Time-dependent patterns in quasivertical cylindrical binary convection

This paper reports on numerical investigations of the effect of a slight inclination a on pattern formation in a shallow vertical cylindrical cell heated from below for binary mixtures with a positive value of the Soret coefficient. By using direct numerical simulation of the three-dimensional Boussinesq equations with Soret effect in cylindrical geometry, we show that a slight inclination of the cell in the range a˜0.036rad=2° strongly influences pattern selection. The large-scale shear flow (LSSF) induced by the small tilt of gravity overcomes the squarelike arrangements observed in noninclined cylinders in the Soret regime, stratifies the fluid along the direction of inclination, and produces an enhanced separation of the two components of the mixture. The competition between shear effects and horizontal and vertical buoyancy alters significantly the dynamics observed in noninclined convection. Additional unexpected time-dependent patterns coexist with the basic LSSF. We focus on an unsual periodic state recently discovered in an experiment, the so-called superhighway convection state (SHC), in which ascending and descending regions of fluid move in opposite directions. We provide numerical confirmation that Boussinesq Navier-Stokes equations with standard boundary conditions contain the essential ingredients that allow for the existence of such a state. Also, we obtain a persistent heteroclinic structure where regular oscillations between a SHC pattern and a state of nearly stationary longitudinal rolls take place. We characterize numerically these time-dependent patterns and investigate the dynamics around the threshold of convection.Postprint (author's final draft

Pattern selection near the onset of convection in binary mixtures in cylindrical cells

We report numerical investigations of three-dimensional pattern formation of binary mixtures in a vertical cylindrical container heated from below. Negative separation ratio mixtures, for which the onset of convection occurs via a subcritical Hopf bifurcation, are considered. We focus on the dynamics in the neighbourhood of the initial oscillatory instability and analyze the spatio-temporal properties of the patterns for different values of the aspect ratio of the cell, 0.25 less than or similar to Gamma less than or similar to 11 (Gamma equivalent to R/d, where R is the radius of the cell and d its height). Despite the oscillatory nature of the primary instability, for highly constrained geometries, Gamma less than or similar to 2.5, only pure thermal stationary modes are selected after long transients. As the aspect ratio of the cell increases, for intermediate aspect ratio cells such as Gamma = 3, multistability and coexistence of stationary and time-dependent patterns is observed. In highly extended cylinders, Gamma approximate to 11, the dynamics near the onset is completely different from the pure fluid case, and a startling diversity of confined patterns is observed. Many of these patterns are consistent with experimental observations. Remarkably, though, we have obtained persistent large amplitude highly localized states not reported previously.Postprint (published version

Thermal binary mixture convection in inclined cylindrical containers

Convection in a fluid layer is affected by its orientation with respect to the gravitational field. In the present work, we investigate numerically pattern selection in a cylindrical cell heated from below and inclined against gravity. We are interested in analyzing the effect of inclination on pattern formation near the onset of convection. We will focus on thermophobic mixtures, i.e. mixtures in which the heavier component of the fluid is driven into the direction of lower temperature, where square patterns, roll structures and cross-roll regimes are expected to arise. In agreement with experimental observations, we will show that pattern formation in disklike cylinders is strongly affected even by very small inclinations.Postprint (published version

Stationary localized solutions in binary convection in slightly inclined rectangular cells

We analyze numerically the effect of a slight inclination in the lowest part of the snaking branches of convectons that are present in negative separation ratio binary mixtures in two-dimensional elongated rectangular cells. The exploration reveals the existence of novel stationary localized solutions with striking spatial features different from those of convectons. The numerical continuation of these solutions with respect to the inclination of the cell unveils the existence of even further families of localized structures that can organize in closed branches. A variety of localized solutions coexist for the same heating and inclination, depicting a highly complex scenario for solutions in the lowest part of the snaking diagrams for moderate to high heating. The different localized solutions obtained in the horizontal cell are discussed in detail.Postprint (author's final draft

Effect of small inclination on binary convection in elongated rectangular cells

We analyze the effect of a small inclination on the well-studied problem of two-dimensional binary fluid convection in a horizontally extended closed rectangular box with a negative separation ratio, heated from below. The horizontal component of gravity generates a shear flow that replaces the motionless conduction state when inclination is not present. This large-scale flow interacts with the convective currents resulting from the vertical component of gravity. For very small inclinations the primary bifurcation of this flow is a Hopf bifurcation that gives rise to chevrons and blinking states similar to those obtained with no inclination. For larger but still small inclinations this bifurcation disappears and is superseded by a fold bifurcation of the large-scale flow. The convecton branches, i.e., branches of spatially localized states consisting of counterrotating rolls, are strongly affected, with the snaking bifurcation diagram present in the noninclined system destroyed already at small inclinations. For slightly larger but still small inclinations we obtain small-amplitude localized states consisting of corotating rolls that evolve continuously when the primary large-scale flow is continued in the Rayleigh number. These localized states lie on a solution branch with very complex behavior strongly dependent on the values of the system parameters. In addition, several disconnected branches connecting solutions in the form of corotating rolls, counterrotating rolls, and mixed corotating and counterrotating states are also obtained.Postprint (published version

Localized pinning states in closed containers: homoclinic snaking without bistability

Binary mixtures with a negative separation ratio are known to exhibit time-independent spatially localized convection when heated from below. Numerical continuation of such states in a closed two-dimensional container with experimental boundary conditions and parameter values reveals the presence of a pinning region in Rayleigh number with multiple stable localized states but no bistability between the conduction state and an independent container-filling state. An explanation for this unusual behavior is offered.Postprint (published version

Travelling convectons in binary fluid convection

Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd- and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton’s law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift–Hohenberg equation by Houghton & Knobloch (Phys. Rev. E, vol. 84, 2011, art. 016204). We use the results to identify stable drifting convectons and employ direct numerical simulations to study collisions between them. The collisions are highly inelastic, and result in convectons whose length exceeds the sum of the lengths of the colliding convectons.Postprint (published version

Numerical simulation of the genesis of superhighway convection in a slightly inclined layer of a binary liquid mixture

Convection in a fluid layer is affected by its orientation with respect to the gravitational field. In the present work, we investigate numerically pattern selection in a vertical cylindrical cell heated from below for positive Soret coefficient mixtures and analyse the effect of marginal inclinations of gravity in pattern formation. The dynamics of mixtures with a positive value of the Soret coefficient without inclination has essentially been studied in laboratory experiments, and numerical simulations reduce to periodic domains. According to these studies, close to convective onset, the motion is dominated by the solute gradient, and a stationary square pattern with negligible change in heat transport is reached (Soret regime). Far from threshold, convection selects the usual roll structure observed in pure fluid convection, where a strong change in heat transport takes place. In the crossover region, a cross roll regime is observed and the competition between square and roll patterns leads to oscillations. Interestingly, positive Soret coefficient mixtures have been used in the recent experimental work of Croccolo et al. to investigate the effect of inclination of the layer on the long-term stability. At small Rayleigh numbers, the mass transfer is dominated by the induced large scale shear flow, while at larger Rayleigh numbers, it is dominated by solutal convection. Unexpected results are reported at the transition: drifting columnar flows moving in opposite directions along parallel lanes in a superhighway configuration have been observed. We will present simulations corresponding to both non-inclined and inclined cells. In particular, we have been able to obtain numerically superhighway convection (SHC). The numerical analysis should shed some light on the origin of these fast drifting columnar flows observed in experiments.Postprint (author's final draft

Analyzing slightly inclined cylindrical binary fluid convection via higher order dynamic mode decomposition

An extended dynamical system is considered that shows some striking, very complex spatio-temporal patterns. Specifically, we consider superhighway patterns that appear in binary fluid convection in slightly inclined, shallow cylindrical containers. These patterns show a number of parallel thermal lanes, each containing aligned coherent structures that counterpropagate in adjacent lanes. Several types of superhighway convection states have been obtained by direct numerical simulation. The numerical outcomes are analyzed using a recent data processing tool, known as higher order dynamic mode decomposition, which efficiently identifies relevant spatio-temporal patterns in numerically computed data.Postprint (author's final draft

On the determination of diffusion coefficients in two-component alloys and doped semiconductors: several implications concerning the International Space Station

The accurate determination of mass diffusion coefficients is a technologically relevant problem that has implications on the modelling and control of material processes such as crystal growth and casting. It is also important in the validation of different theories of atomic diffusion. The experimental determination of these coefficients, when there is a liquid phase, is difficult due to the unavoidable presence of buoyancy driven convection currents that enhance mass transport and disturb diffusion measurements. To minimize as much as possible these problems, long capillaries are used in order to confine the fluid and reduce the intensity of the convective motions. These measurements have also been done in reduced gravity environments, but the residual gravity may still be able to induce buoyancy driven convection motions. The aim of our work is to analyze the impact of low solutal Rayleigh number environments on the accuracy of the interdiffusion coefficient measurements using long capillaries. In the present study we deal with two liquid systems; photovoltaic silicon and Al-based liquid binary alloys at high temperature. We have numerically simulated two different experimental techniques used to determine the diffusion coefficients; the shear cell and the long capillary techniques. We also consider the effect of rotating the cylindrical cell along their axis as a mechanism to reduce axial convective transport even in Earth laboratories. Finally, we use typical accelerometric signals from the International Space Station (ISS) in the quasi-steady range of frequencies. The signals concentrate on typical station reboosts because the accelerometric level of the rest of potentially dangerous disturbances - dockings, undockings and Extra Vehicular Activities, EVAs - is considerably lower.Peer ReviewedPostprint (author's final draft