Wall effect on the bubble behaviour in highly viscous liquids

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Abstract
A theoretical and experimental study is carried out for the problem of the wall effect experienced by a fluid body moving with a constant speed along the axis of a vertical circular tube filled with a highly viscous liquid. In the theoretical study the body is limited to being either spherical or cylindrical and an optimization process with least squares is used to write the no-slip condition on the tube wall. Comparisons between the hydrodynamic and kinematic behaviour of a rigid, liquid and gaseous body are established. Furthermore, from an experimental investigation, based upon a fine visualization technique and rising-speed measurements, the respective limits of validity of the calculations have been found in the case of an air bubble. Information concerned especially with the shape of this bubble, and the hydrodynamic field that it generates, is given for the whole domain of the bubble and tube diameter ratio ranging from no wall influence to maximum wall influence.