plateau region is at low pressure. The continuous liquid phase is held to the bubble surfaces by the surfactant molecules that make up the solution being foamed. This fixation is important because otherwise the foam becomes very unstable as the liquid drains into the plateau region making the lamellae thin. Once the lamellae become too thin they will rupture. Theory Young-Laplace equation As vapor bubbles form in a liquid solvent, interfacial tension causes a pressure difference, Δp, across the surface given by the Young-Laplace equation. The pressure is greater on the concave side of the liquid lamellae (the inside of the bubble) with radius, R, dependent on the pressure differential. For spherical bubbles in a wet foam and standard surface tension , the equation for the change in pressure is as follows: As the vapor bubbles distort and take the form of a more complex geometry than a simple sphere, the two principal radii of curvature and would be used in the following equation: As pressure grows inside the bubbles, the liquid lamellae shown in the figure above will forced to move toward plateau borders causing a collapse of the lamellae. Gibbs adsorption isotherm The Gibbs adsorption isotherm can be used to determine the change in surface tension with changing concentration. Since chemical potential varies with a change in concentration, the following equation can be used to estimate the change in surface tension where is the change in surface tension of the interface, is the surface excess of the solvent, is the surface excess of the solute (surfactant), is the change in chemical potential of the solvent, and is the change in chemical potential of the solute: For ideal cases, and the created foam is dependent on the change in chemical potential of the solute. During foaming, the solute experiences a change in chemical potential as it goes from the bulk solution to the foam surface. In this case, the following equation can be applied where is the activity of the surfactant, is the gas constant, and is the absolute temperature: In order solve for the area on the foam surface occupied by one adsorbed molecule, , the following equation can be used where is the Avogadro constant. Applications Wastewater treatment Continuous foam separation is used in wastewater treatment to remove detergent-derived foaming agents such as ABS, which became common in wastewater by the 1950s. In 1959 it was shown