Publications

2024

1. Solid mechanics

   Curvature controls beading in soft coated elastic cylinders: Finite wavemode instability and localized modulations

   Matteo Taffetani, and Matthew G Hennessy

   Journal of the Mechanics and Physics of Solids, 2024

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   Axisymmetric beading instabilities in soft, elongated cylinders have been observed in a plethora of scenarios, ranging from cellular nanotunnels and nerves in biology to swollen cylinders and electrospun fibers in polymer physics. One of the common geometrical features that can be seen in these systems is the finite wavelength of the emerging pattern. However, modelling studies often predict that the instability has an infinite wavelength, which can be associated with localized necking or bulging. In this paper, we consider a soft elastic cylinder with a thin coating that resists bending, as described by the Helfrich free energy functional. The bending stiffness and natural mean curvature of the coating are two novel features whose competition against bulk elasticity and capillarity is investigated. For intermediate values of the bending stiffness, a linear stability analysis reveals that the mismatch between the current and natural mean curvature of the coating can lead to patterns emerging with a finite wavelength. This analysis creates a continuous bridge between the classical solutions of the shape equation obtained from the Helfrich functional and a curvature-controlled zero-wavemode instability, similar to the one induced by the competition between bulk elasticity and capillarity. A weakly non-linear analysis predicts that the criticality of the bifurcation depends on the controlling parameter, with both supercritical and subcritical bifurcations possible. When capillarity is introduced, the criticality of the bifurcation changes in a non-trivial way.

2023

1. Gels

   Breakdown of electroneutrality in polyelectrolyte gels

   Matthew G Hennessy, Giulia L Celora, Andreas Münch, and 2 more authors

   European Journal of Applied Mathematics, 2023

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   Mathematical models of polyelectrolyte gels are often simplified by assuming the gel is electrically neutral. The rationale behind this assumption is that the thickness of the electric double layer (EDL) at the free surface of the gel is small compared to the size of the gel. Hence, the thin-EDL limit is taken, in which the thickness of the EDL is set to zero. Despite the widespread use of the thin-EDL limit, the solutions in the EDL are rarely computed and shown to match to the solutions for the electrically neutral bulk. The aims of this paper are to study the structure of the EDL and establish the validity of the thin-EDL limit. The model for the gel accounts for phase separation, which gives rise to diffuse interfaces with a thickness described by the Kuhn length. We show that the solutions in the EDL can only be asymptotically matched to the solutions for an electrically neutral bulk, in general, when the Debye length is much smaller than the Kuhn length. If the Debye length is similar to or larger than the Kuhn length, then phase separation can be initiated in the EDL. This phase separation spreads into the bulk of the gel and gives rise to electrically charged layers with different degrees of swelling. Thus, the thin-EDL limit and the assumption of electroneutrality only generally apply when the Debye length is much smaller than the Kuhn length.

2. Gels

   Fiber reinforced hydrated networks recapitulate the poroelastic mechanics of articular cartilage

   Axel C Moore, Matthew G Hennessy, Liebert P Nogueira, and 14 more authors

   Acta Biomaterialia, 2023

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   The role of poroelasticity on the functional performance of articular cartilage has been established in the scientific literature since the 1960s. Despite the extensive knowledge on this topic there remain few attempts to design for poroelasticity and to our knowledge no demonstration of an engineered poroelastic material that approaches physiological performance. In this paper, we report on the development of an engineered material that begins to approach physiological poroelasticity. We quantify poroelasticity using the fluid load fraction, apply mixture theory to model the material system, and determine cytocompatibility using primary human mesenchymal stem cells. The design approach is based on a fiber reinforced hydrated network and uses routine fabrication methods (electrohydrodynamic deposition) and materials (poly[ɛ-caprolactone] and gelatin) to develop the engineered poroelastic material. This composite material achieved a mean peak fluid load fraction of 68%, displayed consistency with mixture theory, and demonstrated cytocompatibility. This work creates a foundation for designing poroelastic cartilage implants and developing scaffold systems to study chondrocyte mechanobiology and tissue engineering.

3. Drying

   Time-dependent modelling of thin poroelastic films drying on deformable plates

   Matthew G Hennessy, Richard V Craster, and Omar K Matar

   European Journal of Applied Mathematics, 2023

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   Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. The cantilever experiment allows the stress in a drying film that has been deposited onto a thin plate to be quantified. Mechanical stresses in the film are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Foppl-von Karman (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from t to t^1/2, in agreement with experiments

4. Gels

   The dynamics of a collapsing polyelectrolyte gel

   Giulia L Celora, Matthew G Hennessy, Andreas Münch, and 2 more authors

   SIAM Journal on Applied Mathematics, 2023

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   We analyse the dynamics of different routes to collapse of a constrained polyelectrolyte gel in contact with an ionic bath. The evolution of the gel is described by a model that incorporates non-linear elasticity, Stefan-Maxwell diffusion and interfacial gradient free energy to account for phase separation of the gel. A bifurcation analysis of the homogeneous equilibrium states reveals three solution branches at low ion concentrations in the bath, giving way to only one above a critical ion concentration. We present numerical solutions that capture both the spatial heterogeneity and the multiple time-scales involved in the process of collapse. These solutions are complemented by two analytical studies. Firstly, a phase-plane analysis that reveals the existence of a depletion front for the transition from the highly swollen to the new collapsed equilibrium state. This depletion front is initiated after the fast ionic diffusion has set the initial condition for this time regime. Secondly, we perform a linear stability analysis about the homogeneous states that show that for a range of ion concentrations in the bath, spinodal decomposition of the swollen state gives rise to localized solvent-rich(poor) and, due to the electro-neutrality condition, ion-poor(rich) phases that coarsen on the route to collapse. This dynamics of a collapsing polyelectrolyte gel has not been described before.

2022

1. Drug delivery

   Optimal loading of hydrogel-based drug-delivery systems

   Matthew J Penn, and Matthew G Hennessy

   Applied Mathematical Modelling, 2022

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   Drug-loaded hydrogels provide a means to deliver pharmaceutical agents to specific sites within the body at a controlled rate. The aim of this paper is to understand how controlled drug release can be achieved by tuning the initial distribution of drug molecules in a hydrogel. A mathematical model is presented for a spherical drug-loaded hydrogel. The model captures the nonlinear elasticity of the polymer network and thermodynamics of swelling. By assuming that the drug molecules are dilute, the equations for hydrogel swelling and drug transport partially decouple. A fast optimisation method is developed to accurately compute the optimal initial drug concentration by minimising the error between the numerical drug-release profile and a target profile. By taking the target drug efflux to be piecewise constant, the optimal initial configuration consists of a central drug-loaded core with isolated drug packets near the free boundary of the hydrogel. The optimal initial drug concentration is highly effective at mitigating the burst effect, where a large amount of drug is rapidly released into the environment. The hydrogel stiffness can be used to further tune the rate of drug release. Although stiffer gels lead to less swelling and hence reduce the drug diffusivity, the drug-release kinetics are faster than for soft gels due to the decreased distance that drug molecules must travel to reach the free surface.

2. Granular media

   Fluid-fluid phase separation in a soft porous medium

   Oliver W Paulin, Liam C Morrow, Matthew G Hennessy, and 1 more author

   Journal of Mechanics and Physics of Solids, 2022

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   Various biological and chemical processes lead to the nucleation and growth of non-wetting fluid bubbles within the pore space of a granular medium, such as the formation of gas bubbles in liquid-saturated lake-bed sediments. In sufficiently soft porous materials, the non-wetting nature of these bubbles can result in the formation of open cavities within the granular solid skeleton. Here, we consider this process through the lens of phase separation, where thermomechanics govern the separation of the non-wetting phase from a fluid-fluid-solid mixture. We construct a phase-field model informed by large-deformation poromechanics, in which two immiscible fluids interact with a poroelastic solid skeleton. Our model captures the competing effects of elasticity and fluid-fluid-solid interactions. We use a phase-field damage model to capture the mechanics of the granular solid. As a model problem, we consider an initial distribution of non-wetting fluid in the pore space that separates into multiple cavities. We use simulations and linear-stability analysis to identify the key parameters that control phase separation, the conditions that favour the formation of cavities, and the characteristic size of the resulting cavities.

3. Drying

   Drying-induced stresses in poroelastic drops on rigid substrates

   Matthew G Hennessy, Richard V Craster, and Omar K Matar

   Physical Review E, 2022

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   We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a non-monotonic drop profile at gelation. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localise the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.

4. Gels

   A kinetic model of a polyelectrolyte gel undergoing phase separation

   Giulia L Celora, Matthew G Hennessy, Andreas Münch, and 2 more authors

   Journal of Mechanics and Physics of Solids, 2022

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2021

1. Heat transfer

   Guyer–Krumhansl Heat Conduction in Thermoreflectance Experiments

   Matthew G Hennessy, and Timothy G Myers

   Multidisciplinary Mathematical Modelling, 2021

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2. Carbon capture

   A Mathematical Model of Carbon Capture by Adsorption

   Francesc Font, Timothy G Myers, and Matthew G Hennessy

   In Multidisciplinary Mathematical Modelling, 2021

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2020

1. Carbon capture

   Mathematical modelling of carbon capture in a packed column by adsorption

   Timothy G Myers, Francesc Font, and Matthew G Hennessy

   Applied Energy, 2020

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2. Batteries

   Asymptotic reduction and homogenization of a thermo-electrochemical model for a lithium-ion battery

   Matthew G Hennessy, and Iain R Moyles

   Applied Mathematical Modelling, 2020

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3. Phase change

   The one-dimensional Stefan problem with non-Fourier heat conduction

   Marc Calvo-Schwarzwälder, Timothy G Myers, and Matthew G Hennessy

   International Journal of Thermal Sciences, 2020

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4. Gels

   Phase separation in swelling and deswelling hydrogels with a free boundary

   Matthew G Hennessy, Andreas Münch, and Barbara Wagner

   Physical Review E, 2020

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5. Phase change

   The Stefan problem with variable thermophysical properties and phase change temperature

   Timothy G Myers, Matthew G Hennessy, and Marc Calvo-Schwarzwälder

   International Journal of Heat and Mass Transfer, 2020

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6. Heat transfer

   Phonon hydrodynamics in frequency-domain thermoreflectance experiments

   A Beardo, Matthew G Hennessy, L Sendra, and 4 more authors

   Physical Review B, 2020

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2019

1. Phase change

   Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation

   Matthew G Hennessy, Marc Calvo-Schwarzwälder, and Timothy G Myers

   Applied Mathematical Modelling, 2019

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2. Phase change

   Elastic suppression of boiling in network fluids: A mechanism for hard-to-boil massecuite

   Matthew G Hennessy, Iain R Moyles, and Stuart J Thomson

   International Journal of Thermal Sciences, 2019

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3. Batteries

   Asymptotic reduction of a porous electrode model for lithium-ion batteries

   Iain R Moyles, Matthew G Hennessy, Timothy G Myers, and 1 more author

   SIAM Journal on Applied Mathematics, 2019

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2018

1. Heat transfer

   Effective thermal conductivity of rectangular nanowires based on phonon hydrodynamics

   Marc Calvo-Schwarzwälder, Matthew G Hennessy, Pol Torres, and 2 more authors

   International Journal of Heat and Mass Transfer, 2018

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2. Phase change

   Asymptotic analysis of the Guyer–Krumhansl–Stefan model for nanoscale solidification

   Matthew G Hennessy, Marc Calvo Schwarzwälder, and Timothy G Myers

   Applied Mathematical Modelling, 2018

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3. Heat transfer

   A slip-based model for the size-dependent effective thermal conductivity of nanowires

   M Calvo-Schwarzwälder, MG Hennessy, P Torres, and 2 more authors

   International Communications in Heat and Mass Transfer, 2018

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2017

1. 3D printing

   Coarse-grained models for frontal photopolymerization with evolving conversion profile

   Aloisius R Purnama, Matthew G Hennessy, Alessandra Vitale, and 1 more author

   Polymer International, 2017

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2. Fluids

   A minimal model for solvent evaporation and absorption in thin films

   Matthew G Hennessy, Giulia L Ferretti, João T Cabral, and 1 more author

   Journal of Colloid and Interface Science, 2017

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3. 3D printing

   Monomer diffusion into static and evolving polymer networks during frontal photopolymerisation

   Matthew G Hennessy, Alessandra Vitale, Omar K Matar, and 1 more author

   Soft Matter, 2017

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2016

1. Drying

   A two-phase model for evaporating solvent-polymer mixtures

   Matthew G Hennessy, Christopher JW Breward, and Colin P Please

   SIAM Journal on Applied Mathematics, 2016

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2. Gel

   Surface waves on a soft viscoelastic layer produced by an oscillating microbubble

   Marc Tinguely, Matthew G Hennessy, Angelo Pommella, and 2 more authors

   Soft Matter, 2016

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2015

1. 3D printing

   A unified approach for patterning via frontal photopolymerization

   Alessandra Vitale, Matthew G Hennessy, Omar K Matar, and 1 more author

   Advanced Materials, 2015

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2. Phase change

   Mathematical modelling of Tyndall star initiation

   Andrew A Lacey, Matthew G Hennessy, Peter Harvey, and 1 more author

   European Journal of Applied Mathematics, 2015

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3. 3D printing

   Role of heat generation and thermal diffusion during frontal photopolymerization

   Matthew G Hennessy, Alessandra Vitale, Joao T Cabral, and 1 more author

   Physical Review E, 2015

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4. 3D printing

   Controlling frontal photopolymerization with optical attenuation and mass diffusion

   Matthew G Hennessy, Alessandra Vitale, Omar K Matar, and 1 more author

   Physical Review E, 2015

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5. 3D printing

   Interfacial profile and propagation of frontal photopolymerization waves

   Alessandra Vitale, Matthew G Hennessy, Omar K Matar, and 1 more author

   Macromolecules, 2015

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6. Polymers

   Controlled topological transitions in thin-film phase separation

   Matthew G Hennessy, Victor M Burlakov, Alain Goriely, and 2 more authors

   SIAM Journal on Applied Mathematics, 2015

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2014

1. Drying

   Dynamics of a slowly evaporating solvent–polymer mixture with a deformable upper surface

   Matthew G Hennessy, and Andreas Münch

   The IMA Journal of Applied Mathematics, 2014

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2. Polymers

   Propagating topological transformations in thin immiscible bilayer films

   Mathew G Hennessy, Victor M Burlakov, Andreas Münch, and 2 more authors

   Europhysics Letters, 2014

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2013

1. Fluids

   The primary flow transition in a differentially heated rotating channel of fluid with O (2) symmetry

   Matthew G Hennessy, and Gregory M Lewis

   Journal of Computational and Applied Mathematics, 2013

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2. Drying

   A Multiple-Scale Analysis of Evaporation Induced Marangoni Convection

   Matthew G. Hennessy, and Andreas Münch

   SIAM Journal on Applied Mathematics, 2013

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