Author
Brian R. Duffy
Other affiliations: University of Cambridge, University of Bristol, University of Liverpool
Bio: Brian R. Duffy is an academic researcher from University of Strathclyde. The author has contributed to research in topics: Newtonian fluid & Free surface. The author has an hindex of 27, co-authored 131 publications receiving 3851 citations. Previous affiliations of Brian R. Duffy include University of Cambridge & University of Bristol.
Topics: Newtonian fluid, Free surface, Cylinder, Shear stress, Liquid crystal
Papers published on a yearly basis
Papers
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TL;DR: In this article, the tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described, and a Mathematica package ATFM is presented to deal with the tedious algebra and outputs directly the required solutions.
790 citations
TL;DR: In this paper, the authors report the results of physical experiments that demonstrate the strong influence of the thermal conductivity of the substrate on the evaporation of a pinned droplet and show that this behaviour can be captured by a mathematical model including the variation of the saturation concentration with temperature, and hence coupling the problems for the vapour concentration in the atmosphere and the temperature in the liquid and the substrate.
Abstract: We report the results of physical experiments that demonstrate the strong influence of the thermal conductivity of the substrate on the evaporation of a pinned droplet. We show that this behaviour can be captured by a mathematical model including the variation of the saturation concentration with temperature, and hence coupling the problems for the vapour concentration in the atmosphere and the temperature in the liquid and the substrate. Furthermore, we show that including two ad hoc improvements to the model, namely a Newton's law of cooling on the unwetted surface of the substrate and the buoyancy of water vapour in the atmosphere, give excellent quantitative agreement for all of the combinations of liquid and substrate considered.
281 citations
TL;DR: In this paper, an explicit travelling solitary wave solution to a compound KdV-Burgers equation is obtained by using an automated method. And a two-dimensional generalization is discussed.
278 citations
TL;DR: In this paper, the sn-and cn-function methods for finding nonsingular periodic-wave solutions to nonlinear evolution equations are described in a form suitable for automation, where sn and cn are the elliptic Jacobi snoidal andcnoidal functions, respectively.
256 citations
TL;DR: In this article, the lifetime of a droplet on a solid substrate evaporating in a'stick-slide' mode is described and the unexpectedly subtle relationship between the life cycle of a single droplet and the lifetimes of initially identical droplets in the extreme modes (namely the constant contact radius and constant contact angle modes) is described.
Abstract: The complete description of the lifetime of a droplet on a solid substrate evaporating in a 'stick–slide' mode is obtained. The unexpectedly subtle relationship between the lifetime of such a droplet and the lifetimes of initially identical droplets evaporating in the extreme modes (namely the constant contact radius and constant contact angle modes) is described and summarised in an appropriate master diagram. In particular, it is shown that the lifetime of a droplet is not, in general, constrained by the lifetimes of the extreme modes.
190 citations
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TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.
3,015 citations
TL;DR: In this article, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid is examined, while the hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film.
Abstract: Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.
2,501 citations
TL;DR: In this article, an extended tanh-function method is proposed for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way, and the key idea of this method is to take full advantage of a Riccati equation involving a parameter and use its solutions to replace the tanh function.
1,830 citations
TL;DR: The (G'/G)-expansion method is firstly proposed in this paper, where G = G(xi) satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling wave solutions involving parameters of the KdV equation, the mKdV equations, the variant Boussinesq equations and the Hirota-Satsuma equations are obtained when the parameters are taken as special values.
1,673 citations
TL;DR: In this article, a Jacobi elliptic function expansion method was proposed to construct the exact periodic solutions of nonlinear wave equations, which includes some shock wave solutions and solitary wave solutions.
1,231 citations