The Visco-Elastic Behavior of Confined Liquid Films in the Direction Normal to the Plane of the Film

Abstract

When a thin film of liquid is confined between parallel rigid plates and stressed in a direction normal to the plane of the film, visco-elastic behavior is obtained provided the rate of loading is sufficiently high. The measured (apparent) complex modulus is always higher than three times the complex shear modulus (the value to be expected for shear behavior) but less than the complex bulk modulus. For sinusoidal loading, linear visco-elastic theory predicts an approximate relationship between the measured complex modulus, the complex shear modulus, and the degree of confinement of the liquid as given by the radius/thickness ratio of the film. The ratio of the measured complex modulus to the complex shear modulus, when both are measured at the same temperature and rate of loading (frequency), is predicted to be proportional to the square of the radius/thickness ratio of the film when this ratio is greater than one. Complex modulus measurements under sinusoidal loading on a petroleum bitumen, a silicone oil, and water have confirmed the validity of this relationship.