Three-dimensional solid particle self-assembly in thermovibrational flow: the case with unidirectional temperature gradient and concurrent vibrations

As a follow up to an earlier work (Phys. Fluids 34, 014108, 2022), where the main focus was on the modes of convection in a three-dimensional cubic enclosure filled with a Pr=7 liquid undergoing vibrations in a direction 'parallel' to the imposed temperature gradient, the present study considers the modes of particle clustering, which occur when solid spheres, with density ratio ξ=1.85 or 0.3 and Stokes number (St) between 0.5 and 3.5 x 10^-5, are added to the fluid. Starting from a uniform distribution of solid particles and fluid in quiescent conditions, the governing equations for the involved phases are numerically solved in their complete, time-dependent and non-linear form for a representative vibrational Rayleigh number (8.34×10⁴), angular frequency Ω=50 and non-dimensional acceleration amplitude (γ) spanning the interval 0.4x10⁷≤
γ≤3.4x10⁷. It is shown that, while for relatively high values of St and/or γ, only degenerate states are obtained, where all particles collapse on planar structures, for intermediate values of such parameters, interesting (heretofore unseen) patterns are enabled. The hallmark of these phenomena is an endless squeezing and expansion of the particle formations along the direction of the temperature gradient. As confirmed by the numerical simulations, the underlying formation mechanisms rely on the combined action of the body force acting on particles due to their different density with respect to the host fluid and the additional drag that is produced when the carrier thermovibrational flow enters a specific stage, known as "convective burst", where the magnitude of the fluid velocity increases dramatically.