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Autumn 2024

Seminars Ìýtake place online onÌýTuesdays at 3.00pm on Zoom via the linkÌý. ManyÌýof 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 OctoberÌý2024 in TBC

Speaker: Gunnar PengÌý(°×С½ãÂÛ̳)

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.