Thèse Simulation Numérique Directe et Modélisation Thermodynamique du Transfert de Matière Gaz-Liquide en Présence d'Espèces Tensioactives H/F Doctorat.Gouv.Fr

La contamination interfaciale affecte le transfert de matière par deux mécanismes fondamentalement différents. D'une part, l'adsorption modifie la tension interfaciale et génère des contraintes de Marangoni, modifiant l'hydrodynamique des bulles, la mobilité interfaciale et le transport convectif. D'autre part, la couche adsorbée peut constituer une résistance supplémentaire au transfert moléculaire à travers l'interface, dont la contribution reste à élucider. Distinguer ces deux contributions est essentiel en vue d'une modélisation fiable.

La thèse développera des simulations numériques et une approche basée sur la thermodynamique pour interpréter les résultats de transfert autour de bulles. Des expériences contrôlées sur des bulles confinées ellipsoïdales ou de Taylor fournissent des données sur l'inhibition du transfert dans différentes solutions de tensio-actifs. Des simulations numériques directes (DNS) de l'hydrodynamique et du transfert de matière seront d'abord réalisées. Dans un premier temps, elles prendront en compte les gradients de concentration en espèces adsorbées et les contraintes de Marangoni qui en découlent, afin de quantifier leur contribution à la réduction mesurée du transfert. Cette approche permettra alors d'évaluer l'importance de l'autre contribution, due à la barrière interfaciale au transfert, pour les bulles confinées. Ensuite, une approche thermodynamique prenant en compte la composition du mélange interfacial et la production d'entropie sera couplée aux DNS afin de compléter le modèle par la résistance associée à la couche adsorbée. Les résultats seront confrontés aux expériences. Une modélisation globale, basée sur la théorie du double film, sera ensuite développée et affinée, de telle sorte qu'elle repose sur des paramètres d'entrée facilement mesurables ou accessibles.
Après validation, la méthodologie sera étendue aux bulles non confinées, offrant une configuration plus générale dans laquelle les effets Marangoni solutaux et ceux dus à la couverture interfaciale interagissent davantage. Enfin, l'approche sera appliquée à des milieux plus complexes : mélanges concentrés avec des tensioactifs ioniques et des sels, eau de mer, eaux usées à traiter...

L'objectif est ainsi d'établir un cadre reliant thermodynamique interfaciale et transfert gaz-liquide, avec une méthodologie de validation par approche couplée entre DNS et expériences. Cela fournira une base pour prédire l'efficacité du transfert gaz-liquide lorsque les conditions et la composition évoluent, en milieux complexes, et en vue d'optimiser les technologies intensifiées d'aération et autres procédés diphasiques multi-constituants.

In gas-liquid systems such as rising bubbles in stagnant liquids containing surface-active species, several experimental studies have reported a significant decrease of the mass transfer rate, as compared to a clean interface. Surfactants are amphiphilic molecules that adsorb at interfaces and strongly affect the bubble hydrodynamics by generating additional interfacial forces such as Marangoni stresses. Even at very low concentrations, they can reduce both the bubble rise velocity and gas-liquid mass transfer rate [1]. In concentrated surfactant solutions or complex media such as wastewater, a strong decrease in mass transfer has been observed [2,3,4]. Experimental data obtained with confined ellipsoidal bubbles [5] have shown that, despite similar rise velocities to those measured in purified water, the mass transfer coefficient can be reduced by a factor of four in the presence of surfactants. This result suggests that, in addition to hydrodynamic effects, an additional mass transfer hindrance can exist, associated with the adsorbed layer at the interface.
Regarding the isolated effect of Marangoni stresses, theoretical approaches have been proposed to predict the mass transfer coefficient [6], as well as semi-empirical correlations based on Direct Numerical Simulation (DNS) with insoluble [7] or soluble surfactants [8]. Regarding the possibility of accounting for an additional interfacial resistance to mass transfer, a thermodynamically consistent framework has been developed [9] in parallel, and applied to experimental results with confined bubbles [5]. However, discriminating between these two effects when interpreting experimental measurements remains an open question, as does incorporating both mechanisms into predictive modelling approaches. For chemical and environmental engineering applications involving gas dissolution and gas-liquid mass transfer, existing models remain insufficiently predictive in the presence of species adsorbed at the interfaces, such as surfactants, contaminants, alcohols or biological molecules encountered in industrial and natural systems. Current modelling approaches do not fully account for the coupled effects of interfacial contamination, interfacial thermodynamics and hydrodynamics, and therefore have limited ability to predict mass transfer rates in complex multicomponent media.

The objective of the project is to develop a physics-based and predictive methodology linking interfacial thermodynamics, bubble hydrodynamics and gas-liquid mass transfer. The approach will first use well-defined model systems to disentangle the different mechanisms induced by interfacial contamination, and then extend the methodology to more complex multicomponent two-fluid systems relevant to environmental and industrial applications.

A particular objective is to distinguish and quantify the respective contributions of surface-active species to mass transfer through (i) the modification of interfacial hydrodynamics and (ii) the additional potential barrier to molecular transfer associated with the adsorbed layer at the interface.
The resulting framework will then be developed towards predictive models based on physically measurable parameters, providing a transferable methodology for gas-liquid mass transfer in complex liquid media. As experimental results are available for both unconfined [2,3] and confined [4,5] bubbles in the presence of surfactants, the PhD will combine Direct Numerical Simulations (DNS) and modelling approaches to interpret these experimental measurements and develop a predictive framework at both local and global scales.

The in-house DIVA code [7,8,10] for two-phase flows, developed at LGC in collaboration with IMFT, will be used for the DNS. It relies on the Level-Set method to capture the interface and the Ghost Fluid method to account for interfacial jumps. Numerical developments have already been carried out to model surfactant transport, both in the bulk phase and along the interface, as well as Marangoni stresses. Results have been obtained for bubble hydrodynamics and mass transfer around unconfined rising bubbles in the presence of soluble surfactants, in axisymmetric 2D configurations (PhD thesis of Dr. Kalyani Kentheswaran). An extension of the implementation of interfacial Marangoni forces to the 3D version of the code will be performed during the present PhD. In addition, a subgrid-scale model to account for the very thin mass boundary layers associated with surfactant exchange between the bulk and the interface could also be developed, with strong interests for the present problem in order to consider large Schmidt numbers in the simulations, based on previous work carried out within Prof. Bothe's group [11].

Numerical simulations of confined ellipsoidal and Taylor bubbles rising in a pipe will be performed under conditions close to those of the experimental study in [5], first in axisymmetric 2D and then in 3D (in order to consider large bubble Reynolds numbers). In a first step, the simulations will account only for the effect of Marangoni stresses and surface tension reduction caused by adsorbed surfactants on bubble dynamics and gas-liquid mass transfer rates. They will be used to quantify the extent to which the experimentally observed transfer reduction can be explained by hydrodynamic effects alone. In a second step, the thermodynamic model developed in [9,5] will be coupled with the simulations to explicitly account for the effect of the local interfacial composition on the mass transfer rate, and the results will again be compared with the experimental measurements.

The model will then be further refined, and a global modelling approach will be developed based on an extended two-film theory, with the aim of consistently predicting the mass transfer rate in the confined bubble configuration without adjustable parameters.

Subject to progress, the validated methodology (both the simulation-based approach, using DNS coupled with the thermodynamic model, and the global modelling approach) will finally be tested on one or more increasingly complex liquid media, selected among concentrated mixtures containing ionic surfactants and salts, seawater and wastewater, and extended to unconfined rising bubbles. These applications will be used to assess the transferability of the framework beyond the benchmark confined bubble configurations.