La digitation visqueuse est une instabilité hydrodynamique apparaissant lorsque, dans un milieu poreux, un fluide moins visqueux déplace un fluide plus visqueux. L'objectif de notre thèse est l'étude expérimentale des propriétés des motifs de digitation lorsque l'échantillon de fluide visqueux est de taille finie et lorsqu'une réaction chimique modifie la viscosité dans un milieu poreux modèle, en l'occurrence une cellule de Hele-Shaw. En particulier, notre étude a permis de quantifier la contribution de dispersion et de la digitation visqueuse, l'étalement dans l'espace d'échantillons de taille finie en fonction des paramètres expérimentaux (contraste de viscosité, vitesse de déplacement et taille de l'échantillon). Pour les fluides réactifs, nous analysons la digitation induite par une réaction A + B C dont le produit C est plus visqueux que les réactifs A et B, ceux-ci ayant la même viscosité. Nous mettons en évidence l'effet des concentrations en réactifs, du choix du fluide vecteur et du débit d'injection sur le motif de digitation. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

[pt] A perfuração de poços de petróleo, principalmente em ambientes offshore, é uma operação que demanda um custo muito elevado, portanto a minimização de problemas e danos ao reservatório produtor é muito importante. O projeto de um fluido de perfuração que garanta a mínima invasão na rocha reservatório é um tópico fundamental, como consequência a indústria petrolífera tem investido em estudos com o intuito de evitar que este problema ocorra. Sendo assim, nesse trabalho estudou-se o escoamento de fluidos em um meio poroso ideal, a célula de Hele-Shaw. Para realizar esse trabalho foram utilizados dois fluidos não newtonianos: uma solução aquosa de um polímero flexível, a poliacrilamida; e uma solução aquosa de um polímero rígido, a goma xantana. Esses fluidos não newtonianos representaram o fluido de perfuração, já o papel do petróleo presente na rocha reservatório foi desempenhado pelo óleo mineral. A partir desse experimento é possível observar a instabilidade de Saffman-Taylor ou viscous fingers, que é um fenômeno observado quando um fluido de menor viscosidade desloca outro de maior viscosidade. Esse fenômeno é muito importante em diversas aplicações, tais como: invasão de fluido de perfuração em meios porosos (caso que será estudado), recuperação secundária e terciária de petróleo, fraturamento hidráulico, processamento de polímeros, hidrologia e filtração. O experimento consiste em analisar a evolução da interface entre os dois fluidos através de uma câmera filmadora. A partir das imagens é determinada qualitativamente a eficiência do deslocamento. Com o conjunto de imagens é possível observar também em quais parâmetros dinâmicos e reológicos ocorre a transição fingers (interface instável) para plug (interface estável), e viceversa. Também foram realizados testes reológicos nos quais foi possível conhecer o comportamento dos fluidos não newtonianos utilizados. Com base nos dados coletados observou-se que tanto para a poliacrilamida quanto para a goma xantana a transição ocorre a uma taxa de cisalhamento adimensional próxima de 3. / [en] The drilling of oil wells, particularly in offshore environments, is an operation which demands a high cost, thus, the minimization of problems and damage to the producing reservoir is very important. The design of a drilling fluid that ensures minimum invasion into the reservoir rock is a major topic, consequently the oil industry has invested in research in order to prevent this problem from occurring. Therefore, this research studied the displacement of fluids in an ideal porous medium, a Hele-Shaw cell. To accomplish this task, the following two non-Newtonian fluids were used: an aqueous solution of a flexible polymer, polyacrylamide; and the other an aqueous solution of a rigid polymer, xanthan gum. Such non-Newtonian fluids represent the drilling fluid, while the function of oil present in the reservoir rock was represented by mineral oil. From this experiment it is possible to observe the Saffman-Taylor instability or viscous fingers, which is a phenomenon observed when a low viscosity fluid displaces a higher viscosity fluid. This phenomenon is very important in many applications, such as drilling fluid invasion in porous media, secondary and tertiary oil recovery, hydraulic fracturing, polymer processing, hydrology and filtration. The experiment consists in analyzing the evolution of the interface between two fluids through a digital camera, and determining the displacement efficiency qualitatively from the imagens. With the set of images is possible to observe in which dynamic and rheological parameters the transition from fingers (unstable interface) to plug (stable interface) occurs, and vice versa. Also, rheological tests were performed in which it was possible to know the behavior of non-Newtonian fluids used in the study. From the data collected it was observed that both the polyacrylamide and for xanthan gum transition occurs near the dimensionless shear rate of 3.

Dans cette thèse, nous avons étudié expérimentalement, numériquement et théoriquement la sédimentation d’un soluté en cellule de Hele-Shaw, modèle analogue de milieu poreux, avec un écoulement zonal horizontal. Une cellule, alimentée par deux grands réservoirs assurant un écoulement zonal uniforme, a été réalisée au laboratoire. La vitesse a été mesurée par PIV. L’injection d’une solution saline dans cet écoulement permet de visualiser la propagation du panache de pollution, et de mesurer le champ de concentration par LIF. Trois configurations typiques ont été observées : panache sans digitation (« stable »), avec une seule digitation (« faiblement instable »), et avec de nombreuses digitations (« fortement instable »). L’influence du contraste de densité, de la vitesse zonale, et du débit d’injection sur la stabilité du panache a été analysée. Ces résultats ont été comparés à des simulations numériques sous COMSOL Multiphysics®. Les champs de concentration simulés sont en accord quantitatif avec les champs expérimentaux. Ces simulations ont de plus permis d’étudier l’influence de l’anisotropie du tenseur de dispersion sur la stabilité du panache. Une étude théorique linéaire, effectuée à partir d’un écoulement de base unidirectionnel et quasi-stationnaire, est venue compléter ces résultats. Elle montre que le panache est toujours convectivement instable pour les valeurs des paramètres considérées, et permet de retrouver et de quantifier les principaux résultats mis en évidence lors des études expérimentale et numérique, comme l’effet stabilisant de la dispersivité longitudinale ou l’effet déstabilisant du contraste de densité / This thesis is an experimental and numerical investigation of solute transport and sedimentation in a Hele-Shaw cell with zonal flow. A vertical cell joining two large tanks has been built to provide a uniform horizontal flow, the velocity of which has been measured by using PIV. The concentration field of a solute injected in this flow has been measured by using LIF. Three typical plume configurations have been observed: without digitations (“stable”), with a single digitation (“weakly unstable”), and with various digitations appearing at the lower interface (“unstable plume”). The influence of density contrast, zonal flow and solute flow rate on the appearance of the various configurations has been investigated. These results have been compared to numerical simulations using the COMSOL Multiphysics® software. The numerical concentration fields are in qualitative agreement with the experimental ones. In addition, these simulations allowed us to investigate the effect of the anisotropy of the dispersion tensor on the occurrence of unstable configurations. A linear stability analysis based on a uniform parallel flow superposed to a quasi-steady horizontal layer of solute has been performed. It shows that the plume is convectively unstable for the parameters considered here, and confirms the various behaviors observed in both the experimental and the numerical analyses, like the stabilizing effect of the longitudinal dispersivity or the destabilizing effect of the solute concentration

[pt] Uma abordagem experimental foi utilizada para o estudo da eficiência de varredura de fluidos viscoplásticos na célula de Hele-Shaw , que representa um meio poroso com porosidade constante. A análise baseia-se em um fluido empurrando outro onde, pela razão de viscosidades acima do punto de referência , manifesta-se a instabilidade de Saffman-Taylor, que desencadeia em uma interface instável com divisões sucessivas conhecidas como viscous fingers. A formação da instabilidade é considerada uma condição indesejável, e no caso da indústria petrolífera, torna-se de interesse na invasão da formação pelo fluido de perfuração, pasta de cimento, e no deslocamento de petróleo pesado em reservatórios entre outros. Apesar de que o fenômeno é vastamente estudado utilizando a célula de Hele-Shaw, a maioria dos trabalhos concentram-se no deslocamento de líquidos newtonianos por ar, deixando uma ampla gama de possibilidades de estudo, particularmente no que diz respeito aos fluidos não newtonianos. Utilizando equipamentos que permitem assegurar uma vazão constante de injeção, testou-se três concentrações diferentes de solução aquosa de carbopol em duas configurações diferentes onde o líquido viscoplástico é o deslocador e vice-versa. Fazendo uso do processamento digital de imagens, avaliou-se a forma da interface em função do desvio padrão, além da velocidade e da eficiência de varredura no deslocamento. Determinaram-se parâmetros adimensionais em função da geometria da bancada e dos fatores dinâmicos e reológicos dos fluidos onde se obtiveram duas zonas vem marcadas de varredura. Observou-se que a razão de viscosidades e o número de capilaridade modificada crítica são os indicadores que governam o deslocamento. / [en] An experimental approach has been used to study the sweep efficiency of viscoplastic fluid in a Hele-Shaw cell, which represents a porous medium with constant porosity. The analysis is based on a lower viscosity fluid pushing a more viscous through a geometry, which manifests the instability of Saffman-Taylor, that result in an unstable interface with successive divisions known as viscous fingers. The occurrence of instability is considered an undesirable condition, and in the petroleum oil industry, it becomes of interest in the reservoir oil invasion and heavy oil displacement in reservoirs. Despite being widely studied, most studies focus on the displacement of Newtonian liquids by air, leaving the field of study of non-Newtonian fluids without being evaluated where none of viscosities of the fluids involved can be considered negligible. Using equipment that ensures a constant flow rate of injection three different aqueous concentrations of carbopol were tested in two different configurations: carbopol as the displacing fluid and vice-versa. Using digital image processing, the shape interface was evaluated according to their standard deviation, average velocity and efficiency sweep during the displacement. Determined dimensionless parameters was evaluated in function of the experimental geometry, dynamic and rheological factors of the fluids in order to get benchmark that allow separating interfaces zones that tend to 100 per cent or plugs and the zone where the viscous fingers reveal themselves. It was found that the viscosity ratio and modified critical capillary govern the displacement.

La propagation d'un front de réaction-diffusion est étudiée expérimentalement dans un écoulement cellulaire multiéchelle. Le front est produit par réaction autocatalytique en solution. L'écoulement est réalisé en géométrie de Hele-Shaw par électroconvection, son caractère multiéchelle étant réalisé par l'action combinée de deux nappes d'aimants d'échelles différentes. La géométrie du front et sa vitesse moyenne de propagation sont déterminées pour une large gamme d'intensité des vortex de chaque échelle. Elles sont confortées par une simulation numérique de l'avancée du domaine brulé dans le domaine frais. L'effet de la nature multiéchelle de l'écoulement sur la vitesse moyenne du front est compris par une méthode de renormalisation dont la validation est fournie par l'obtention d'un courbe maitresse pour l'ensemble des données. / The propagation of a reaction-diffusion front is experimentally studied in a multi-scale cellular flow. The front is produced by an autocatalytic chemical reaction in an aqueous solution. The flow is generated by electroconvection and its multi-scale nature is induced by overlaying magnets of different scales. This enables an independent tune of the flow intensity at each scale. The geometry and the mean velocity of the front have been determined over a large range of scale intensities. These features are confirmed by a numerical simulation based on a burnt and fresh domain dynamics, the burnt domain expanding across the fresh one. The effect of the multi-scale nature of the flow on the mean front velocity is recovered by a renormalisation method validated by a collapse of the data onto a single curve.

L'étude décrite dans cette thèse porte sur l'injection ponctuelle d'une solution saline au sein d'une cellule dite de Hele-Shaw, afin de caractériser le comportement dispersif d'un polluant en milieu poreux. L'approche expérimentale employée est basée sur l'implémentation originale d'un dispositif de Fluorescence Induite par Laser (LIF) dans la cellule. La mise en place d'un protocole de mesure efficace permet de mener une analyse quantitative des résultats expérimentaux. En outre, en appliquant la méthode des moments, il est possible de caractériser avec précision le comportement dispersif de la zone de mélange de la solution injectée. Parallèlement aux expériences, à l'aide du code numérique FRIPE, les injections ont été simulées numériquement. L'analyse quantitative a été appliquée à ces dernières. Une comparaison poussée des résultats expérimentaux et numériques a donc été effectuée, du point de vue qualitatif mais aussi sur l'expression de la dispersion du panache de la zone de mélange de la solution / The study described in this thesis is about punctual injection of a saline solution inside a "Hele-Shaw cell" in order to characterize the dispersive behavior of a pollutant in porous media. The chosen experimental approach is based on the setup of an original Laser Induced Fluorescence (LIF) in the Hele-Shaw cell. The setting of the experimental apparatus allows quantitative data reduction of the experimental results. Moreover the "Moments Method" studied precisely the solution mixing dispersive behavior. Using the numerical code FRIPE the same injections have been simulated. The same quantitative data reductions have been applied to the numerical results. This led to an extensive comparison of the numerical and the experimental results, qualitatively but also of the dispersion in the mixing area of the injected solution

In verfahrenstechnischen Anlagen der Flüssig-Flüssig-Stoffübertragung kommt es an der Phasengrenze zwischen den nicht mischbaren Flüssigphasen häufig zur Ausbildung hydrodynamischer Instabilitäten. Sie sind mit komplexen Geschwindigkeitsfeldern in den Flüssigphasen, insbesondere in den grenzschichtnahen Regionen verbunden und führen zu einem starken Anstieg der pro Zeiteinheit übertragenen Stoffmenge. Die Lösung der Diffusionsgleichung reicht in diesem Fall zur Vorausberechnung des für Auslegungszwecke bedeutsamen Stoffdurchgangskoeffizienten nicht mehr aus. Chemische Reaktionen stellen Quellen oder Senken von Wärme und Stoff dar, die das Auftreten von Instabilitäten begünstigen und die mathematische Beschreibung zusätzlich erschweren. Im Rahmen der vorliegenden Arbeit wurden experimentelle und numerische Untersuchungen zum Flüssig-Flüssig-Stoffübergang in einem vertikalen Kapillarspalt durchgeführt. Reaktionsfreie Stoffübergänge und solche mit einer exothermen chemischen Reaktion an der Phasengrenze zeigten eine große Vielfalt von Konvektionsstrukturen, wie Rollzellen, Thermiken und das doppeldiffusive Fingerregime. Die Visualisierung der Transportvorgänge erfolgte durch das Schattenschlierenverfahren. Die Beobachtungen wurden hinsichtlich geometrischer Eigenschaften von Konvektionsstrukturen sowie deren zeitlicher Änderung ausgewertet. Dazu zählten insbesondere das Längenwachstum von Thermiken und horizontale Wellenlängen von Fingerstrukturen. Zur mathematischen Beschreibung der Phänomene im Kapillarspalt wurde ein Modell entwickelt, welches auf den gekoppelten, zweidimensionalen Transportgleichungen von Impuls, Wärme und Stoff beruht. Es berücksichtigt dichte- und grenzflächenspannungsgetriebene Instabilitätsmechanismen sowie die besonderen Durchströmungseigenschaften des Kapillarspalts. Die Phasengrenze wurde als eben angenommen. Die Lösung der Modellgleichungen erfolgt auf numerischem Wege durch ein Computerprogramm. Das Modell ist in der Lage, die beobachteten Instabilitätsphänomene qualitativ richtig wiederzugeben. Mit Hilfe von Simulationsrechnungen konnte der Mechanismus aufgeklärt werden, der zum schnelleren Rückgang des Stoffdurchgangskoeffizienten im Rollzellenregime der rein grenzflächenspannungsgetrieben Instabilität im Vergleich zum Vorgang mit überlagerter Dichtekonvektion führt. Des Weiteren gelang der Nachweis des doppeldiffusiven Fingerregimes beim Stoffübergang mit exothermer Grenzflächenreaktion. Die berechnete Erhöhung des Stoffdurchgangskoeffizienten stimmt mit Angaben in experimentellen Arbeiten anderer Autoren überein.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-06-29T13:52:59Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) tese_final.pdf: 5635071 bytes, checksum: b300efb627e9ece412ad5936ab67e8e2 (MD5) / Made available in DSpace on 2016-06-29T13:52:59Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) tese_final.pdf: 5635071 bytes, checksum: b300efb627e9ece412ad5936ab67e8e2 (MD5) Previous issue date: 2013-08-26 / CNPq / No presente trabalho duas classes de problemas são abordadas. Primeiramente, são apresentados estudos computacionais sobre o modelo O(n) de spins na rede quadrada, e em seguida apresentamos novas soluções exatas para a dinâmica de bolhas na célula de Hele-Shaw. O estudo do modelo O(n) é feito utilizando sua representação em laços (cadeias fechadas), a qual é obtida a partir de uma expansão para altas temperaturas. Nesse representação, a função de partição do modelo possui uma expansão diagramática em que cada termo depende do número e comprimento total de laços e do número de (auto)interseções entre esses laços. Propriedades críticas do modelo de laços O(n) são obtidas através de conceitos oriundos da teoria de percolação. Para executar as simulações Monte Carlo, usamos o eficiente algoritmo WORM, o qual realiza atualizações locais através do movimento da extremidade de uma cadeia aberta denominada de verme e não sofre com o problema de "critical slowing down". Para implementar esse algoritmo de forma eficiente para o modelo O(n) na rede quadrada, fazemos uso de um nova estrutura de dados conhecida como listas satélites. Apresentamos estimativas para o ponto crítico do modelo para vários valores de n no intervalo de 0 < n ≤ 2. Usamos as estatísticas de laços e vermes para extrair, respectivamente, os expoentes críticos térmicos e magnéticos do modelo. No estudo de dinâmica de interfaces, apresentamos uma solução exata bastante geral para um arranjo periódico de bolhas movendo-se com velocidade constante ao longo de uma célula de Hele-Shaw. Usando a periodicidade da solução, o domínio relevante do problema pode ser reduzido a uma célula unitária que contém uma única bolha. Nenhuma imposição de simetria sobre forma da bolha é feita, de modo que a solução é capaz de produzir bolhas completamente assimétricas. Nossa solução é obtida por métodos de transformações conformes entre domínios duplamente conexos, onde utilizamos a transformação de Schwarz-Christoffel generalizada para essa classe de domínios. / In this thesis two classes of problems are discussed. First, we present computational studies of the O(n) spin model on the square lattice and determine its critical properties, whereas in the second part of the thesis we present new exact solutions for bubble dynamics in a Hele-Shaw cell. The O(n) model is investigated by using its loop representation which is obtained from a high-temperature expansion of the original model. In this representation, the partition function admits an diagrammatic expansion in which each term depends on the number and total length of loops (closed graphs) as well as on the number of intersections between these loops. Critical properties of the O(n) model are obtained by employing concepts from percolation theory. To perform Monte Carlo simulations of the model, we use the WORM algorithm, which is an efficient algorithm that performs local updates through the motion of one of the ends (called head) of an open chain (called worm) and hence does not suffer from “critical slowing down”. To implement this algorithm efficiently for the O(n) model on the square lattice, we make use of a new data structure known as a satellite list. We present estimates for the critical point of the model for various values of n in the range 0 < n ≤ 2. We use the statistics about the loops and the worm to extract the thermal and magnetic critical exponents of the model, respectively. In our study about interface dynamics, we present a rather general exact solution for a periodic array of bubbles moving with constant velocity in a Hele-Shaw cell. Using the periodicity of the solution, the relevant domain of the problem can be reduced to a unit cell containing a single bubble. No symmetry requirement is imposed on the bubble shape, so that the solution is capable of generating completely asymmetrical bubbles. Our solution is obtained by using conformal mappings between doubly-connected domains and employing the generalized Schwarz-Christoffel formula for this class of domains.

La dispersion de particules par une onde de souffle ou de choc induit la formation de structures régulières qui prennent la forme de jets de particules. Jusqu'à présent, les expériences n'ont été réalisées qu'en trois dimensions rendant difficile l'exploitation des données. Dans cette étude, une onde de souffle, générée à l'extrémité d'un tube à choc, débouche au centre d'un anneau de particules solides initialement confiné dans une cellule de Hele-Shaw. Pour la première fois, à partir d'une expérience de laboratoire, la formation de jets de particules est observée dans une configuration quasi bi-dimensionnelle et pour de faibles niveaux de pression. Grâce à un système de visualisation ultra-rapide, il a été mis en évidence que la sélection du nombre de jets de particules est un processus instationnaire. Nous avons observé que les jets de particules sont initialement formés à l'intérieur de l'anneau et sont ensuite expulsés à l'extérieur du front de particules en expansion. L'influence de nombreux paramètres, tels que la densité et le diamètre des particules, la surpression générée et la géométrie de l'anneau, ont été étudiées. La synthèse des résultats expérimentaux obtenus a permis d'établir certaines relations empiriques reliant le nombre de jets aux propriétés initiales. De plus, la formation de fines perturbations sur le front externe de la couche de particules a été observée. Ce phénomène est quant à lui indépendant des jets principaux et dépend seulement de la nature des particules. / The dispersion of particles by a blast or a shock wave induces the formation of coherent structures which take the form of particle jets. All the experiments conducted so far have been performed in three-dimensional geometry. In the present study, a blast wave, issuing from the discharge of a planar shock wave at the exit of a conventional shock tube, is generated in the center of a granular medium ring initially confined inside a Hele-Shaw cell. With the present experimental set-up, under impulsive acceleration, a solid particle jet formation is clearly obtained and observed in a quasi-two-dimensional configuration, for the first time. From fast flow visualizations, we highlighted that the selection of the number of jets is unsteady. We noticed, in all instances, that the jets are initially generated inside the particle ring and thereafter expelled outward. This point has not been observed in three-dimensional experiments. The influence of many parameters such as density and diameter of particles, the generated pressure and the geometry of the ring, has been studied. Empirical relationships were deduced from the experimental curves. Moreover, we observed in detail the formation of very thin perturbations created around the external surface of the dispersed particle layer. This phenomenon is independent of the main jet formation and solely depends on the nature of particles.

In verfahrenstechnischen Anlagen der Flüssig-Flüssig-Stoffübertragung kommt es an der Phasengrenze zwischen den nicht mischbaren Flüssigphasen häufig zur Ausbildung hydrodynamischer Instabilitäten. Sie sind mit komplexen Geschwindigkeitsfeldern in den Flüssigphasen, insbesondere in den grenzschichtnahen Regionen verbunden und führen zu einem starken Anstieg der pro Zeiteinheit übertragenen Stoffmenge. Die Lösung der Diffusionsgleichung reicht in diesem Fall zur Vorausberechnung des für Auslegungszwecke bedeutsamen Stoffdurchgangskoeffizienten nicht mehr aus. Chemische Reaktionen stellen Quellen oder Senken von Wärme und Stoff dar, die das Auftreten von Instabilitäten begünstigen und die mathematische Beschreibung zusätzlich erschweren. Im Rahmen der vorliegenden Arbeit wurden experimentelle und numerische Untersuchungen zum Flüssig-Flüssig-Stoffübergang in einem vertikalen Kapillarspalt durchgeführt. Reaktionsfreie Stoffübergänge und solche mit einer exothermen chemischen Reaktion an der Phasengrenze zeigten eine große Vielfalt von Konvektionsstrukturen, wie Rollzellen, Thermiken und das doppeldiffusive Fingerregime. Die Visualisierung der Transportvorgänge erfolgte durch das Schattenschlierenverfahren. Die Beobachtungen wurden hinsichtlich geometrischer Eigenschaften von Konvektionsstrukturen sowie deren zeitlicher Änderung ausgewertet. Dazu zählten insbesondere das Längenwachstum von Thermiken und horizontale Wellenlängen von Fingerstrukturen. Zur mathematischen Beschreibung der Phänomene im Kapillarspalt wurde ein Modell entwickelt, welches auf den gekoppelten, zweidimensionalen Transportgleichungen von Impuls, Wärme und Stoff beruht. Es berücksichtigt dichte- und grenzflächenspannungsgetriebene Instabilitätsmechanismen sowie die besonderen Durchströmungseigenschaften des Kapillarspalts. Die Phasengrenze wurde als eben angenommen. Die Lösung der Modellgleichungen erfolgt auf numerischem Wege durch ein Computerprogramm. Das Modell ist in der Lage, die beobachteten Instabilitätsphänomene qualitativ richtig wiederzugeben. Mit Hilfe von Simulationsrechnungen konnte der Mechanismus aufgeklärt werden, der zum schnelleren Rückgang des Stoffdurchgangskoeffizienten im Rollzellenregime der rein grenzflächenspannungsgetrieben Instabilität im Vergleich zum Vorgang mit überlagerter Dichtekonvektion führt. Des Weiteren gelang der Nachweis des doppeldiffusiven Fingerregimes beim Stoffübergang mit exothermer Grenzflächenreaktion. Die berechnete Erhöhung des Stoffdurchgangskoeffizienten stimmt mit Angaben in experimentellen Arbeiten anderer Autoren überein.