Time-dependent patterns in quasivertical cylindrical binary convection

Abstract

This paper reports on numerical investigations of the effect of a slight inclination α 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 α≈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.

Nonequilibrium solid-solid phase transition in a lattice of liquid jets

“…Conversely, the pattern formation process in an inclined layer of a binary liquid mixture has been investigated only recently using computational methods by Alonso et al [33]. The authors of this study simulated the three dimensional Boussinesq equations for a binary liquid mixture with positive Soret coefficient, using parameters mirroring those of experiments on SHC [32] and solving numerically the equations by using the algorithms described in [41].…”

“…When the mixture is heated from below, the unstable density profile generated by thermal dilation and by the concentration profile induced by the Soret effect can give rise to convective motions. Under particular conditions the convective flux takes the form of vertical jets of ascending and descending fluid, arranged into configurations mimicking the structure of amorphous [17] and crystalline alloys [21,32,33]. When the layer of liquid is horizontal, square lattices of jets can be obtained both for heat convection in simple liquids [20] and for solutal convection in binary mixtures [21], provided that the sample is close to the threshold of convection and that the horizontal boundaries are poor conductors of heat and mass, respectively.…”

“…1(c)]. The square and centered-rectangular structures can be accessed independently by preparing the system in an initial configuration where the concentration of the mixture is uniform and suddenly applying a carefully chosen temperature difference [32,33].…”

“…The imposition of a shear stress, attained by inclining the layer of liquid to induce a large scale flow, significantly alters the convective patterns of a simple fluid [24][25][26][27][28][29][30][31]. In the case of a binary liquid mixture, recent experiments [32] and simulations [33] have shown that the imposition of marginal inclination induces a shear stress acting on the square lattice of jets, which determines the transition to an ordered configuration with different symmetry. This feature suggests the opportunity of using this kind of system as a model to investigate at the macroscopic scale the solid-solid phase transitions encountered in atomic and colloidal systems.…”

Effect of small inclination on binary convection in elongated rectangular cells

“…Among relevant work on inclined two-dimensional binary fluid convection is an analytical and numerical study of natural binary fluid convection in an inclined shallow cavity with fixed flux boundary conditions on the temperature [19] and, more usefully for the present work, a related study of the onset of convection in an inclined infinite slot with fixed temperature boundary conditions [20]. More recently, experimental and numerical studies of convection in a slightly inclined disk-like cylinder filled with a S > 0 mixture and subject to fixed temperature boundary conditions at the top and bottom [21,22] indicate that pattern formation is strongly affected even by small inclinations. Taken together, existing results on the tilted problem thus suggest that even very small inclinations produce substantial changes in the flow structure and result in new phenomena.…”