Effect of the supporting disks shape on nonlinear flow dynamics in a liquid bridge

Abstract

The stability of convective flows in a non-homogeneous temperature field is affected by the shape of the container hosting the fluid. We present a nonlinear two-phase computational study of convection in a liquid bridge that develops under the action of buoyancy and Marangoni forces. The hydrothermal instability is examined for three shapes of disks supporting liquid bridge: both disks flat, the upper (hot) disk tapered, and the lower (cold) disk tapered. Steady flow is also analyzed for the case that both disks are tapered. In all the cases of instability, the flow pattern comprises, but is not limited to, a hydrothermal wave with an azimuthal wavenumber m ¼ 2. An intriguing flow pattern is observed in the case of flat disks when the nonlinear interaction between the modes m ¼ 0 and m ¼ 2 leads to quasiperiodic motion forming a torus in the phase space. The torus originates from two traveling waves (TW) with the same mode m ¼ 2 but with distinct (close) frequencies. Note that this was not observed in the one-phase model. The case with a tapered cold disk reveals an oscillatory state with a single TW wave associated with m ¼ 2 mode. In the case of a tapered hot disk, an axially symmetric TW with m ¼ 0 is observed first and, at later times, is accompanied by a TW with m ¼ 2.

Pattern selection for convective flow in a liquid bridge subjected to remote thermal action

“…Even though the gas/liquid viscosity ratio is low, the gas motion changes the temperature distribution near the interface. Thus, consideration of the two-phase problem brings numerical predictions closer to experimental observations 32,33 . Particular attention to the role of viscous shear was given in the numerical analysis by Shevtsova et al 34 considering axisymmetric flows in LB at relatively high velocities of the ambient gas flow.…”

“…The post-processing approach which has been described previously 33,37 is applied here to precisely define the properties of hydrothermal waves in a three-dimensional flow. In the supercritical region, the time-periodic solution has the form…”

“…The problem was solved using dimensional variables (x, y, z), and the variables were transformed accordingly. Numerical convergence was previously tested 33,34,37 for a similar configuration, and we take these results as a reference for validation of the code.…”

“…For instance, recent very accurate but complicated experiments in a liquid bridge with a coaxial gas flow required a shift of ∆T by 4 K to get an excellent agreement of nonlinear dynamics comparing with simulations 37 . Surely, the numerical model is ideal and does not take into account imperfections of experimental arrangement, for example, small non-flatness of supporting disks 33 . A two-dimensional axisymmetric motion equivalent to a Marangoni convection at ∆T = 0.2 K was observed in a liquid bridge experiment without obvious driving force 40 .…”

On the role of heat source location and multiplicity in topographically controlled Marangoni–Rayleigh–Bénard convection

“…Clever & Busse 1994;Li & Khayat 2005;Lappa & Boaro 2020) and the equivalent buoyancy flow in laterally heated systems (the so-called Hadley problem, Kaddeche, Henry & Ben Hadid (2003), Lappa (2005a,b), Melnikov & Shevtsova (2005), Gelfgat (2020) and references therein). A similar concept holds if variations of density are replaced with gradients of surface tension: the different orientation of the imposed temperature difference with respect to the free interface (temperature gradient perpendicular or parallel to it) gives rise to two different variants of surface-tension-driven convection, generally known as Marangoni-Bénard (MB) (Nepomnyashchy & Simanovskii 1995;Ueno, Kurosawa & Kawamura 2002;Lyubimova, Lyubimov & Parshakova 2015;Lyubimov et al 2018) and thermocapillary (or simply Marangoni) flow (Shevtsova, Nepomnyashchy & Legros 2003;Shevtsova, Melnikov & Nepomnyashchy 2009;Kuhlmann et al 2014;Lappa 2016Gaponenko et al 2021), respectively.…”