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Autumn 2024
Seminars take place online on Tuesdays at 3.00pm on Zoom via the link https://ucl.zoom.us/j/99614222402. Many of the seminars will be 'hybrid' (i.e. in person +zoom). If you require any more information on the Applied seminars please contact Prof Jean-Marc Vanden-Broeck (e-mail: j.vanden-broeck AT ucl.ac.uk or tel: 020-7679-2835) or Prof Ilia Kamotski (e-mail: i.kamotski AT ucl.ac.uk or tel: 020-7679-3937).
Tuesday 8 October 2024 in Engineering Front Building, Executive Suite 103
Speaker: Gunnar Peng (UCL)
Title: Singularity and instability in drop electrohydrodynamics
Abstract:
Electrical manipulation of microscale flows has applications in e.g. printing, coating, microfabrication and microfluidics. Due to the nonlinear coupling between electrical and flow fields, even the simple case of a drop in an electric field can exhibit complex phenomena such as streaming from the poles or equator, and symmetry-breaking Quincke rotation or equatorial vortices. We consider a two-dimensional circular drop, neglecting deformation, and show that the Taylor-Melcher leaky-dielectric model reduces to a nonlinear integro-differential equation for the time evolution of the surface-charge density, which we simulate using a finite-difference scheme and analyse using asymptotic methods. We identify and charactarise a steady-state singularity in which the surface-charge density blows up as x^(-1/3), a finite-time singularity in which it blows up as (t0-t)^(-1/2), and a symmetry-breaking instability to Quincke rotation which can be subcritical, resulting in multi-stability.
Tuesday 15 October 2024 in Engineering Front Building, Executive Suite 103
Speaker: Dmitri Tseluiko (Loughborough)
Title: Singularity formation in inverted film flow and transition to dripping
Abstract:
The gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Travelling-wave solutions are analysed assuming either a fixed fluid volume or a fixed flow rate for two thin-film models with either linearised or full curvature (the LCM and FCM, respectively) and the full equations of Stokes flow. Of particular interest is the breakdown of travelling-wave solutions as the plate inclination angle is increased, which is associated with the onset of dripping and which is analysed by asymptotic analysis and by constructing bifurcation diagrams for a wide range of parameters. It is found that the thin-film models either provide an accurate prediction for dripping onset or else supply an upper bound on the critical inclination angle [1]. The predictions from the asymptotic analysis and bifurcation diagrams are corroborated by direct numerical simulations for the Navier-Stokes equations using the open-source volume-of-fluid Gerris software.