Le phénomène de coalescence. Etude bibliographique Coalescence Phenomena. A Review

Abstract

Nous présentons une revue des différents travaux expérimentaux et théoriques effectués sur le phénomène de coalescence en limitant principalement notre discussion au cas de la coalescence d'une goutte isolée à une interface plane ou déformable. La coalescence se divise en deux phases distinctes : le drainage et la rupture du film interfacial. Ce film est constitué du liquide de la phase continue séparant la goutte de l'interface. La condition de rupture est principalement contrôlée par les forces électrostatiques dues à la double couche et par les forces de Van der Waals. Les résultats expérimentaux mettent en évidence un phénomène de coalescence partielle ainsi que l'existence d'une distribution statistique du temps de coalescence. Ils montrent également l'influence complexe de nombreux paramètres physiques et physico-chimiques sur le temps de coalescence. On rappelle les principaux modèles théoriques décrivant le drainage et la rupture des films liquides. Ces modèles permettent, entre autre, d'aboutir à des expressions mathématiques reliant le temps de coalescence à des paramètres tels que la tension interfaciale, les densités et les viscosités des fluides, la taille des gouttes. The problem linked to the stability of oil-in-water emulsions (e. g. deoiling of water) and water-in-oil emulsions (e. g. dehydration of crudes) is one of the major problems encountered in the petroleum industry. From the thermodynamic standpoint, an emulsion is always unstable (Fig. I. 1). The kinematic stability characterizing the separation rate of the dispersed phase from the continuous phase can nonetheless be controlled by the coalescence of droplets present in the emulsion (Fig. I. 2). This article reviews various experimental and theoretical works on the phenomenon of coalescence but the discussion is limited mainly to the coalescence of an single drop at a flat or deformable interface. The coalescence of a single drop is governed by the drainage and rupture of the thin liquid film of continuous phase separating it from its homophase or from another drop. Let us consider the coalescence of a drop at an interface (Fig. I. 3). When the distance h between the drop and the interface becomes less or equal to the radius Rd of the drop (h < ou = Rd), the pressure inside the film increases. This pressure is responsible for the apparent immobilization of the drop, its deformation, and the drainage of the film. Depending on the case, the film can then reach either an extreme thickness hf or a critical thickness delta beyond which the film becomes unstable and breaks down. In the latter case there is coalescence. Experimental research has shown the existence of :(a) A statistical distribution of the coalescence time (Fig. I. 6). This distribution seems to be linked to the presence of impurities in the systems investigated. (b) A phenomenon of partial coalescence (Fig. I. 7). The coalescence of a drop generally occurs in several stages. The experimental results of several authors concerning the influence of physical and physicochemical parameters on the coalescence time are given in Table I. 1. Quantitative as well as qualitative differences can be seen (e. g. influence of the diameter of the drops). Drainage of the filmReynolds model (Fig. II. 1) : We consider the flow of a thin liquid film of viscosity µc between two parallel rigid disks of radius R and area A. The disks are pulled together by an external force F. The thinning rate Vre of the film and the coalescence time tau(re) are given by. In this model, the drainage of a film is governed by the viscous dissipations inside this film. In the more general case of a flat or curved film of constant thickness h, these expressions become here n, the number of immobile interfaces, can take the value 0,1 or 2 (Fig. II. 2). The mobilityor immobilityof the interfaces are defined by the following boundary conditions in which vr is the radial component of the fluid velocity. The mobility of an interface in governed by two factors :(a) The ratio of the dispersed-phase viscosity to the continuous-phase viscosity. (b) The gradient of concentration of the surfactants at the interfaces (Fig. II. 4). In reality, the interfaces are never either perfectly mobile or perfectly immobile. Therefore, the thinning rate expression given above must be altered. It is given by Eq. II. 16 for pure systems, and by Eq. II. 21 in the presence of surfactants. When the external force F corresponds to the forces of gravity, the area of the external film A depends on the Bond number Nbd (Fig. II. 6), given by where g, DeltaP, gamma and Psi represent the acceleration of gravity, the difference in density, the interfacial tension and the volume of the drop respectively. The general expressions of Vre and tau(re) are given in Table II. 1. During the coalescence of a drop, the thickness of the film is not uniform. Generally the thickness of the film reaches its maximum at the middle and its minimum at the outer edge (experimental results in Figs. II. 7-11; theoretical results - SLCH model - in Fig. II. 14). This is called the dimple phenomenon and it is due to the existence of a radial pressure gradient inside the film (Figs. II. 15-16). The thinning rate at the outer edge of the film differs from Vre only by a multiplicative constant (Eq. II. 39). Rupture of the filmThe thickness at which disturbances present at the interfaces may develop is called the critical thickness delta. If these disturbances do develop, the film becomes unstable and breaks down causing the coalescence of the drop. The conditions for film rupture are governed by the disjunction pressure Pi, which depends mainly on electrostatic intermolecular forces and Van der Waals forces. Some theoretical results for the critical thickness value and the corresponding coalescence time are given for different cases in the third section (Eqs. III. 12,16,17,18; Table III. 1). Theoretical models of the drainage and the rupture of thin liquid films may explain the experimental results. They allow one to clearly see the influence on the coalescence time of the following factors : the interfacial tension, the fluids density and viscosity, the drops size, the presence of surfactants, and the intermolecular forces.