Existence Conditions and Formation Process of Second Type of Spiral Loop Particle Accumulation Structure (SL-2 PAS) in Half-zone Liquid Bridge

Particle accumulation structures in noncylindrical liquid bridges under microgravity conditions

“…Though this numerical approach should clearly be regarded as a simplification of reality (obviously this scheme cannot describe particle interaction when accumulation takes place), it has enjoyed a widespread use in the literature for the study of PAS ([3-5], [10], [29], [34][35][36], [43], [48]) . A justification or rationale for such a practice can be found in available experimental observations or data ( [2], [6][7][8][9], [19], [37][38][39][40][41], [44]). Indeed, experiments dealing with a variety of fluids and particle types have shown that once particles enter the attractor (the KAM torus), they can no longer leave it (inter-particle forces are not sufficiently strong to allow particles to get away from the attractor).…”

“…While some properties of these structures are inherited from the underlying flow pattern (the number of blades or 'petals' characterizing the projection of the particle circuit on a plane perpendicular to the liquid bridge axis generally reflects the so-called azimuthal wavenumber of the traveling wave, i.e. the number of sinusoidal distortions affecting the toroidal roll in the circumferential direction), other topological properties can display a varying nature, which has puzzled the investigators for years [6,8,9,18,[37][38][39].…”

“…Some studies have also demonstrated that different types of highly ordered PAS structures may co-exist in the same regions of the space of parameters [7,10,35,37] and that asymmetric variants of PAS, i.e. windmills that display an eccentricity with respect to the axis of the liquid bridge, are possible [10,43].…”

“…windmills that display an eccentricity with respect to the axis of the liquid bridge, are possible [10,43]. Such line of inquiry has progressed with the aid and support of both experimental results and numerical simulations, which have shown that the aforementioned set of influential conditions can encompass a wide range of factors such as (but not limited to) the size of particles [36], their density [7,19] or 'initial position' [10], the mono-or multi-dispersed nature of the dispersion [7], and the properties of the carrier flow (Marangoni convection) as determined by the value of the Marangoni number and the aspect ratio of the related toroidal vortex [9,37]. A similar concept also applies to the influence of the volume of liquid effectively held between the two disks supporting the liquid bridge for a fixed geometrical aspect ratio.…”

“…This case is of special interest as available results are relatively rare and sparse. Indeed, if the literature extensively described in the introduction were reconsidered under a different perspective, that is, the value of the azimuthal wavenumber, it would become evident that the majority of existing studies on PAS have been conducted considering states with m = 2 [5, 7, 10] or m = 3[2, 6,36,37,42]. The amount of information about the mode m = 1, the related multiplicity of solutions and relation with the basin of attraction is relatively limited ([19]).…”