Anomalous diffusion of hydrocarbon vapor through an aqueous foam bubble structure

Abstract

Hydrocarbons are known as “anti-foamers” because they cause bubble rupture, coalescence, and reduce foaming. We show that the dynamics of bubble structure allows hydrocarbon vapors permeate rapidly when an aqueous foam is placed on a hydrocarbon pool. Two distinct foam layers are formed. Vapor accumulates in an expanding bottom layer at the foam-pool interface where bubbles grow rapidly, rupture, and coalesce. Simultaneously, vapor diffuses through a top layer having small bubble structure, which changes slowly due to Ostwald-ripening. Very little vapor accumulates in the top layer, which has a constant thickness equal to the initial foam thickness. Surprisingly, both accumulation in the bottom layer and diffusion through top layer occur at constant rates, which are independent of time and initial foam thickness. The vapor diffusion rate in the top layer should have decreased, inversely proportional to the initial foam thickness, based on classical diffusion theory; only the fluorosurfactant containing foam (RefAFFF) placed on gasoline follows the classical theory where the bottom foam layer is absent. Therefore, we propose a theory to show a linear increase in diffusion time with initial foam thickness using an effective diffusion-coefficient. Experiments show that this variation could be because of increased liquid drainage, drying, and bubble coarsening, which are not considered explicitly in the theory. We also describe a theory for the expanding bottom layer to show that most vapor formed at the pool surface accumulates for very volatile hydrocarbons. The vapor diffusion controls foam ignition. We show that the measured foam ignition time also increases linearly with initial foam thickness, qualitatively consistent with the predicted diffusion time. By employing different hydrocarbons, we show that the measured foam ignition times decrease inversely proportion to square root of hydrocarbon vapor concentration for a given surfactant. This could be because a surfactant exhibits different degrees of oleophobicity towards different hydrocarbons that can reduce vapor adsorption, solubility, and diffusion at a bubble surface. Different surfactants also exhibit different degrees of oleophobicity towards a given hydrocarbon (n-pentane) and increase ignition times by a factor of six: RefAFFF having the longest ignition time, followed by siloxane-polyoxyethylene formulation, and its individual surfactant components.