Topology of hydrothermal waves in liquid bridges and dissipative structures of transported particles

Abstract

High-resolution three-dimensional numerical simulations are carried out for hydrothermal waves in a thermocapillary liquid bridge with Prandtl number Pr=4 and length-to-radius aspect ratio Γ=0.66. The flow topology is analyzed using Poincaré sections in a frame of reference co-rotating with the phase velocity of the wave. We find regions of regular and chaotic motion. The regular regions are shown to be of key importance for dissipative structures of transported particles. Suspended particles which are passively advected in the bulk, but experience dissipation in a thin layer below the free surface, can rapidly form dissipative structures, also called particle accumulation structures. The shape and the formation time of the particulate structures are determined by the location of the invariant tori of the flow field with respect to the sub-surface layer in which the dissipation of the particle motion acts. The results from a hard-wall particle-free-surface interaction model are in good agreement with experimental observations.

Secondary instability induced by thermocapillary effect in half-zone liquid bridge of high Prandtl number fluid

“…Red and sky-blue surfaces correspond to the isosurfaces ofT = ±0.06, respectively. Under this condition, the flow after the primary instability exhibits a rotating flow with m 0 = 3 as indicated in the previous works (Mukin and Kuhlmann, 2013;Muldoon and Kuhlmann, 2013;Romanò and Kuhlmann, 2018).That is, there exist three sets of pairs of positive and negative temperature deviations in three-fold rotational symmetry. The number of the sets corresponds to the fundamental modal number m 0 , thus m 0 = 3 in this case.…”

Particle–boundary interaction in a shear-driven cavity flow

“…After an inelastic contact the particle is assumed to slide along the free surface, being pushed toward it by the outward-normal velocity component of the flow at the particle centroid, up to the release point at which the surface-outward-normal velocity component of the flow turns negative upon which the particle detaches from the free surface. Introducing the interaction length Δ, Mukin and Kuhlmann [17] pointed out that the minimum distance of the centroid of the particle from the free surface is necessarily larger than the particle radius and the lubrication gap must be included in Δ. Such PSI model is also justified by the observation that the true particle trajectory is nearly rectilinear and parallel to the stress boundary over quite some distance for small and heavy particles.…”

“…4 the results of the numerical calculations are presented, focusing on the role of the particle-boundary interaction. Based on the comparison of the fully resolved simulations with results obtained by one-way coupling supplemented by the particle-surface interaction (PSI) model of Hofmann and Kuhlmann [16] (see also [7,17]), an improved particle-surface interaction model is suggested which closely approximates the particle-motion attractors obtained by the fully resolved simulations. The influence of the particle radius and the particle-to-fluid density ratio on the particle-boundary interaction is investigated for a constant shear Reynolds number Re = 1000.…”

Interaction of a finite‐size particle with the moving lid of a cavity

“…Even for small particles with Stokes numbers as small as 10 −5 the influence of the moving boundary on the trajectories of nearby particles can lead to a significant accumulative effect. As shown by [1][2][3] this can result in rapid particle accumulation for certain free-surface flows.…”