Pedro L. Garcia-Ybarra

Mass transfer dominated by thermal diffusion in laminar boundary layers

The concentration distribution of massive dilute species (e.g. aerosols, heavy vapours, etc.) carried in a gas stream in non-isothermal boundary layers is studied in the large-Schmidt-number limit, Sc [Gt ]1, including the cross-mass-transport by thermal diffusion (Ludwig–Soret effect). In self-similar laminar boundary layers, the mass fraction distribution of the dilute species is governed by a second-order ordinary differential equation whose solution becomes a singular perturbation problem when Sc [Gt ]1. Depending on the sign of the temperature gradient, the solutions exhibit different qualitative behaviour. First, when the thermal diffusion transport is directed toward the wall, the boundary layer can be divided into two separated regions: an outer region characterized by the cooperation of advection and thermal diffusion and an inner region in the vicinity of the wall, where Brownian diffusion accommodates the mass fraction to the value required by the boundary condition at the wall. Secondly, when the thermal diffusion transport is directed away from the wall, thus competing with the advective transport, both effects balance each other at some intermediate value of the similarity variable and a thin intermediate diffusive layer separating two outer regions should be considered around this location. The character of the outer solutions changes sharply across this thin layer, which corresponds to a second-order regular turning point of the differential mass transport equation. In the outer zone from the inner layer down to the wall, exponentially small terms must be considered to account for the diffusive leakage of the massive species. In the inner zone, the equation is solved in terms of the Whittaker function and the whole mass fraction distribution is determined by matching with the outer solutions. The distinguished limit of Brownian diffusion with a weak thermal diffusion is also analysed and shown to match the two cases mentioned above.

A nonlinear evolution equation for Bénard-Marangoni convection with deformable boundary

Abstract For the case of small Biot number, i.e. small heat transfer, a nonlinear evolution equation is derived for the deformable upper surface in a liquid layer heated from below and open to the ambient air (Benard-Marangoni convection). As a byproduct of our analysis, threshold values and other relevant findings are obtained for the onset of convection.

Transport of Particles and Vapors in Flue Gases and Deposition on Cold Surfaces

In coal combustion processes, a large amount of nonvolatile material is emitted as particular matter carried by the gas stream. Moreover, some condensable vapors (usually sulfates and nitrates) are formed by reaction in the flue gases. The control of these particles and vapors is a key factor in clean coal conversion technologies. Thus, the formation of soot and fly ash deposits and the condensation of vapors over heat exchanger tubes and exhaust lines reduce the heat transfer efficiency and promote corrosion problems, leading to shorter lifetimes of the equipment and increasing the production and maintenance costs. Also, the emission of submicron particles to the ambient air is an environmental issue of capital importance. Moreover, the bulk (porosity, hardness) and surface (roughness) properties of the formed deposit depend on the particle arrival dynamics. Therefore, the analysis of particle and vapor transport under controlled conditions and the study of deposit formation from particle laden gases are problems of wide practical implications in coal combustion. In particular, there is a need of theoretical analysis on the dynamics of particles in gases under strong temperature differences and intense radiative fluxes, as well as on the behavior of particles near obstacles to evaluate the deposition rates. Some model problems linked to the behavior of particles and vapors in gases and deposit formation will be discussed here.

Morphological instability of a thermophoretically growing deposit

The stability of the planar interface of a structureless solid growing from a depositing component dilute in a carrier fluid is studied when the main solute transport mechanism is thermal (Soret) diffusion. A linear stability analysis, carried out in the limit of low growth Peclet number, leads to a dispersion relation which shows that the planar front is unstable either when the thermal diffusion factor of the condensing component is positive and the latent heat release is small or when the thermal diffusion factor is negative and the solid grows over a thermally-insulating substrate. Furthermore, the influence of interfacial energy effects and constitutional supersaturation in the vicinity of the moving interface is analyzed in the limit of very small Schmidt numbers (small solute Fickian diffusion). The analysis is relevant to physical vapor deposition of very massive species on cold surfaces, as in recent experiments of organic solid film growth under microgravity conditions.

The Vortical Structure of Flame Spreading over Liquid Fuels

Understanding flame spreading is a matter of both fundamental interest and crucial practical importance, mainly for its relevance to safety issues, as it is the base for the knowledge and ultimate control of fire propagation/suppression mechanisms. The fuel vapor surrounding a condensed fuel in an oxidizing atmosphere can support the propagation of a flame over the fuel surface. If the fuel temperature, and therefore the fuel vapor pressure, is high enough, then propagation occurs in the premixed (triple) flame regime [1] through the fuel vapor-air mixture. If the fuel temperature is decreased down to values that make this combustion regime impossible, due to heat loses towards the fuel and/or to adverse kinetics conditions, then the chemical reaction can still proceed, provided the chemical heat release is high enough to vaporize such an amount of fuel as to increase locally the Damkholer number above its extinction value. In this case, flame spreading relies on relatively slow mechanisms of heat and mass transfer across the fuel-gas interface, which render spreading slower than it was at high temperatures. When the fuel is a liquid, these mechanisms include convection, induced by thermocapillarity and/or buoyancy, which leads to characteristic propagation regimes [2] absent for solid fuels; see [3] for a review. Thermocapillary convection around a fluid-fluid interface occurs when temperature differences along the interface establish an imbalance of surface forces by inducing changes in the surface tension

Influence of mass diffusion on the stability of thermophoretic growth of a solid from the vapor phase

Abstract The stability of solid planar growth from a binary vapor phase with a condensing species dilute in a carrier gas is studied when the ratio of depositing to carrier species molecular masses is quite large and the main diffusive transport mechanism is thermophoresis (thermal diffusion). Direct Fick/Brownian transport is important only in a thin layer (of relative thickness given by the inverse of the Schmidt number Sc ⪢ 1) adjacent to the solid-vapor interface. Then, only disturbances with a large wavenumber k are affected by Brownian diffusion and a linear stability analysis is performed in the limit k = O(Sc). The resulting dispersion relation shows that there exist three different regions: i ) for small wavenumber disturbances the planar front is unstable when the ratio of fluid to deposit thermal conductivities is less than unity, ii ) for very large wavenumbers interfacial tension effects damp out all disturbances, and iii ) in the intermediate range of wavenumbers the amplification rate depends on the degree of constitutional supersaturation.

Structure of Granular Deposits Formed by Aerosol Particles Conveyed by Fluid Streams

Aerosols (particles carried by gas streams) appear in many practical applications and the understanding of their dynamics [1, 4] is needed to control processes such as, for instance, heterogeneous nucleation of vapors on preexisting particles, evolution of clouds, pollution dispersion and production of new materials from powders [3]. In this area, there is a need of controlling and characterizing the structure of granular materials formed by depositing aerosol particles. The main morphological features of these granular deposits as their bulk properties (density, porosity and structure) and interface properties (roughness and thickness of the active region) depend on the way that new particles arrive to form the deposit. The granular structure affects the chemical, optical and mechanical properties of the product and it should be tailored for new materials applications: nanostructured deposits, catalytic surfaces, layered materials and others.

Cooling of the Heavy-Oil Trapped in the Reservoirs of the Sunk Oil Tanker Prestige

The cooling down of hot heavy-oil trapped within the reservoirs of a sunk tanker has been theoretically analysed and numerically simulated. Using the best available oil properties, and approximating the initial and boundary conditions in a rational way, a two-dimensional case-study has been investigated by several research groups. The volume average temperature within the lateral tank reaches 10°C after three months, while it takes five months for the central reservoir. Grid refinement tests have been conducted. The pressure dependence of the oil viscosity might have an important effect on the cooling time.Copyright