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High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems (2024)
Journal Article
Wray, A., & Moore, M. (2024). High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems. Scientific reports, 14(1), Article 4225. https://doi.org/10.1038/s41598-024-54377-2

The classical problem of determining the density and capacity of arrays of potential sources is studied. This corresponds to a wide variety of physical problems such as electrostatic capacitance, stress in elastostatics and the evaporation of fluid d... Read More about High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems.

Gravitational effects on coffee-ring formation during the evaporation of sessile droplets (2023)
Journal Article
Moore, M., & Wray, A. (2023). Gravitational effects on coffee-ring formation during the evaporation of sessile droplets. Journal of Fluid Mechanics, 967, Article A26. https://doi.org/10.1017/jfm.2023.493

We consider the role of gravity in solute transport when a thin droplet evaporates. Under the physically relevant assumptions that the contact line is pinned and the solutal Péclet number, Pe , is large, we identify two asymptotic regimes that depen... Read More about Gravitational effects on coffee-ring formation during the evaporation of sessile droplets.

Near edge tractions for a rounded quarter-plane pressed into an elastically similar half-plane (2023)
Journal Article
Eames, B., Hills, D., & Moore, M. (2023). Near edge tractions for a rounded quarter-plane pressed into an elastically similar half-plane. Tribology International, Article 108582. https://doi.org/10.1016/j.triboint.2023.108582

Asymptotic forms are a useful way of representing the state of stress at a contact edge, allowing us to characterise the region in which cracks nucleate. The asymptotes must match the behaviour implied by the local geometry. In this paper, we study t... Read More about Near edge tractions for a rounded quarter-plane pressed into an elastically similar half-plane.

Evaporation of non-circular droplets (2023)
Journal Article
Wray, A., & Moore, M. (2023). Evaporation of non-circular droplets. Journal of Fluid Mechanics, 961, Article A11. https://doi.org/10.1017/jfm.2023.229

The dynamics of thin, non-circular droplets evaporating in the diffusion-limited regime is examined. The challenging non-rectilinear mixed boundary problem this poses is solved using a novel asymptotic approach and an asymptotic expansion for the eva... Read More about Evaporation of non-circular droplets.

A novel asymptotic formulation for partial slip half-plane frictional contact problems (2022)
Journal Article
Moore, M., & Hills, D. (2022). A novel asymptotic formulation for partial slip half-plane frictional contact problems. Theoretical and Applied Fracture Mechanics, 121, Article 103457. https://doi.org/10.1016/j.tafmec.2022.103457

A method of solution and the necessary calibrations are given to permit the steady-state extent of slip to be found in contacts properly described within a half-plane formulation using only two parameters: the contact law and the first-order descript... Read More about A novel asymptotic formulation for partial slip half-plane frictional contact problems.

The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis (2022)
Journal Article
Moore, M., Vella, D., & Oliver, J. (2022). The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis. Journal of Fluid Mechanics, 940, Article A38. https://doi.org/10.1017/jfm.2022.251

We consider the effect of droplet geometry on the early-stages of coffee ring formation during the evaporation of a thin droplet with an arbitrary simple, smooth, pinned contact line. We perform a systematic matched asymptotic analysis of the small-c... Read More about The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis.

Analysing the accuracy of asymptotic approximations in incomplete contact problems (2022)
Journal Article
Moore, M., & Hills, D. (2022). Analysing the accuracy of asymptotic approximations in incomplete contact problems. International Journal of Solids and Structures, 253, Article 111557. https://doi.org/10.1016/j.ijsolstr.2022.111557

The error incurred in the representation of the contact pressure at the edges of incomplete contacts by first order asymptotes is treated, and the maximum value of the relative error found for a range of geometries, both symmetric and non-symmetric.... Read More about Analysing the accuracy of asymptotic approximations in incomplete contact problems.

Introducing pre-impact air-cushioning effects into the Wagner model of impact theory (2021)
Journal Article
Moore, M. R. (2021). Introducing pre-impact air-cushioning effects into the Wagner model of impact theory. Journal of engineering mathematics, 129(1), Article 6. https://doi.org/10.1007/s10665-021-10137-z

In this analysis, we consider the effects of non-quiescent initial conditions driven by pre-impact air–water interactions on the classical Wagner model of impact theory. We consider the problem of a rigid, solid impactor moving vertically towards a l... Read More about Introducing pre-impact air-cushioning effects into the Wagner model of impact theory.

Explicit and asymptotic solutions for frictional incomplete half-plane contacts subject to general oscillatory loading in the steady-state (2020)
Journal Article
Andresen, H., Fleury, R., Moore, M., & Hills, D. (2021). Explicit and asymptotic solutions for frictional incomplete half-plane contacts subject to general oscillatory loading in the steady-state. Journal of the Mechanics and Physics of Solids, 146, Article 104214. https://doi.org/10.1016/j.jmps.2020.104214

This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not only to ap... Read More about Explicit and asymptotic solutions for frictional incomplete half-plane contacts subject to general oscillatory loading in the steady-state.

Representation of incomplete contact problems by half-planes (2020)
Journal Article
Andresen, H., Hills, D., & Moore, M. (2021). Representation of incomplete contact problems by half-planes. European Journal of Mechanics - A/Solids, 85, Article 104138. https://doi.org/10.1016/j.euromechsol.2020.104138

for finding the optimal choices of the applied remote loads – the applied normal force, moment, shear force and remote bulk stresses – needed to solve frictional contact problems in partial-slip using half-plane theory are derived by using data from... Read More about Representation of incomplete contact problems by half-planes.

Extending the Mossakovskii method to contacts supporting a moment (2020)
Journal Article
Moore, M. R., & Hills, D. A. (2020). Extending the Mossakovskii method to contacts supporting a moment. Journal of the Mechanics and Physics of Solids, 141, Article 103989. https://doi.org/10.1016/j.jmps.2020.103989

In this article, we extend the Mossakovskii approach to half-plane contacts supporting a moment. Since the method relies on approximating the punch geometry by a series of flat punches, we choose the load path in (P, M)-space that fixes the body tilt... Read More about Extending the Mossakovskii method to contacts supporting a moment.

The steady state partial slip problem for half plane contacts subject to a constant normal load using glide dislocations (2019)
Journal Article
Andresen, H., Hills, D., & Moore, M. (2020). The steady state partial slip problem for half plane contacts subject to a constant normal load using glide dislocations. European Journal of Mechanics - A/Solids, 79, Article 103868. https://doi.org/10.1016/j.euromechsol.2019.103868

A new solution for general half-plane contact problems subject to a constant normal load together with alternating shear loads and tension in the steady state is presented. The method uses a formulation where a displacement correction is made to the... Read More about The steady state partial slip problem for half plane contacts subject to a constant normal load using glide dislocations.

Early-time jet formation in liquid–liquid impact problems: theory and simulations (2018)
Journal Article
Cimpeanu, R., & Moore, M. R. (2018). Early-time jet formation in liquid–liquid impact problems: theory and simulations. Journal of Fluid Mechanics, 856, 764-796. https://doi.org/10.1017/jfm.2018.704

We perform a thorough qualitative and quantitative comparison of theoretical predictions and direct numerical simulations for the two-dimensional, vertical impact of two droplets of the same fluid. In particular, we show that the theoretical predicti... Read More about Early-time jet formation in liquid–liquid impact problems: theory and simulations.

Methods to solve half-plane partial slip contact problems (2018)
Journal Article
Hills, D., Ramesh, R., Barber, J., & Moore, M. (2018). Methods to solve half-plane partial slip contact problems. International Journal of Solids and Structures, 155, 155-159. https://doi.org/10.1016/j.ijsolstr.2018.07.019

There exists a family of methods for finding the extent of partial slip in contact problems between elastically similar bodies, capable of idealisation by half-planes. Closed form solutions are given to problems subject to a constant normal load and... Read More about Methods to solve half-plane partial slip contact problems.

Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension (2018)
Journal Article
Moore, M., Ramesh, R., Hills, D., & Barber, J. (2018). Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension. Journal of the Mechanics and Physics of Solids, 118, 245-253. https://doi.org/10.1016/j.jmps.2018.05.017

This article provides a new form of solution to half-plane contact problems in partial slip where a normal load has been applied, held constant and is subsequently loaded with both a shear force and differential bulk tension. It uses a formulation wh... Read More about Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension.

On the deflection of a liquid jet by an air-cushioning layer (2018)
Journal Article
Moore, M. R., Whiteley, J. P., & Oliver, J. M. (2018). On the deflection of a liquid jet by an air-cushioning layer. Journal of Fluid Mechanics, 846, 711-751. https://doi.org/10.1017/jfm.2018.310

A hierarchy of models is formulated for the deflection of a thin two-dimensional liquid jet as it passes over a thin air-cushioning layer above a rigid flat impermeable substrate. We perform a systematic derivation of the leading-order equations of m... Read More about On the deflection of a liquid jet by an air-cushioning layer.

Solution of half-plane contact problems by distributing climb dislocations (2018)
Journal Article
Moore, M., & Hills, D. (2018). Solution of half-plane contact problems by distributing climb dislocations. International Journal of Solids and Structures, 147, 61-66. https://doi.org/10.1016/j.ijsolstr.2018.04.017

We derive a novel method for addressing half-plane contact problems by using distributions of climb dislocations over the contact patch to balance the relative overlapping profile of the contacting bodies. Using this technique, we are able to forgo i... Read More about Solution of half-plane contact problems by distributing climb dislocations.

Ice formation within a thin film flowing over a flat plate (2017)
Journal Article
Moore, M. R., Mughal, M. S., & Papageorgiou, D. T. (2017). Ice formation within a thin film flowing over a flat plate. Journal of Fluid Mechanics, 817, 455-489. https://doi.org/10.1017/jfm.2017.100

We present a model for ice formation in a thin, viscous liquid film driven by a Blasius boundary layer after heating is switched off along part of the flat plate. The flow is assumed to initially be in the Nelson et al. (J. Fluid Mech., vol. 284, 199... Read More about Ice formation within a thin film flowing over a flat plate.

On air cushioning in axisymmetric impacts (2014)
Journal Article
Moore, M., & Oliver, J. (2014). On air cushioning in axisymmetric impacts. IMA Journal of Applied Mathematics, 79(4), 661-680. https://doi.org/10.1093/imamat/hxu026

This paper extends the work of Moore et al. (2013, Air-cushioning in impact problems. IMA J. Appl. Math., 78, 818–838) by using a displacement potential formulation to analyse the post-impact effect of an air-cushioning layer on the normal impact of... Read More about On air cushioning in axisymmetric impacts.

Capillary and viscous perturbations to Helmholtz flows (2014)
Journal Article
Moore, M., Ockendon, H., Ockendon, J., & Oliver, J. (2014). Capillary and viscous perturbations to Helmholtz flows. Journal of Fluid Mechanics, 742, Article R1. https://doi.org/10.1017/jfm.2014.39

Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p. 264506) relating to droplet impact, this paper presents an analysis of the perturbations to the free surface caused by small surface tension and viscosity in ste... Read More about Capillary and viscous perturbations to Helmholtz flows.

Air-cushioning in impact problems (2013)
Journal Article
Moore, M. R., Ockendon, J. R., & Oliver, J. M. (2013). Air-cushioning in impact problems. IMA Journal of Applied Mathematics, 78(4), 818-838. https://doi.org/10.1093/imamat/hxt026

This paper concerns the displacement potential formulation of the post-impact influence of an air-cushioning layer on the 2D impact of a liquid half-space by a rigid body. The liquid and air are both ideal and incompressible and attention is focussed... Read More about Air-cushioning in impact problems.

A note on oblique water entry (2012)
Journal Article
Moore, M., Howison, S., Ockendon, J., & Oliver, J. (2013). A note on oblique water entry. Journal of engineering mathematics, 81(1), 67-74. https://doi.org/10.1007/s10665-012-9570-0

A minor error in Howison et al. (J. Eng. Math. 48:321–337, 2004) obscured the fact that the points at which the free surface turns over in the solution of the Wagner model for the oblique impact of a two-dimensional body are directly related to the t... Read More about A note on oblique water entry.

Three-dimensional oblique water-entry problems at small deadrise angles (2012)
Journal Article
Moore, M., Howison, S., Ockendon, J., & Oliver, J. (2012). Three-dimensional oblique water-entry problems at small deadrise angles. Journal of Fluid Mechanics, 711, 259-280. https://doi.org/10.1017/jfm.2012.391

This paper extends Wagner theory for the ideal, incompressible normal impact of rigid bodies that are nearly parallel to the surface of a liquid half-space. The impactors considered are three-dimensional and have an oblique impact velocity. A formula... Read More about Three-dimensional oblique water-entry problems at small deadrise angles.