Symmetry breaking phenomena in thermovibrationally driven particle accumulation structures

Abstract

Following the recent discovery of new three-dimensional particle attractors driven by joint (fluid) thermovibrational and (particle) inertial effects in closed cavities with various shapes and symmetries (Phys. Fluids, 26(9), 093301, 2014 and Phys. Fluids, 31(7), 073303, 2019), the present analysis continues this line of inquiry by probing influential factors hitherto not considered; among them, the role of the steady component of thermovibrational convection, i.e. the time-averaged velocity field that is developed by the fluid due to the non-linear nature of the overarching balance equations. It is shown how this apparently innocuous problem opens up a vast parameter space, which includes several variables, comprising (but not limited to) the frequency of vibrations, the socalled 'Gershuni number', the size of particles (Stokes number) and their relative density with respect to the surrounding fluid (density ratio). A variety of new particle structures (2D and 3D) are uncovered and a complete analysis of their morphology is presented. The results reveal an increase in the multiplicity of solutions brought in by the counter-intuitive triadic relationship among particle inertial effects and the instantaneous and time-averaged thermovibrational phenomena. Finally, a universal formula is provided that is able to predict correctly the time required for the formation of all the observed structures.

The Zoo of Modes of Convection in Liquids Vibrated along the Direction of the Temperature Gradient

“…However, before starting to deal with thermal effects, we wish to remark that an extra layer of validation (with respect to that illustrated in Section 4) has been implemented comparing the results obtained here for the new cases (using OpenFOAM) with those provided by the same code used by Lappa [25] and Lappa and Burel [29] (see Figure 7). Both OpenFOAM and this code pertain to the same class of pressure-velocity methods discussed before.…”

“…Both OpenFOAM and this code pertain to the same class of pressure-velocity methods discussed before. However, while OpenFOAM is based on an implicit approach (for what concerns the time integration) and on a collocated distribution of unknowns, the computational platform used by Lappa [25] and Lappa and Burel [29] relies on an explicit approach and a 'staggered' arrangement of variables, respectively. It can be seen that despite the differences highlighted above, the shape and periodicity of the signals produced by both codes are in agreement (the discrepancy in signal amplitude can be expected as the exact location of the probes and the positive direction of the axes of the reference Cartesian system differ from solver to solver).…”

“…In addition to the acceleration amplitude, the imposed ∆T, and the aforementioned angle Θ, an additional degree of freedom influencing the dynamics is represented by the 'frequency' of vibrations. Nevertheless, only a limited number of studies are available in the literature where this variant of buoyancy flow was considered (Monti et al [8]; Alexander [9]; Alexander et al [10,11]; Feonychev and Dolgikh [12]; Gershuni and Lyubimov [13]; Monti et al [14]; Naumann [15]; Mialdun et al [16]; Melnikov et al [17]; Lyubimova et al [18]; Bouarab et al [19]; Shevtsova et al [20,21]; Maryshev et al [22]; Vorobev and Lyubimova [23]; Lappa, [24][25][26][27][28]; Lappa and Burel [29]). Still fewer articles have been devoted to the case where vibrations and temperature gradient are parallel.…”

Competition of overstability and stabilizing effects in viscoelastic thermovibrational flow

“…Unlike standard flows of thermogravitational nature (which can be found in a plethora of natural and industrial terrestrial processes), this specific form of fluid motion is extremely relevant to the area of space research; indeed, interest in it has sharply increased over recent years as a result of the advent of new orbiting platforms, which have made relatively long microgravity times available, and new technologies based on standard and complex fluids possible (see, e.g., [39][40][41][42][43]).…”

Three-dimensional simulation of clouds of multi-disperse evaporating saliva droplets in a train cabin

“…Accordingly, each droplet is tracked individually throughout the computational domain. Although this approach may look less convenient than other methods where all coexisting phases are dealt with in the framework of a single Eulerian treatment (typically based on the introduction of a volume of fraction variable or similar concepts, see, e.g., Capobianchi et al 48 and Lappa 49 ), the hybrid Eulerian–Lagrangian has distinct advantages, which make it particularly suitable (see, e.g., Capobianchi and Lappa; 50 Lappa and Burel; 51 and Lappa 52 ) for the analysis of the problems like that being addressed in the present work. For each droplet, in particular, a set of 3 differential equations are solved, which describe the evolution of its position (and velocity), mass, and temperature, respectively.…”