Effective Surface and Boundary Condition for Heterogeneous Salt Media with Insoluble Material

Effective Surface and Boundary Condition for Heterogeneous Salt Media with Insoluble Materia

Salt crystallisation at the surface of a heterogeneous porous medium

Evaporation of saline solutions from a porous medium often leads to the precipitation of salt at the surface of the porous medium. It is commonly observed that the crystallized salt does not form everywhere at the porous medium surface but only at some specific locations. To explain this phenomenon, we consider efflorescence formation at the surface of a saturated heterogeneous porous column (finer porous medium in coarse porous medium background) in the wicking situation. We study the impact of permeability and porosity contrasts on the efflorescence formation location from a simple visualisation experiment and Darcy's scale numerical simulations. We show that the porosity is the most sensitive parameter for our experiment and that efflorescence forms at the surface of the medium of lower porosity. A simple efflorescence growth model is then used to explain why the efflorescence continues to grow at the surface of the lower porosity medium without spreading over the adjacent surface of the greater porosity medium

Discrete Salt Crystallization at the Surface of a Porous Medium

Efflorescence refers to crystallized salt structures that form at the surface of a porous medium. The challenge is to understand why these structures do not form everywhere at the surface of the porous medium but at some specific locations and why there exists an exclusion distance around an efflorescence where no new efflorescence forms. These are explained from a visualization experiment, pore-network simulations and a simple efflorescence growth model

Sur le phénomène de cristallisation discrète à la surface ou à l'intérieur d'un milieu poreux

L'évaporation d'eau chargée en sels fait partie des processus de dégradation d'un milieu poreux. Lors de l'évaporation, les sels vont s'accumuler à l'interface liquidegaz, pouvant aller jusqu'à la cristallisation. Lors de la cristallisation, des contraintes importantes sont exercées sur lamatrice solide dumilieu poreux, ce qui à terme peut la détériorer. Les travaux présentés ici portent sur l'évaporation d'une solution de NaCl en situation demèche et se focalisent sur les phénomènes de transport jusqu'à la cristallisation. Nous avons analysé le lien entre le transport de la vapeur, l'écoulement induit dans la solution par l'évaporation, le transport de sel depuis le réservoir de solution saline vers l'interface, et la cristallisation. Plusieurs études expérimentales ont été réalisées pour différentes configurations de mèche. Par ailleurs, nous avons aussi mis en place divers modèles numériques (approche continue 1D et 2D, réseaux de pores 2D et 3D). Une première étude sur unemèche saturéemet en évidence l'influence de la cristallisation sur les différents transports. Les cristaux forment un nouveaumilieu poreux, favorisant l'évaporation et générant un effet de pompage sur la solution saline. Une deuxième étude sur des mèches saturées a permis d'analyser l'influence de l'évaporation et des propriétés du milieu poreux sur la localisation et le temps d'apparition de la cristallisation. Les expériences montrent une cristallisation discrète à la surface des mèches, se formant préférentiellement dans les zones où l'évaporation est la plus intense. Dans le cas des milieux hétérogènes, la localisation de la cristallisation dépend des propriétés des milieux poreux formant les mèches (porosité et perméabilité). Finalement, la situation d'évaporation en milieu partiellement saturé est étudiée et montre aussi une cristallisation discrète. Nous avons constaté qu'une approche continue classique ne permet pas de prédire correctement la cristallisation en raison des hétérogénéités des fronts. Pour palier ce manque, des modèles de réseaux de pores ont été développés. Les résultats obtenus indiquent que pour une évaporation insuffisante, la cristallisation n'a jamais lieu à l'interface. Lorsque l'évaporation augmente, la proportion de fronts amenant à la cristallisation augmente. Lorsque l'évaporation devient suffisamment intense, la totalité des fronts atteignent la cristallisation. Les zones de cristallisation préférentielles le long des fronts sont identifiées et caractérisées. ABSTRACT : The evaporation of water with dissolved salt is a main source of degradation of porousmedia. As water evaporates, dissolved salts accumulate under the liquid-gas interface, possibly reaching crystallization. As crystals grow, stresses can be generated andmay deteriorate pore walls. In this context, our study focuses onNaCl transport and crystallization processwhich result from evaporation inside or at the surface of the porousmedium. The link between vapour transport, brine flow, salt transport and crystallization, is studied with both experiments and numerical simulations (continuummodels and pore network models). A firstwork on saturatedwicks shows howthe growth of efflorescences affects the different transports occurring during evaporation. Efflorescences create a new porous medium which increases evaporation, and consequently salt transport through the wick, generating a "pumping effect". The influences of evaporation rate distributions and porous medium properties on crystallization are also analysed. Results showthat crystallization occurs in a discrete way over the surface of the saturated wicks, due to the porous medium disorder. In addition, it is found that efflorescences tend to grow preferentially in strong evaporating areas. For heterogeneousmedia, results show that crystallization occurs over the less permeable and the less porousmedium. A study of evaporation inside partially saturatedwicks also indicates discrete crystallization at the front. Classic continuum models can not predict accurately the crystallization over this kind of heterogeneous interface. Pore network models are more suitable to simulate transports with these large scale heterogeneities. Results show that depending on the global evaporation rate at the front, crystallization never occurs, may occur with a certain probability or always occurs. The relation between fronts structures, evaporation rate distribution and transports in the liquid phase, is analysed in order to understand and predict crystallization localization. These crystallization spots are then identified and characterized

Evaporation of a sodium chloride solution from a saturated porous medium with efflorescence formation

Precipitation of sodium chloride driven by evaporation at the surface of a porous medium is studied from a combination of experiments, continuum simulations, pore network simulations and a simple efflorescence growth model on a lattice. The distribution of ions concentration maxima at the porous medium surface, which are seen as the incipient precipitation spots, is shown to be strongly dependent on the factors affecting the velocity field within the porous medium owing to the significance of advection on ions transport. These factors are the evaporation flux distribution at the surface at Darcy’s scale as well as the scale of surface menisci and the internal disorder of the porous medium, which induce spatial fluctuations in the velocity field. The randomness of the velocity field within the porous medium and at its surface explains the discrete nature of incipient precipitation spots at the surface of porous medium. Experiments varying the mean size of the beads forming the porous medium lead to identify two main types of efflorescence, referred to as crusty and patchy, whose impacts on evaporation are completely different. The crusty efflorescence severely reduces the evaporation rate whereas the patchy efflorescence can enhance the evaporation rate compared to pure water. The crusty–patchy transition is analyzed from a simple growth model on a lattice taking into account the porous nature of efflorescence structures

Effective surface and boundary conditions for heterogeneous surfaces with mixed boundary conditions.

To deal with multi-scale problems involving transport from a heterogeneous and rough surface characterized by a mixed boundary condition, an effective surface theory is developed, which replaces the original surface by a homogeneous and smooth surface with specific boundary conditions. A typical example corresponds to a laminar flow over a soluble salt medium which contains insoluble material. To develop the concept of effective surface, a multi-domain decomposition approach is applied. In this framework, velocity and concentration at micro-scale are estimated with an asymptotic expansion of deviation terms with respect to macro-scale velocity and concentration fields. Closure problems for the deviations are obtained and used to define the effective surface position and the related boundary conditions. The evolution of some effective properties and the impact of surface geometry, Péclet, Schmidt and Damköhler numbers are investigated. Finally, comparisons are made between the numerical results obtained with the effective models and those from direct numerical simulations with the original rough surface, for two kinds of configurations

Fractal Phase Distribution and Drying: Impact on Two-Phase Zone Scaling and Drying Time Scale Dependence.

In an article published in 2008, Professor A.R. Mujumdar and his colleagues reviewed some applications of fractal concept on drying. As a modest continuation to this article, we give an overview on three drying-related issues where fractal aspects are present. First, we discuss within the framework of the theory of invasion percolation in a gradient the characteristic lengths that determine the extent of the hydraulically connected region during drying. It is pointed out that the scaling of this region is fundamentally different in 2D and in 3D, owing to the different percolation properties in 2D and 3D. In particular, it is shown that the fractal region only represents a small region of a drying front in 3D systems. Then a situation is described where fractal porous structures form as a result of an evaporation process. Finally, we consider drying in systems characterized by an initial fractal distribution of the liquid phase (invasion percolation cluster), a situation expected to happen in PEM fuel cells, and explore the size-dependent property of the overall drying time from pore network simulations

Discrete crystallization phenomenon at the surface or inside a porous medium

L’évaporation d’eau chargée en sels fait partie des processus de dégradation d’un milieu poreux. Lors de l’évaporation, les sels vont s’accumuler à l’interface liquide-gaz, pouvant aller jusqu’à la cristallisation. Lors de la cristallisation, des contraintes importantes sont exercées sur la matrice solide du milieu poreux, ce qui à terme peut la détériorer.Les travaux présentés ici portent sur l’évaporation d’une solution de NaCl en situation de mèche et se focalisent sur les phénomènes de transport jusqu’à la cristallisation. Nous avons analysé le lien entre le transport de la vapeur, l’écoulement induit dans la solution par l’évaporation, le transport de sel depuis le réservoir de solution saline vers l’interface, et la cristallisation. Plusieurs études expérimentales ont été réalisées pour différentes configurations de mèche. Par ailleurs, nous avons aussi mis en place divers modèles numériques (approche continue 1D et 2D, réseaux de pores 2D et 3D).Une première étude sur une mèche saturée met en évidence l’influence de la cristallisation sur les différents transports. Les cristaux forment un nouveau milieu poreux, favorisant l’évaporation et générant un effet de pompage sur la solution saline. Une deuxième étude sur des mèches saturées a permis d’analyser l’influence de l’évaporation et des propriétés du milieu poreux sur la localisation et le temps d’apparition de la cristallisation. Les expériences montrent une cristallisation discrète à la surface des mèches, se formant préférentiellement dans les zones où l’évaporation est la plus intense. Dans le cas des milieux hétérogènes, la localisation de la cristallisation dépend des propriétés des milieux poreux formant les mèches (porosité et perméabilité).Finalement, la situation d’évaporation en milieu partiellement saturé est étudiée et montre aussi une cristallisation discrète. Nous avons constaté qu’une approche continue classique ne permet pas de prédire correctement la cristallisation en raison des hétérogénéités des fronts. Pour palier ce manque, des modèles de réseaux de pores ont été développés. Les résultats obtenus indiquent que pour une évaporation insuffisante, la cristallisation n’a jamais lieu à l’interface. Lorsque l’évaporation augmente, la proportion de fronts amenant à la cristallisation augmente. Lorsque l’évaporation devient suffisamment intense, la totalité des fronts atteignent la cristallisation. Les zones de cristallisation préférentielles le long des fronts sont identifiées et caractérisées.The evaporation of water with dissolved salt is a main source of degradation of porousmedia. As water evaporates, dissolved salts accumulate under the liquid-gas interface, possibly reaching crystallization. As crystals grow, stresses can be generated andmay deteriorate pore walls. In this context, our study focuses onNaCl transport and crystallization processwhich result from evaporation inside or at the surface of the porousmedium. The link between vapour transport, brine flow, salt transport and crystallization, is studied with both experiments and numerical simulations (continuummodels and pore network models). A firstwork on saturatedwicks shows howthe growth of efflorescences affects the different transports occurring during evaporation. Efflorescences create a new porous medium which increases evaporation, and consequently salt transport through the wick, generating a "pumping effect". The influences of evaporation rate distributions and porous medium properties on crystallization are also analysed. Results showthat crystallization occurs in a discrete way over the surface of the saturated wicks, due to the porous medium disorder. In addition, it is found that efflorescences tend to grow preferentially in strong evaporating areas. For heterogeneousmedia, results show that crystallization occurs over the less permeable and the less porousmedium. A study of evaporation inside partially saturatedwicks also indicates discrete crystallization at the front. Classic continuum models can not predict accurately the crystallization over this kind of heterogeneous interface. Pore network models are more suitable to simulate transports with these large scale heterogeneities. Results show that depending on the global evaporation rate at the front, crystallization never occurs, may occur with a certain probability or always occurs. The relation between fronts structures, evaporation rate distribution and transports in the liquid phase, is analysed in order to understand and predict crystallization localization. These crystallization spots are then identified and characterized

Chapter 8. Evaporation and Wicking

Wicking and evaporation occur simultaneously in a variety of situations. In this chapter, we present and study several aspects of wicking/evaporation when evaporation is external mass transfer driven and unconfined or weakly confined. These include the influence of evaporation on the final impregnation height and the impregnation dynamics, the structure and the influence of the evaporation flux density distribution along the wick surface and the transport of a dissolved species. Other effects, still poorly studied, such as the influence of liquid films or the shape of the internal evaporation front in the wick are also addressed. Despite the practical importance of wicking / evaporation situations, this chapter also shows that further works are needed to increase our understanding of the combined action of wicking and evaporation and our prediction capabilities

Chapitre 6. Impact of Heterogeneity on Evaporation from Bare Soils

Heterogeneity in soil hydraulic properties has a significant impact on evaporation, and could be harnessed to reduce water losses and improve soil water conservation. This is illustrated through the consideration of the effect of Darcy scale heterogeneities resulting from horizontal layering. The impact of permeability gradient and thickness of layers has been investigated from evaporation experiments performed from homogeneous as well as horizontally multi-layered soil columns. Two main cases are distinguished depending on the sign of the permeability gradient, the unstable case when the permeability increases with depth and the stable case when, on the contrary, the permeability decreases with depth. The results indicate an interesting competition between stabilizing gravity effects and destabilizing or stabilizing permeability gradient effects and lead to the emergence of the concept of two-scale evaporation process