Effective foam viscosity

Effective Foam Viscosity For foam flowing in porous media, the foam s effective viscosity is that calculated from Darcy s law. This value is an approximation because foams are compressible and are also usually non-Newtonian. 

The superficial gas velocity Og is G/A, where A is the horizontal cross-sectional area of the empty vertical foam column. Also, g is the acceleration of gravity, p is the liquid density, p is the ordinary liquid viscosity and p, is the effective surface viscosity. 

This work shows that high shear rates are required before viscous effects make a significant contribution to the shear stress at low rates of shear the effects are minimal. However, Princen claims that, experimentally, this does not apply. Shear stress was observed to increase at moderate rates of shear [64]. This difference was attributed to the use of the dubious model of all continuous phase liquid being present in the thin films between the cells, with Plateau borders of no, or negligible, liquid content [65]. The opposite is more realistic i.e. most of the liquid continuous phase is confined to the Plateau borders. Princen used this model to determine the viscous contribution to the overall foam or emulsion viscosity, for extensional strain up to the elastic limit. The results indicate that significant contributions to the effective viscosity were observed at moderate strain, and that the foam viscosity could be several orders of magnitude higher than the continuous phase viscosity. 

A subsequent analysis [66] also employed this model, with the inclusion of results for the shear strain. The dependence of the viscous effects on initial foam orientation was also noted. Further work [67] on monodisperse wet foams, where is between 0.9069 and 0.9466, demonstrated that, under shear flow, the foam viscosity increased with increasing < > (decreasing liquid content). In contrast, for small deformations, the viscous contribution to the overall stress was found to be independent of liquid content. 

The stability of foams in constraining media, such as porous media, is much more complicated. Some combination of surface elasticity, surface viscosity and disjoining pressure is still needed, but the specific requirements for an effective foam in porous media remain elusive, partly because little relevant information is available and partly because what information there is appears to be somewhat conflicting. For example, both direct [304] and inverse [305] correlations have been found between surface elasticity and foam stability and performance in porous media. Overall, it is generally found that the effectiveness of foams in porous media is not reliably predicted based on bulk physical properties or on bulk foam measurements. Instead, it tends to be more useful to study the foaming properties in porous media at various laboratory scales micro-, meso-, and macro-scale. 

The critical analysis of the results on foam rheology, proposed by Heller and Kuntamukkula [16], has shown that in most of the experiments the structural viscosity depends on the geometrical parameters of the device used to study foam flow. This means that incorrect data about flow regime and boundary conditions, created at the tube and capillary walls, etc., are introduced in the calculation of viscosity (slip or zero flow rate). Most unclear remains the problem of the effect of the kind of surfactant and its surface properties on foam viscosity and on the regime of foam flow (cross section rate profile and condition of inhibition of motion at the wall surface). 

The foam-dilatational viscosity, K, arises because of two primary mechanisms (37) (1) viscous flow within the thin films, and (2) interfacial tension gradients acting along the foam bubble surfaces. The effect of interfacial tension gradients is to increase the foam viscosity as they impede flow near the surfaces of the thin foam films by contributing to a larger film stress. As in the wet foam (eq 6), the foam dilatational viscosity for a dry foam, K, is inversely proportional to film thickness as well (eq 9). 

Effective Viscosity. Considerable evidence indicates that in some gas-occupied channels, confined foam bubbles transport as bubble-trains. Effluent bubble sizes from 0.8-/ m2 Berea sandstone reflect expected sizes and their predicted shift with flow velocity (20). Likewise, pregenerated foam is reshaped to the same average exiting bubble size quite independent of the average inlet size (20). As with trapped foam, there is ample direct visual documentation of flowing foam bubble-trains in both micromodels (26) and in bead packs (9, 48). The flow resistance of transporting bubble-trains is best addressed in terms of an effective gas viscosity. 

Foam Mobility. The objective of foam is to control acid mobility in high permeability zones. The mobility of a given fluid (M) in a reservoir zone or layer is simply the ratio of the permeability of this zone to the effective fluid viscosity, which is given by Darcy s law as ... 

None of the studies summarized above were concerned with deactivation per se of these hydrocarbon-based antifoams. They are, therefore, limited in scope and do not fully address the issues concerning deactivation in general and deactivation by disproportionation in particular. There is, therefore, a need for systematic studies of this issue with antifoams prepared from different hydrophobic particles and oils where prolonged foam generation is combined with observations of the state of dispersion of the antifoam. Obviously, the role of particle sizes and shapes, state of aggregation in the oil, and resultant rheology, etc., should also be included. The oil types should be selected to include consideration not only of the effect of viscosity but also of their spreading behavior at air-water smfaces. 

It has been shown (16) that a stable foam possesses both a high surface dilatational viscosity and elasticity. In principle, defoamers should reduce these properties. Ideally a spread duplex film, one thick enough to have two definite surfaces enclosing a bulk phase, should eliminate dilatational effects because the surface tension of an iasoluble, one-component layer does not depend on its thickness. This effect has been verified (17). SiUcone antifoams reduce both the surface dilatational elasticity and viscosity of cmde oils as iUustrated ia Table 2 (17). The PDMS materials are Dow Coming Ltd. polydimethylsiloxane fluids, SK 3556 is a Th. Goldschmidt Ltd. siUcone oil, and FC 740 is a 3M Co. Ltd. fluorocarbon profoaming surfactant. 

Both high bulk and surface shear viscosity delay film thinning and stretching deformations that precede bubble bursting. The development of ordered stmctures in the surface region can also have a stabilizing effect. Liquid crystalline phases in foam films enhance stabiUty (18). In water-surfactant-fatty alcohol systems the alcohol components may serve as a foam stabilizer or a foam breaker depending on concentration (18). 

Pasteurizing of egg white could cause adverse effects on whipping properties. Whipping aids are presented as an optional ingredient in Hquid and frozen egg white. For example, triethylcitrate [77-93-OJ, 0 2 200, is sometimes added as a whipping aid, as well as a gum to increase viscosity and to improve stabiHty of the egg white foam. 

---