Models for thin viscous sheets

Leading-order equations governing the dynamics of a two-dimensional thin viscous sheet are derived. The inclusion of inertia effects is found to result in an ill-posed model when the sheet is compressed, and the resulting paradox is resolved by rescaling the equations over new length- and timescales which depend on the Reynolds number of the flow and the aspect ratio of the sheet. Physically this implies a dominant lengthscale for transverse displacements during viscous buckling. The theory is generalised to give new models for fully three-dimensional sheets

The instability of a viscous sheet floating on an air cushion

The dynamics of a thin sheet of viscous liquid levitating on an air cushion is studied. Experimentally, it is observed that, after an initial settling stage, a local disturbance grows, eventually leading to the sheet blowing up like a viscous balloon. We derive a dynamical model for the levitating sheet and propose a mechanism for the onset of the instability. This instability is driven by the local drainage of the sheet due to a growing disturbance on its lower surface and is moderated by surface tension, the bending stiffness of the sheet and advection in the air layer. The balance between these effects determines the most unstable wavelength and this is illustrated by some numerical simulations

Time–geography, gentlemen, please: chronotopes of publand in Patrick Hamilton's London trilogy

This paper considers the time and the place of drinking in modern British life, as represented in Patrick Hamilton’s trilogy of novels set in the publand of London’s West End in the interwar years, and through Mikhail Bakhtin’s concept of the chronotope and with critical nods to Hagerstrand’s timegeography corpus. The chronotopes of pubs and their neighbourhoods, which we term ‘publand’, are discussed initially in their novelistic presentation in Twenty Thousand Streets Under the Sky (1935), and then in relation to the ‘character zones’ of the novels’ principal protagonists. The key themes, defined in the paper are the asynchronicity of personal and social relations, the dialogic construction of heterochronicity, and the presentation of a prosaic chronotope. Though the paper is a contribution to literary geography, we aim to contribute to the cultural geographic understanding of the timespace rhythms and routines of everyday leisure drinking, making claims for the wider significance of chronotopic analysis.This is the author accepted manuscript. The final version is available via http://dx.doi.org/10.1080/14649365.2015.104005

Boundary conditions for free surface inlet and outlet\ud problems

We investigate and compare the boundary conditions that are to be applied to free surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well-known that the flux scales with Ca2/3, but this classical result is nonuniform as the contact angle approaches . By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed

What’s Cool About Hot Stars? Cataclysmic Variables in the Mid-Infrared

We review recent results from mid-infrared observations of cataclysmic variables with the Spitzer Space Telescope. In general, these observations have revealed mid-infrared excesses, above the level expected from the stellar and accretion components, in numerous systems. This excess can be modeled as originating from circumstellar and/or circumbinary dust. We present an overview of spectral energy distributions spanning the ultraviolet to the mid-infrared, as well as mid-infrared light curves, of disk-accreting and magnetic cataclysmic variables. Physically realistic models constructed to reproduce these data indicate that the mid-infrared luminosity of many cataclysmic variables is dominated by emission from warm (T < 2000 K) dust. The presence and characteristics of dust in cataclysmic variables has potentially important implications for the secular evolution scenario for interacting binary stars

A model for the screen printing of Newtonian fluids

A preliminary investigation into aspects of the off-contact screen-printing process is presented. A mathematical model for the printing of a thin film of Newtonian fluid is proposed, in which the screen is modelled as a permeable membrane, and the entire region above and below the screen is flooded. By drawing upon widely used industrial circuit printing practices, the distinguished limit of greatest interest to this industry is identified. Numerical and asymptotic solutions of this distinguished limit are presented that reproduce many of the features observed in industrial screen-printing

Mathematical modelling of elastoplasticity at high stress

This paper describes a simple mathematical model for one-dimensional elastoplastic wave propagation in a metal in the regime where the applied stress greatly exceeds the yield stress. Attention is focussed on the increasing ductility that occurs in the over-driven limit when the plastic wave speed approaches the elastic wave speed. Our model predicts that a plastic compression wave is unable to travel faster than the elastic wave speed, and instead splits into a compressive elastoplastic shock followed by a plastic expansion wave