Abstract : Interfacial flows arise in numerous natural and technological applications spanning a wide range of length scales from lab-on-a-chip systems to planetary-scale flows. From a purely scientific perspective, these flows pose fundamental theoretical, computational, and experimental challenges to explain complex phenomena including the formation of coherent structures and wave-breaking, as well as phase and topological transitions. Advances in understanding have opened the way for new schemes that allow for precision optimisation and control. This minisymposium will bring together an array of cross-disciplinary specialists, working at the cutting edge of the field, to share their expertise and to exchange ideas.
Organizer(s) : Mark Blyth, Anna Kalogirou, Alexander Wray
[02292] Interfacial flows and their modelling and control
Format : Online Talk on Zoom
Author(s) :
Alexander Wray (University of Strathclyde)
Radu Cimpeanu (University of Warwick)
Susana Gomes (University of Warwick)
Abstract : Interfacial flows are ubiquitous in nature and industry, and modelling, understanding and controlling them has applications everywhere from carbon sequestration to medical diagnostics. As an introduction to this session, we provide an overview of the topic area, particularly with regards to the state of the art and relevant applications. We also discuss our recent work on controlling the full Navier-Stokes equations using reduced-order models as an example of tying together many of these research strands.
[05417] New perspectives on continuous film flow over non-planar substrate: a family affair
Format : Talk at Waseda University
Author(s) :
Markus Scholle (Heilbronn University )
Philip H. Gaskell (Durham University)
Abstract : Film flow on curved substrate is investigated theoretically for: (i) continuously-fed, full coverage; (ii) partial coverage following deposition of a fixed liquid volume; (iii) rivulet formation. Using a novel variational formulation uncovers the presence of an interrelated family of flows for 3D axisymmetric geometries and related 2D counterparts. Analytic solutions for local film thickness and the internal flow are obtained, together with rigorous identification of associated timescales, via asymptotic analysis combined with the long-wave approximation.
[02788] Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel
Format : Talk at Waseda University
Author(s) :
Anna Kalogirou (University of Nottingham)
Mark Blyth (University of East Anglia)
Abstract : The Rayleigh-Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications, revealing a number of interfacial phenomena including finger-like protrusions, coalescence, saturated travelling waves, and near-segregation of the two fluids. The finer structure of the interface is exposed through asymptotic analysis and is compared to numerical results of the lubrication model as well as direct numerical simulations, displaying an excellent agreement between the three in terms of interfacial structure, wave speed and film thicknesses.
[04110] Neural network methods for solving interface problems
Format : Talk at Waseda University
Author(s) :
Te-Sheng Lin (National Yang Ming Chiao Tung University)
Ming-Chih Lai (National Yang Ming Chiao Tung University, Taiwan)
Wei-Fan Hu (National Central University)
Yu-Hau Tseng (National University of Kaohsiung)
Abstract : Neural networks have emerged as powerful tools for numerically solving partial differential equations. In this talk, we will discuss our recent work using neural network approaches to elliptic interface problems, and possible extensions to deal with models arising from interfacial phenomena. Specifically, we will introduce a structure enforcement layer in the network to enforce the inherent properties of the solutions to given problems, such as discontinuity or periodicity. The structure enforcement layer offers a new approach to solving such problems compared to traditional neural networks, which may struggle to represent discontinuous functions and may not have built-in periodicity.
[05355] On the transition to dripping of an inverted liquid film
Format : Talk at Waseda University
Author(s) :
Mark Blyth (University of East Anglia)
Dmitri Tseluiko (Loughborough)
Te-Sheng Lin (National Yang Ming Chiao Tung University)
Abstract : We discuss the transition to dripping in the gravity-driven motion of a liquid film under an inclined plate. Attention is focused on calculating travelling-wave solutions, for fixed fluid volume and fixed flow rate, using model lubrication equations and the full Stokes equations, and tracking the travelling-wave solution branch as the inclination angle of the plate is increased. Where the branch reaches a turning point we posit that the onset to dripping occurs.
[03447] Influence of an elastic sheet on impact on a liquid surface
Format : Talk at Waseda University
Author(s) :
Doireann O'Kiely (MACSI, University of Limerick)
Finn Box (University of Manchester)
Ousmane Kodio (MIT)
Dominic Vella (University of Oxford)
Abstract : Impact at a liquid-air interface changes when an elastic sheet floats on the liquid surface. A ripple propagates out from the point of impact, but has a wavefront $r_m \sim t^{1/2}$ rather than the $r_m \sim t^{2/3}$ typical of capillary waves. We discuss the behaviour of the ``elastocapillary ripple’’, and reduce this new impact problem to a one-parameter similarity problem which interpolates between the limits of a point impactor and Wagner theory.
[03420] Spin Coating on a Non-Axisymmetric Curved Substrate
Format : Talk at Waseda University
Author(s) :
Ross Geoffrey Shepherd (University of Cambridge)
Edouard Boujo (Ecole Polytechnique Federale de Lausanne)
Mathieu Sellier (University of Canterbury)
Abstract : Spin coating is used to apply functional coatings to flat substrates in the manufacturing of a range of electronic and optical components. Here, we develop a generalised model for the flow of a spin-coated film over an arbitrary substrate geometry, incorporating gravitational, surface tension, centrifugal, and Coriolis forces. In particular, we demonstrate the effects of the Coriolis force on the formation of fingering instabilities and the flow during the early stages of spin coating.
[05432] Evaporation and the coffee-ring effect for non-circular droplets
Format : Online Talk on Zoom
Author(s) :
Madeleine Moore (University of Hull)
Alexander Wray (University of Strathclyde)
Abstract : Diffusion-limited evaporation of liquid droplets is commonplace in industrial applications such as microscale patterning and Q/OLED production. However, beyond simple geometries, there are few analytical solutions. Here, we derive asymptotic results for the evaporative flux of a weakly non-circular droplet and demonstrate how these may be used to find the ‘coffee ring’ for large droplets, with excellent agreement to numerical simulations. Then, we show how the mathematical framework may be extended to polygonal drops.
