Session RH: Convection and Buoyancy Driven Flows VI

Hots spots in fingering of exothermic autocatalytic chemical fronts

Across traveling autocatalytic fronts, density differences can result from composition and temperature changes. These density differences lead to buoyancy-driven hydrodynamic instabilities when the heavier solution overlies the lighter one. Using combined experimental and theoretical approaches, we examine the properties of the temperature field around such a buoyantly unstable exothermic autocatalytic front in presence of heat losses. Experimentally, the dynamics of the chlorite-tetrathionate reaction are studied in a Hele-Shaw cell. The concentration field is observed by a color indicator while the two-dimensional thermal field is obtained by an interferometric technique. Because of the heat losses, products are cooled down behind the reaction zone. The interferometric analysis moreover reveals the presence of hot spots, i.e. local areas where the temperature is larger than in a stable front. To understand the properties of the hot spots, we have developed a theoretical model coupling the evolution of the concentration and temperature fields to that of the velocity field. We show that hot spots exist in the presence of buoyancy-induced convection only if heat diffuses faster than mass and/or in presence of heat losses. We quantify the maximum value of temperature obtained in presence of convection as a function of the various parameters of the problem.   

Hydrodynamic Instabilities of Acid-Base Reaction Fronts: Active Role of a Color Indicator

Chemical reactions are able to trigger hydrodynamic flows by, for example changing the density of the solutions across the reactive interfaces. In this work we present an experimental and theoretical study of the buoyancy-driven hydrodynamic instabilities that can occur when two miscible reactive solutions of an acid-base system are put in contact in the gravity field. We compare situations where a hydrochloric acid aqueous solution is put on top of a sodium hydroxide aqueous solution with or without a color indicator (Bromocresol Green). We also analyze the situation where a hydrochloric acid is put on top of an aqueous solution of a color indicator without any base. We show that the patterns observed and the instabilities taking place strongly depend on the presence of a color indicator. Using a reaction-diffusion model for the concentrations of all species (including the color indicator) we analyze the different possible sources of destabilization of the acid-base front and explain the various instabilities observed in each experimental system.   

Numerical study of thermo-solutal convection induced by evaporation

During the drying of a volatile solution, both termal and mass effects are coupled. The instability mechanism is first of the solutal Marangoni type. In order to understand why experimentalists observe thermal convective patterns at the beginning of the process, numerical studies are performed and thermal and mass effects are separately studied. In both cases, convection is considered as significant when the P\'eclet number ($Pe$) is greater than $1$. The time evolution of $Pe$ is studied to explore the transient character of the problem. A stability map as a function of experimental parameters (thickess and viscosity of the solution) is drawn and the results are compared with expermimental datas. A comparison between solutal and thermal induced velocities and wave lenghts is also provided.   

Inclusion of buoyancy effects in the evaporating liquid film evolution equation

Macroscopic liquid films are entities that are important in biophysics, physics, and engineering, as well as in natural settings. They can be composed of common liquids such as water or oil, rheologically complex materials such as polymers solutions or melts, or complex mixtures of phases or components. When the films are subjected to the action of various mechanical, thermal, or structural factors, they display interesting dynamic phenomena such as wave propagation, wave steepening, and development of chaotic responses. Such films can display rupture phenomena creating holes, spreading of fronts, and the development of fingers. Researchers have conducted stability analysis on evaporating liquid films and have developed an evolution equation describing the effect of various physical mechanisms that affect evaporating liquid films. The present work extends the evolution equation proposed in literature by including the effect of buoyancy through the Boussinesq approximation. The extended evolution equation allows for capturing buoyancy effects inherent in evaporating thick liquid films.   

Hydrothermal waves in evaporating annular pools and sessile drops using DNS

Thermocapillary effects generated due to thermal gradients in annular liquid pools and resulting in hydrothermal waves under inert, saturated and evaporating atmospheres are investigated using two-phase direct numerical simulations in 3D. For annular pools under inert environments, the volume-of-fluid method is used to capture the interface, with special attention towards the grid resolution near the vapour-liquid interface. The results show that the interface temperature distribution follows a regular azimuthal pattern, representative of hydrothermal wave structures, along with small-amplitude interfacial waves. The effects of evaporation fluxes and the interfacial depths on the linear (early-time) and non-linear (late-time) development of hydrothermal temperature and interfacial waves will be presented. Under inert environments, the azimuthal structures qualitatively agree with experimental and numerical studies (with a single-phase model and a non-deformable free surface) of Schwabe et. al. (2003). Evaporating sessile droplets simulated using diffuse-interface method will be presented and compared against analytical integral balance models.