Flow of a thin liquid-metal film in a toroidal magnetic field

Abstract

We investigate the gravity-driven flow of a thin film of liquid metal on a conducting conical substrate in the presence of a strong toroidal magnetic field (transverse to the flow and parallel to the substrate). We solve the leading-order governing equations in a physically relevant asymptotic limit to find the free-surface profile. We find that the leading-order fluid flow rate is a non-monotonic bounded function of the film height, and this can lead to singularities in the free-surface profile. We perform a detailed stability analysis and identify values of the relevant geometric, hydrodynamic and magnetic parameters such that the flow is stable.

Magnetohydrodynamic effects on liquid metal film flowing along an inclined plate relating to plasma facing components

“…It was found that, under the influences of a transverse magnetic field, the free surface waves transit to twodimensional waves; specifically, the surface fluctuation along magnetic field lines are strongly suppressed, leaving the surface waves to propagate in the streamwise direction [45][46][47]. Very recently, Lunz et al [48] modeled the flow of a thin liquid metal film, driven by gravity down a conical substrate in the presence of a strong toroidal magnetic field, and identified values for the relevant situations when the flow is stable, which is important guidance in terms of the design of liquid metal PFCs.…”

Electromagnetically driven flow in unsupported electrolyte layers: lubrication theory and linear stability of annular flow

“…Electromagnetically driven flows in shallow layers and channels of electrically conducting fluids in the presence of deformable interfaces have attracted much attention due to their importance in plasma physics (Fiflis et al 2016;Lunz & Howell 2019) and various microfluidic applications including contactless manipulation of flow in magnetohydrodynamic (MHD) networks (Bau et al 2003), liquid channels embedded into carrier fluids (Dunne et al 2020), droplet microfluidics (Shang, Cheng & Zhao 2017) and electromagnetic stirring (Bau, Zhong & Yi 2001;Qian & Bau 2005).…”

“…The theoretical description and modelling of electromagnetically driven flows in supported films with a free interface are now well developed (Morley & Abdou 1995;Morley & Roberts 1996;Morley & Abdou 1997;Gao, Morley & Dhir 2002;Morley, Smolentsev & Gao 2002;Miloshevsky & Hassanein 2010;Giannakis, Fischer & Rosner 2009a;Giannakis, Rosner & Fischer 2009b;Lunz & Howell 2019) and continue to attract attention mainly due to applications in plasma flows and tokamaks. In the absence of the Lorentz force, the pure hydrodynamic description of the flow in unsupported liquid films was initiated in Prévost & Gallez (1986), Sharma & Ruckenstein (1988) and later received a huge boost because of its relevance to nonlinear film rupture and two-dimensional turbulence problems (Couder, Chomaz & Rabaud 1989;Gharib & Derango 1989;Chomaz & Cathalau 1990;Erneux & Davis 1993;Sharma et al 1995;Van De Fliert, Howell & Ockenden 1995;Wu et al 1995) as reviewed in Kellay & Goldburg (2002) and Oron, Davis & Bankoff (1997).…”