Patterning behavior of gravitationally modulated supercritical Marangoni flow in liquid layers

The objective of the present analysis is the investigation of hybrid convection induced by the joint influence of imposed vibrations (g-jitters) of desired amplitude and frequency and surface-tension-induced forces in a nonisothermal liquid layer. This study may be regarded as the natural extension of an earlier work [V. M. Shevtsova, I. Nepomnyashchy, and J. C. Legros, Phys. Rev. E 67, 066308 (2003)10.1103/PhysRevE.67.066308], where the focus was on convection driven by interacting thermocapillarity and steady gravity. As in that work, conditions are considered for which the unperturbed (vibrationless) Marangoni flow would be characterized by the emergence and propagation of a classical hydrothermal wave, namely, a supercritical thermofluidynamic disturbance propagating continuously in the upstream direction. A number of numerical results are analyzed and discussed. Regimes of quasistationary rolls, standing waves, traveling waves, and modulated (pulsotraveling) disturbances are identified in the considered space of parameters. Most interestingly, it is observed that traveling waves can reverse their direction of propagation in some specific regions of the phase space

Hydrothermal waves in two-dimensional liquid layers with sudden changes in the available cross-section

Purpose – Hydrothermal waves represent the preferred mode of instability of the so-called Marangoni flow for a wide range of liquids and conditions. The related features in classical rectangular containers have attracted much attention over recent years owing to the relevance of these oscillatory modes to several techniques used for the production of single crystals of seminconductor or oxide materials. Control or a proper knowledge of convective instabilities in these systems is an essential topic from a material/product properties saving standpoint. The purpose of this study is to improve our understanding of these phenomena in less ordinary circumstances. Design/methodology/approach – This short paper reports on a numerical model developed to inquire specifically about the role played by sudden changes in the available cross-section of the shallow cavity hosting the liquid. Although accounting for the spanwise dimension would be necessary to derive quantitative results, our approach is based on the assumption of two-dimensional flow, which, for high-Pr fluids, is believed to retain the essence of the involved physical processes. Findings – Results are presented for the case of a fluid with Pr=15 filling an open container with a single backward-facing or forward-facing step on the bottom wall or with an obstruction located in the center. It is shown that the presence of steps in the considered geometry can lead to a variety of situations with significant changes in the local spectral content of the flow and even flow stabilization in certain circumstances. The role of thermal boundary conditions is assessed by considering separately adiabatic and conducting conditions for the bottom wall. Originality/value – Although a plethora of studies have been appearing over recent years motivated, completely or in part, by a quest to identify new means to mitigate these instabilities and produce accordingly single crystals of higher quality for the industry, unfortunately, most of these research works were focusing on very simple geometries. In the present paper, the causality and interdependence among all the kinematic and thermal effects mentioned above is discussed. Keywords – Marangoni flow, hydrothermal waves, Finite difference method, variable section geometries

On the nature, formation and diversity of particulate coherent structures in microgravity conditions and their relevance to materials science and problems of astrophysical interest

Different phenomena related to the spontaneous accumulation of solid particles dispersed in a fluid medium in microgravity conditions are discussed, with an emphasis on recent discoveries and potential links with the general field of astrophysical fluid-dynamics on the one hand, and with terrestrial applications in the field of materials science on the other hand. With special attention to the typical physical forces at play in such an environment, namely, surface-tension gradients, oscillatory residual gravity components, inertial disturbances and forces of an electrostatic nature, specific experimental and numerical examples are presented to provide inputs for an increased understanding of the underlying cause-and-effect relationships. Studying these systems can be seen as a matter of understanding how macroscopic scenarios arise from the cooperative behaviour of sub-parts or competing mechanisms (nonlinearities and interdependencies on various spatial and temporal scales). Through a critical assessment of the properties displayed by the resulting structures (which appear in the form of one-dimensional circuits formed by aligned particles, planar accumulation surfaces, three-dimensional compact structures resembling “quadrics”, micro-crystallites or fractal aggregates), we discuss a possible classification of the related particle attractors in the space of parameters according to the prevailing effect

Numerical study into the morphology and formation mechanisms of three dimensional particle structures in vibrated cylindrical cavities with various heating conditions

The present analysis extends the author’s earlier work (Lappa, Phys. Fluids, 26, 093301, 2014) on the properties of patterns formed by the spontaneous accumulation and ordering of solid particles in certain types of flow. It is shown that under certain conditions, when subjected to vibrations to induce natural flow, non-isothermal fluids with dispersed solid particles are characterized by intervals of solid-pattern-forming behaviour due to particle rearrangements preceded by intervals in which no recognizable structures of solid matter can be detected. The dynamics of these systems are highly nonlinear in nature. Because this new family of particle attractors is known to exhibit strong sensitivity to the “symmetry properties” of the considered vibrated system and related geometrical constraints, the present study attempts to clarify the related dynamics in a geometry with curved walls (cylindrical enclosure). In particular, by assuming vibrations always directed perpendicularly to the imposed temperature gradient, we show that the morphology, spatial extension (percentage of physical volume occupied), “separation” (spatial distance) and mechanisms responsible for the formation of the resulting particle structures change significantly according to whether the temperature gradient is parallel or perpendicular to the symmetry axis of the cylinder. This indicates that the “physics” is not invariant with respect to 90 rotations in space of the specific forcing considered (direction of the imposed temperature gradient and associated perpendicular vibrations). Additional insights into the problem are obtained by assessing separately the influence played by the time-averaged (mean) and oscillatory effects. According to the numerical results, the intriguing diversity of particle agglomerates results from the different role/importance played by (curved or straight) boundaries in constraining particles and, from the different structure and topology of the resulting macroscopic (large-scale) thermovibrational flow oscillating in time at the same acceleration frequency of the imposed vibrations

On the variety of particle accumulation structures under the effect of g-jitters

The present analysis extends the author's earlier work (Lappa, Phys. Fluids, vol. 25, 2003, 012101; Lappa, Chaos, vol. 23, 2003, 013105) on the properties of patterns formed by the spontaneous accumulation and ordering of solid particles in certain types of flow (with a toroidal structure and a travelling wave propagating in the azimuthal direction) by considering the potential impact of 'vibrations' (g-jitters) on such dynamics. It is shown that a kaleidoscope of possible variants exist whose nature and variety calls for a concerted analysis using the tools of computational fluid dynamics in synergy with dimensional arguments and existing theories on the effect of periodic accelerations on fluid systems. A possible categorization of the observed phenomena is introduced according to the type and scale of 'defects' displayed by the emerging particle aggregates with respect to unperturbed (vibration-less) conditions. It is shown that the resulting degree of 'turbulence' depends essentially on the direction (φ), amplitude (γ) and frequency (π{variant}) of the applied inertial disturbance. A range of amplitudes and frequencies exist where the formation of recognizable particle structures is prevented. A quantitative map (in the γ-π{variant}) for their occurrence is derived with the express intent of supporting the optimization of future experiments to be performed in space

On the existence and multiplicity of one-dimensional solid particle attractors in time-dependent Rayleigh-Bénard convection

For the first time evidence is provided that one-dimensional objects formed by the accumulation of tracer particles can emerge in flows of thermogravitational nature (in the region of the space of parameters, in which the so-called OS (oscillatory solution) flow of the Busse balloon represents the dominant secondary mode of convection). Such structures appear as seemingly rigid filaments, rotating without changing their shape. The most interesting (heretofore unseen) feature of such a class of physical attractors is their variety. Indeed, distinct shapes are found for a fixed value of the Rayleigh number depending on parameters accounting for particle inertia and viscous drag. The fascinating "sea" of existing potential paths, their multiplicity and tortuosity are explained according to the granularity of the loci in the physical space where conditions for phase locking between the traveling thermofluid-dynamic disturbance and the "turnover time" of particles in the basic toroidal flow are satisfied. It is shown, in particular, how the observed wealth of geometric objects and related topological features can be linked to a general overarching attractor representing an intrinsic (particle-independent) property of the base velocity field

On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions

This analysis follows and integrates the line of inquiry started in past author’s works (Phys. Fluids, 15(3): 776-789, 2003, and Phys. Fluids 16(2): 331-343, 2004) about the typical instabilities of Marangoni flow and associated hierarchy of bifurcations in laterally heated floating zones with various shapes and aspect ratios. The main motivation for re-examining this kind of problems, which so much attention have attracted over the last twenty years, is the recent discovery (Kudo, Ueno and Kawamura, (2014), in Japanese, DOI: 10.1299/transjsme.2014tep0095) of a chaotic state in region of the space of parameters where on the basis of existing theories and earlier results for the classical liquid-bridge problem with organic fluids, the flow should be relatively regular in time and with a simple structure in space. Axisymmetric computations are used to obtain the steady basic state, and then the Navier Stokes equations are solved in their complete, three-dimensional, time-dependent and non-linear formulation to investigate the evolution of azimuthal disturbances. It is shown that the “apparent” doubling or quadrupling of the azimuthal wavenumber in the equatorial plane, previously reported for the case of floating zones of liquid metals, is replaced for high-Prandtl-number liquids by the complex interaction of disturbances with distinct spatial and temporal scales. These disturbances become critical at relatively comparable values of the Marangoni number. The unexpected multiplicity of waveforms and competition of spatial modes is explained according to the increased complexity of the considered system in terms of flow topology and structure with respect to the classical half-zone configuration

Convective effects and traveling waves in transparent oxide materials processed with the floating zone technique

Zone melting (or zone refining or floating zone process, FZ) is a group of similar methods, specifically conceived for the purification of crystals, in which thermally-driven flows of both gravitational and surface-tension natures are typically produced when the considered material is processed. Since the melt never comes into contact with anything but vacuum (or inert gases), there are no contaminants that the melt may incorporate. Even though compounds with higher purity and improved quality can be obtained with this technique, a typical drawback is represented by the defects potentially induced in the crystalline structure by the unavoidable convection emerging in the fluid phase. In the present chapter, special attention is paid to a specific category of materials known as transparent oxides. A range of conditions is explored, differing in the dominant effect (buoyancy or Marangoni flow), the thermal conditions (heating being provided along the radial or axial direction) and the relative direction of gravity and applied temperature gradient. The hallmark of the entire chapter is our commitment to identify situations in which “waves” are produced and provide a systematic classification of such convective instabilities together with a description of related features based on advanced numerical simulations

Time reversibility and non deterministic behaviour in oscillatorily sheared suspensions of non-interacting particles at high Reynolds numbers

Collections of inertial particles suspended in a viscous fluid and subjected to oscillatory shear have recently attracted much attention due to their relevance to a number of industrial applications and natural phenomena. It is known that, even at very low values of the flow Reynolds number, particle-to-particle interactions can lead to complex chaotic displacements despite the reversibility of the overarching fluid-dynamics (Stokes) equations. For high-Re flows, the loss of predictability after a finite time horizon is generically ascribed to the non-linear nature of the Navier-Stokes equations. Where the sources of nonlinearity are located exactly and how they influence the motion of particles, however, has not been clarified yet. We show that assuming particle interactions to be negligible, surprisingly, at high values of the Reynolds number the major source of non-deterministic behaviour comes from effects of stationary nature in the carrier flow. We report numerical simulations showing precisely how for geometries of finite extent such stationary effects emerge as the time-averaged non-linear response of the Navier-Stokes equations to the applied oscillatory forcing. They cause small deviations of the inertial particle’s trajectory from the streamlines of the instantaneous oscillatory flow, which accumulate in time until the system behaviour becomes essentially non reversible

Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows

Evidence is provided that when the so-called phenomenon of particle accumulation structure (PAS) occurs, extended regions exist where 1/2 of the axial component of vorticity matches the angular frequency of the traveling wave produced by the instability of the Marangoni flow. Several cases are considered in which such axial component is varied by "injecting" vorticity into the system via rotation of one of its endwalls. The results show that both the resulting PAS lines and the trajectories of related solid particles undergo significant changes under the influence of imposed rotation. By analysis of such findings, a validation and a generalization/extension of the so-called "phase-locking" model are provided