerosol transport that balances advection with capture by the mask, and find that there is an ideal permeability, which optimises real-world protection offered by the mask.

physics.flu-dyn↗

arXiv2025

Bridging a gap: A heavy elastica between point supports

We study the deformation and slip-through of a heavy elastic beam suspended above two point supports and subject to an increasing body force -- an idealized model of a fibre trapped in the pores of a filter as flow strength increases, for example. Using both asymptotic and numerical techniques, we investigate the behaviour of the beam under increasing body force and the maximum force that can be supported before it must slip between the supports. We quantify this maximum body force as a function of the separation between the two supports. Surprisingly, we show the existence of a critical separation below which the beam can withstand an arbitrarily large body force, even in the absence of friction. This is understood as the limit of a catenary between the supports that is connected to (and supported by the tension in) a vertically hanging portion outside the supports. We explore how frictional forces impact the deformation and load-bearing capacity of the beam and show that our results are consistent with laboratory experiments.

cond-mat.soft↗

arXiv2024

A homogenised model for dispersive transport and sorption in a heterogeneous porous medium

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous medium; however, this dependence remains poorly understood. For idealised microstructures, one can use the mathematical framework of homogenisation to examine this dependence, but strongly heterogeneous materials are more challenging. 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 microscale problem involving non-periodic cells of varying area to obtain effective continuum equations for macroscale transport and sorption. The equations are characterised by the local porosity, an effective local adsorption rate and an effective local anisotropic solute diffusivity. All of these macroscale properties depend nontrivially on the two degrees of microstructural geometric freedom in our problem; obstacle size and obstacle spacing. Further, the coefficient of effective diffusivity comprises the molecular diffusivity, the suppressive effect of the presence of obstacles and the enhancing effect of dispersion. To illustrate the mathematical model, we focus on a simple example geometry comprising circular obstacles on a hexagonal lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We find a power law for the dispersive component of solute transport, consistent with classical Taylor dispersion.

physics.flu-dyn↗

arXiv2023

The effect of local ventilation on a spatiotemporal model of airborne disease transmission in indoor spaces

We incorporate local ventilation effects into a spatially dependent generalisation of the Wells--Riley model for airborne disease transmission. Aerosol production and removal through ventilation, biological deactivation, and gravitational settling as well as transport around a recirculating air-conditioning flow and turbulent mixing are modelled using an advection--diffusion--reaction equation. The local ventilation model, motivated by air purifiers, is compared with the global ventilation model for a weak purifier (CADR = 140 m$^3$h$^{-1}$) and a strong purifier (CADR = 1,000 m$^3$h$^{-1}$). We find that, as expected, increasing the distance of the infectious person from the purifier reduces the aerosol concentration. Moreover, the concentration is generally lowest when the infectious person is upstream of the purifier, located in regions where the airflow streamlines are directed into the purifier inlet. For these infectious source locations, the global ventilation model significantly overestimates the concentration throughout the room. For infectious sources outside of these regions, there is generally good agreement between the models, particularly for the weak purifier. We also studied, for fixed distance from the purifier, how the infection risk to a susceptible person varies as the infectious person changes location. The infection risk is greatest when the susceptible person is directly downstream of the infectious person. There is better agreement between local and global ventilation models for the weak purifier than the strong purifier.

q-bio.QM↗

arXiv2021

A homogenised model for flow, transport and sorption in a heterogeneous porous medium

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 nontrivially 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.

physics.flu-dyn↗

arXiv2021

Predicting the Spatially Varying Infection Risk in Indoor Spaces Using an Efficient Airborne Transmission Model

We develop a spatially dependent generalisation to the Wells-Riley model and its extensions applied to COVID-19, that determines the infection risk due to airborne transmission of viruses. We assume that the concentration of infectious particles is governed by an advection-diffusion-reaction equation with the particles advected by airflow, diffused due to turbulence, emitted by infected people and removed due to the room ventilation, inactivation of the virus and gravitational settling. We consider one asymptomatic or presymptomatic infectious person who breathes or talks, with or without a mask and model a quasi-3D setup that incorporates a recirculating air-conditioning flow. A semi-analytic solution is available and this enables fast simulations. We quantify the effect of ventilation and particle emission rate on the particle concentration, infection risk and the `time to probable infection' (TTPI). Good agreement with CFD models is achieved. Furthermore, we derive power laws that quantify the effect of ventilation, emission rate and infectiousness of the virus on the TTPI. The model can be easily updated to take into account modified parameter values. This work paves the way for establishing `safe occupancy times' at any location and has direct applicability in mitigating the spread of the COVID-19 pandemic.

q-bio.QM↗

arXiv2020

Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid

Periodically-driven flows are known to generate non-zero, time-averaged fluxes of heat or solute species, due to the interactions of out-of-phase velocity and temperature/concentration fields, respectively. Herein, we investigate such transport (a form of the well-known Taylor--Aris dispersion) in the gap between two parallel plates, one of which oscillates vertically, generating a time-periodic squeeze flow of either a newtonian or Maxwellian fluid. Using the method of multiple time-scale homogenization, the mass/heat balance equation describing transport in this flow is reduced to a one-dimensional advection--diffusion--reaction equation. This result indicates three effective mechanisms in the mass/heat transfer in the system: an effective diffusion that spreads mass/heat along the concentration/temperature gradient, an effective advective flux, and an effective reaction that releases or absorbs mass/heat - in the time-averaged frame. Our results demonstrate that there exist resonant modes under which the velocity peaks when the dimensionless plate oscillation frequency (embodied by the Womersley number, the ratio of the transient inertia to viscous forces) approaches specific values. As a result, transport in this flow is significantly influenced by the dimensionless frequency. On the one hand, the effective, time-averaged dispersion coefficient is always larger than the molecular diffusivity, and is sharply enhanced near resonance. The interaction between fluid elasticity and the oscillatory forcing enhances the efficiency of transport in the system. On the other hand, the identified effective advection and reaction mechanisms may transport mass/heat from regions of high concentration/temperature to those of low concentration/temperature, or vice versa, depending on the value of dimensionless frequency.

physics.flu-dyn↗

arXiv2020

Optimising the flow through a concertinaed filtration membrane

Membrane filtration is a vital industrial process, with applications including air purification and blood filtration. In this paper, we study the optimal design for a concertinaed filtration membrane composed of angled porous membranes and dead-ends. We examine how the filter performance depends on the angle, position, thickness, and permeance of the membrane, through a combination of numerical and asymptotic approaches, the latter in the limit of a slightly angled membrane. We find that, for a membrane of fixed angle and physical properties, there can exist multiple membrane positions that maximise the flux for an applied pressure difference. More generally, we show that while the maximal flux achievable depends on the membrane thickness and permeance, the optimal membrane configuration is always in one of two setups: centred and diagonal across the full domain; or angled and in the corner of the domain.

physics.flu-dyn↗

arXiv2019

The effect of compressibility on the behaviour of filter media

A filter comprises porous material that traps contaminants when fluid passes through under an applied pressure difference. One side-effect of this applied pressure, however, is that it compresses the filter. This changes the permeability, which may affect its performance. As the applied pressure increases the flux of fluid processed by the filter will also increase but the permeability will decrease. Eventually the permeability reaches zero at a point in the filter and the fluid flux falls to zero. In this paper we derive a model for the fluid transport through a filter due to an applied pressure difference and the resulting compression. We use this to determine the maximum operating flux that can be achieved without the permeability reaching zero and the filter shutting down. We determine the material properties that balance the desire to maximize flux while minimizing power use. We also show how choosing an initial spatially dependent permeability can lead to a uniformly permeable filter under operation and we find the permeability distribution that maximizes the flux for a given applied pressure, both of which have desirable industrial implications. The ideas laid out in this paper set a framework for modelling more complex scenarios such as filter blocking.

physics.flu-dyn↗

arXiv2018

The influence of porous media microstructure on filtration

We investigate how a filter media 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 media 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 media in a simple and robust way. We perform a comprehensive investigation of the influence of the filter-media microstructure on filter performance in a spectrum of possible filtration scenarios.

physics.flu-dyn↗

arXiv2017

Nematohydrodynamics for Colloidal Self-Assembly and Transport Phenomena

We study colloidal particles in a nematic-liquid-crystal-filled microfluidic channel and show how elastic interactions between the particle and the channel wall lead to different particle dynamics compared with conventional microfluidics. For a static particle, in the absence of a flow field, the director orientation on the particle surface undergoes a rapid transition from uniform to homeotropic anchoring as a function of the anchoring strength and the particle size. In the presence of a flow field, in addition to fluid viscous stresses on the particle, nematic-induced elastic stresses are exerted as a result of the anchoring conditions. The resulting forces are shown to offer the possibility of size-based separation of individual particles. For multi-particle systems, the nematic forces induce inter-particle attraction induces particle attraction, following which the particles aggregate and reorientate. These results illustrate how coupled nematic-hydrodynamic effects can affect the mobility and spatial reorganization of colloidal particles in microfluidic applications.

cond-mat.soft↗

arXiv2017

Lubricated wrinkles: imposed constraints affect the dynamics of wrinkle coarsening

We study the dynamic coarsening of wrinkles in an elastic sheet that is compressed while lying on a thin layer of viscous liquid. When the ends of the sheet are instantaneously brought together by a small distance, viscous resistance initially prevents the sheet from adopting a globally buckled shape. Instead, the sheet accommodates the compression by wrinkling. Previous scaling arguments suggested that a balance between the sheet's bending stiffness and viscous effects lead to a wrinkle wavelength $λ$ that increases with time $t$ according to $λ\propto t^{1/6}$. We show that taking proper account of the compression constraint leads to a logarithmic correction of this result, $λ\propto (t/\log t)^{1/6}$. This correction is significant over experimentally observable time spans, and leads us to reassess previously published experimental data.

physics.flu-dyn↗

arXiv2016

A multiscale method to calculate filter blockage

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 larger 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 in Dalwadi et al. (2015) 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. Additionally, 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.

physics.flu-dyn↗

arXiv2016

Understanding how porosity gradients can make a better filter using homogenization theory

Filters whose porosity decreases with depth are often more efficient at removing solute from a fluid than filters with a uniform porosity. We investigate this phenomenon via an extension of homogenization theory that accounts for a macroscale variation in microstructure. In the first stage of the paper, we homogenize the problems of flow through a filter with a near-periodic microstructure and of solute transport due to advection, diffusion, and filter adsorption. In the second stage, we use the computationally efficient homogenized equations to investigate and quantify why porosity gradients can improve filter efficiency. We find that a porosity gradient has a much larger effect on the uniformity of adsorption than it does on the total adsorption. This allows us to understand how a decreasing porosity can lead to a greater filter efficiency, by lowering the risk of localized blocking while maintaining the rate of total contaminant removal.

physics.flu-dyn↗

arXiv2015

Interfacial deformation and jetting of a magnetic fluid

An attractive technique for forming and collecting aggregates of magnetic material at a liquid--air interface by an applied magnetic field gradient was recently addressed theoretically and experimentally [Soft Matter, (9) 2013, 8600-8608]: when the magnetic field is weak, the deflection of the liquid--air interface has a steady shape, while for sufficiently strong fields, the interface destabilizes and forms a jet that extracts magnetic material. Motivated by this work, we develop a numerical model for the closely related problem of solving two-phase Navier--Stokes equations coupled with the static Maxwell equations. We computationally model the forces generated by a magnetic field gradient produced by a permanent magnet and so determine the interfacial deflection of a magnetic fluid (a pure ferrofluid system) and the transition into a jet. We analyze the shape of the liquid--air interface during the deformation stage and the critical magnet distance for which the static interface transitions into a jet. We draw conclusions on the ability of our numerical model to predict the large interfacial deformation and the consequent jetting, free of any fitting parameter.

physics.flu-dyn↗

arXiv2014

Particle Capture Efficiency in a Multi-Wire Model for High Gradient Magnetic Separation

High gradient magnetic separation (HGMS) is an efficient way to remove magnetic and paramagnetic particles, such as heavy metals, from waste water. As the suspension flows through a magnetized filter mesh, high magnetic gradients around the wires attract and capture the particles, removing them from the fluid. We model such a system by considering the motion of a paramagnetic tracer particle through a periodic array of magnetized cylinders. We show that there is a critical Mason number (ratio of viscous to magnetic forces) below which the particle is captured irrespective of its initial position in the array. Above this threshold, particle capture is only partially successful and depends on the particle's entry position. We determine the relationship between the critical Mason number and the system geometry using numerical and asymptotic calculations. If a capture efficiency below 100% is sufficient, our results demonstrate how operating the HGMS system above the critical Mason number but with multiple separation cycles may increase efficiency.

physics.flu-dyn↗