On the relationship between solid particle attractors and thermal inhomogeneities in vibrationally driven fluid-particle systems

The present analysis extends earlier authors' work [Crewdson et al., "Two-dimensional vibrationally-driven solid particle structures in non-uniformly heated fluid containers," Chaos 32, 103119 (2022); M. Lappa, "Characterization of two-way coupled thermovibrationally driven particle attractee," Phys. Fluids 34(5), 053109 (2022); M. Lappa and T. Burel, "Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures," ibid.32(5), 053314 (2020); and M. Lappa, "The patterning behavior and accumulation of spherical particles in a vibrated non-isothermal liquid," ibid.26(9), 093301 (2014)] on the existence of solid particle attractee in thermovibrational flow in order to identify new physical principles and enable increased control over the ability of particles to target desired locations into the host fluid. The causality between the thermal boundary conditions and the multiplicity and morphology of emerging particle structures is discussed, and new fundamental topological concepts are harnessed through the combination of two-dimensional and three-dimensional simulations. It is shown that the threefold relationship among the inclination of vibrations, the multi-directional nature of the imposed temperature gradient, and the dimensionality of the system itself can open up new pathways for additional classes of attractors. These can manifest themselves as compact particle structures or completely disjoint sets, apparently behaving as they were driven by different clustering mechanisms (coexisting in the physical space, but differing in terms of characteristic size, shape, and position). A variety of new solutions are presented for a geometry as simple as a cubic enclosure in the presence of localized spots of temperature on otherwise uniformly heated or cooled walls. In order to filter out possible asymmetries due to fluid-dynamic instabilities induced by the back influence of the solid mass on the fluid flow, the analysis is conducted under the constraint of one-way coupled phases.