Mechanisms of Foam Flow in Porous Media: Apparent Viscosity in Smooth Capillaries

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Abstract
The apparent viscosity of foam flowing through smooth capillaries was measured experimentally, and a mathematical model was developed. Foam texture (a measure of bubble volume) is a key parameter in determining the following properties of foam flowing through a capillary: (1) whether the foam exists as bulk foam or as a chain of bubbles where each pair of bubbles is separated by an individual lamella, (2) the number of lamellae per unit length of the capillary, and (3) the radius of curvature of the gas-liquid interface. The apparent viscosity is the sum of three contributions: (1) that from slugs of liquid between bubbles, (2) the resistance to deformation of the interface of a bubble passing through a capillary, and (3) the surface tension gradient that results when surface active material is swept from the front of a bubble and accumulates at the back of it. The sensitivity of both measured and calculated apparent viscosity is presented as a function of bubble size, capillary radius, ratio of bubble radius to capillary radius, velocity, quality, and surface tension gradient.

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