Gravitational film

There are a number of relatively simple experiments with soap films that illustrate beautifully some of the implications of the Young-Laplace equation. Two of these have already been mentioned. Neglecting gravitational effects, a film stretched across a frame as in Fig. II-1 will be planar because the pressure is the same as both sides of the film. The experiment depicted in Fig. II-2 illustrates the relation between the pressure inside a spherical soap bubble and its radius of curvature by attaching a manometer, AP could be measured directly. 

A thin film of hydrocarbon spread on a horizontal surface of quartz will experience a negative dispersion interaction. Treating these as 1 = quartz, 2 = n-decane, 3 = vacuum, determine the Hamaker constant A123 for the interaction. Balance the negative dispersion force (nonretarded) against the gravitational force to find the equilibrium film thickness. 

Single-Bubble Regime Bubbles are produced one at a time, their size being determined primarily by the orifice diameter d, the interfacial tension of the gasdiquid film C, the densities of the liquid Pl and gas Pc, and the gravitational acceleration g according to the relation... 

X = distance film has fallen g = gravitational constant Pi = liquid density = latent heat of vaporization JL = liquid viscosity k = liquid thermal conductivity AT = temperature difference = (Tb bbi,p i -NrUj = local Nusselt number, h x/k, h = local heat transfer coefficient... 

When a drop (water) falls to a flat interface (benzene-water) the entire drop does not always join the pool (water). Sometimes a small droplet is left behind and the entire process, called partial coalescence, is repeated. This can happen several times in succession. High-speed motion pictures, taken at about 2000 frames per second, have revealed the details of the action (W3). The film (benzene) ruptures at the critical film thickness and the hole expands rapidly. Surface and gravitational forces then tend to drag the drop into the main pool (water). But the inertia of the high column of incompressible liquid above the drop tends to resist this pull. The result is a horizontal contraction of the drop into a pillar of liquid above the interface. Further pull will cause the column to be pinched through, leaving a small droplet behind. Charles and Mason (C2) have observed that two pinches and two droplets occurred in a few cases. The entire series of events required about 0.20 sec. for aniline drops at an aniline-water interface (C2, W3). 

Thus we would expect water to climb up the walls of a clean (i.e. water-wetting) glass vessel for a few millimetres but not more, and we would expect a sessile water droplet to reach a height of several mm on a hydrophobic surface, before the droplet surface is flattened by gravitational forces. The curved liquid border at the perimeter of a liquid surface or film is called the Plateau border after the French scientist who studied liquid shapes after the onset of blindness, following his personal experiments on the effects of sunlight on the human eye. 

Estimate the thickness of a water film of 0.1 mM NaCl solntion on a glass plate, 1 cm above a water reservoir. Assume that the water completely wets the glass and that the water/glass interface has an electrostatic potential of -60 mV and that only gravitational and electrical donble-layer forces need be considered. Also assnme that there is no snrface charge at the water/air interface. 

Another process which leads to HIPE instability is gravitational syneresis, or creaming, where the continuous phase drains from the thin films as a result of density differences between the phases. This produces a separated layer of bulk continuous phase and a more concentrated emulsion phase. The separated liquid can be located either above or below the emulsion, depending on whether the continuous phase is more or less dense, respectively, than the dispersed phase. This process has been studied by Princen [111] who suggests that it can be reduced by a number of parameters, including a high internal phase volume, small droplet sizes, a high interfacial tension and a small density difference between phases. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

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. 

There is no simple, direct relationship between elasticity and emulsion or foam stability because additional factors, such as film thickness and adsorption behaviour, are also important [204]. Nevertheless, several researchers have found useful correlations between EM and emulsion or foam stability [131,201,203], The existence of surface elasticity explains why some substances that lower surface tension do not stabilize foams [25]. That is, they do not have the required rate of approach to equilibrium after a surface expansion or contraction as they do not have the necessary surface elasticity. Although greater surface elasticity tends to produce more stable bubbles, if the restoring force contributed by surface elasticity is not of sufficient magnitude, then persistent foams may not be formed due to the overwhelming effects of the gravitational and capillary forces. More stable foams may require additional stabilizing mechanisms. 

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