Foams hydrodynamic drainage

Of the three mechanisms, hydrodynamic drainage due to gravity is usually the most rapid and, if the foam is particularly unstable, leads to total collapse before other mechanisms can become important. In those cases, once the loss of liquid from the lamellar layer produces a critical thickness of 5-15 nm, the liquid film can no longer support the pressure of the gas in the bubble, and film rupture occurs. As a model for gravity drainage, a film may be treated as a vertical slit of thickness S (not to be confused with the solubility parameter... 

Practical mechanisms for extending the persistence of foams can include one or several of the following conditions (1) a high viscosity in the liquid phase, which retards hydrodynamic drainage, as well as providing a cushion effect... 

The role of the liquid crystal in stabilizing a foam can be related to its effect on several mechanisms involved in foam loss, including hydrodynamic drainage, the mechanical strength of the liquid film, and the diffusion rate of... 

The collapse of foam is attributed to (a) the diffusion of gas molecules from a small bubble with higher internal pressure to a large one with lower internal pressure or into the bulk gas phase surrounding the foam system, (b) coalescence of bubbles due to capillary flow that results in rupture of the lamellar film between the adjacent bubbles (usually slower than (a) and occurring even in stabilized foam system), and (c) rapid hydrodynamic drainage of liquid between bubbles that leads to rapid collapse of bubbles [35], In most nonrigid foam systems, all three mechanisms are operative simultaneously to some extent during the foam collapse process. 

When two emulsion drops or foam bubbles approach each other, they hydrodynamically interact which generally results in the formation of a dimple [10,11]. After the dimple moves out, a thick lamella with parallel interfaces forms. If the continuous phase (i.e., the film phase) contains only surface active components at relatively low concentrations (not more than a few times their critical micellar concentration), the thick lamella thins on continually (see Fig. 6, left side). During continuous thinning, the film generally reaches a critical thickness where it either ruptures or black spots appear in it and then, by the expansion of these black spots, it transforms into a very thin film, which is either a common black (10-30 nm) or a Newton black film (5-10 nm). The thickness of the common black film depends on the capillary pressure and salt concentration [8]. This film drainage mechanism has been studied by several researchers [8,10-12] and it has been found that the classical DLVO theory of dispersion stability [13,14] can be qualitatively applied to it by taking into account the electrostatic, van der Waals and steric interactions between the film interfaces [8]. 

To understand drainage we have to discuss the pressure inside the liquid films. At the contact line between liquid films, a channel is formed. This is called the Plateau border. Due to the small bending radius (rP in Fig. 12.18), there is a significant Laplace pressure difference between the inside of the compartment and the liquid phase. The pressure inside the liquid is significantly smaller than in the gas phase. As a result, liquid is sucked from the planar films into the Plateau s border. This is an important effect for the drainage of foams because the Plateau borders act as channels. Hydrodynamic flow in the planar films is a slow process [574], It is for this reason that viscosity has a drastic influence on the evolution of a foam. Once the liquid has reached a Plateau border the flow becomes much more efficient. The liquid then flows downwards driven by gravitation. 

Reynolds relation requires liquid drainage from the film to follow strictly the axial symmetry between parallel walls. Rigid surfaces ensure such drainage through their non-deformability, while non-equilibrium foam films are in fact never plane-parallel. This is determined by the balance between hydrodynamic and capillary pressure. Experimental studies have shown that only microscopic films of radii less than 0.1 mm retain their quasiparallel surfaces during thinning, which makes them particularly suitable for model... 

Langevin et al. [35,71] have proposed a simplified hydrodynamic model of thinning of microscopic foam films that accounts for the influence of surface elasticity on the rate of thinning in a large range of thicknesses and Ap. However, as noted by the authors, in view of the rapid loss of surfactant molecules at the surface during film drainage, the elasticity would not correspond to the actual bulk surfactant concentration but to lower values since the system is very far from equilibrium. Frequency dependence of surface elasticity has been considered by Tambe and Sharma [72]. 

The theoretical analysis indicated that asymmetric drainage was caused by the hydrodynamic instability being a result of surface tension driven flow. A criterion giving the conditions of the onset of instability that causes asymmetric drainage in foam films was proposed. This analysis showed as well that surface-tension-driven flow was stabilised by surface dilational viscosity, surface diffusivity and especially surface shear viscosity. 

The rate of foam drainage is determined not only by the hydrodynamic characteristics of the foam (border shape and size, liquid phase viscosity, pressure gradient, mobility of the Iiquid/air interface, etc.) but also by the rate of internal foam (foam films and borders) collapse and the breakdown of the foam column. The decrease in the average foam dispersity (respectively the volume) leads the liberation of excess liquid which delays the establishment of hydrostatic equilibrium. However, liquid drainage causes an increase in the capillary and disjoining pressure, both of which accelerate further bubble coalescence and foam column breakdown. 

In order to describe quantitatively the hydrodynamic phenomena occurring during foam drainage at high pressure drop as well as during surfactant solution flow through a high... 

A typical dependence of drainage onset on foam column height at foam expansion ratio n = 70 is given in Fig. 5.14. [6,22], For high foam columns (H > 16 cm) zb is small and does not practically depend on H. It is mainly determined by the hydrodynamic properties of the system (borders size and viscosity), i.e. of the microsyneresis rate. For small foam column heights t0 strongly depends on H and is determined by the rate of internal foam collapse. These dependences indicate that for a quantitative description of drainage detailed... 

In the process of reaching equilibrium during the liquid outflow from a foam in a centrifugal field, the expansion ratio increases in the direction opposite to the flow (towards the rotation centre) (Fig. 6.20). That is why the border profile acquires a shape that favours both the strong decrease in hydrodynamic resistance during foam drainage and the decrease in the time of reaching equilibrium pressure and equilibrium border radius. 

The rate of foam drainage is determined by the hydrodynamic characteristics of the foam, as well as the rate of internal foam collapse and breakdown of the foam column. Foam drainage is determined by measuring the quantity of liquid that drains from the foam per unit time. Various types of vessel and graduated tubes can be used to measure the quantity of liquid draining from a foam alternatively, changes in the electrical conductivity of the layer at the vessel mouth can be measured and compared to the electrical conductivity of the foaming solution [4]. 

Under the action of an outer driving force, the flnid particles approach each other. The hydro-dynamic interaction is stronger at the front zones and leads to a weak deformation of the interfaces in this front region. In this case, the nsnal hydrodynamic capillary number, Ca = V[VJa, which is a small parameter for nondeformable surfaces, should be modified to read Ca = y VJiJch, where the distance, h, between the interfaces is taken into account. The shape of the gap between two drops for different characteristic times was calcnlated numerically by many authors. " Experimental investigation of these effects for symmetric and asynunetric drainage of foam films were carried out by Joye et In some special cases, the deformation of the fluid particle can be... 

The mechanism of foam stability in these systems can be explained by the hydrodynamics of foam drainage (82). Because of the buoyancy of the... 

In the paper Effect of Surfactants on Drop Stability and Thin Film Drainage presented by Professor Krassimir Danov (Sofia University, Bulgaria) the stability of suspensions/emulsions is under consideration. Traditional consideration of colloidal systems is based on inclusion only Van-der-Waals (or dispersion) and electrostatic components, which is refereed to as DLVO (Derjaguin- Landau-Verwey-Overbeek) theory. Professor Danov s contribution shows that not only DLVO components but also other types of the inter-particle forces may play an important role in the stability and colloidal systems. Those contributions are due to hydrodynamic interactions, hydration and hydrophobic forces, steric and depletion forced, oscillatory structural forces. The hydrodynamic and colloidal interactions between drops and bubbles emulsions and foams are even more complex (as compared to that of suspensions of solid particles) due to the fluidity and deformability of those colloidal objects. The latter two features and thin film formation between the colliding particles have a great impact on the hydrodynamic interactions, the magnitude of the disjoining pressure and on the dynamic and thermodynamic stability of such colloidal systems. 

The presence of surfactants plays an important role in the drainage behavior of foam films, depending on the surface forces (the disjoining pressure) and hydrodynamic forces in their films [100]. The simultaneous action of disjoining pressure and hydrodynamie forees determines the stage of the formation... 

Essentially, the stability of the foam depends on the stability of the individual film, with champagne foams being a classic example of an unstable foam (Figure 2.2(a)). In this case, the lifetime is controlled by the drainage (hydrodynamics), but also gas diffusion and Oswald ripening probably play a role in destabilizing the system. 

Finally, we consider the hydrodynamic theory of thin liquid film rupture. The stability of the liquid films to a great extent is ensured by the property of the adsorbed surfactant to damp the thermally excited fluctuation capillary waves representing peristaltic variations in the film thickness [6]. In addition to the theory of stability of free foam and emulsion films, we consider also the drainage and stability of wetting films, which find application in various coating technologies [7]. 

---