Creeping sphere motion in Herschel-Bulkley fluids: flow field and drag

Abstract

The results of a comprehensive experimental study on the creeping sphere motion in Herschel-Bulkley model fluids are reported and discussed in this paper. A series of aqueous solutions of different grades of Carbopol resin have been used to encompass wide ranges of rheological model parameters. In particular, the size and shape of the sheared cavity surrounding a moving sphere and the drag behaviour have been investigated in this study. A laser-speckle tracer method was used to obtain information on the structure of the flow field about a sphere which, in turn, shows the size and shape of the underformed regions in the flow domain. The measured terminal velocity data together with the physical properties and dimensions have been used to deduce the values of drag coefficient as a function of the pertinent dimensionless groups. The paper is concluded by presenting extensive comparisons, of both sheared cavity characteristics and drag behaviour, between the present results and the literature correlations and/or data.