The effects of shear and vorticity of the deformation of a drop

The theory for flow behavior of a single Newtonian drop under a uniform stress field was reviewed and applied to flow-induced deformation of the drop in an orthogonal rheometer flow system. This system was chosen in order to isolate the separate effects of the rate of deformation and vorticity on the drop shape and orientation. The results for a single drop were extended to predict the bulk rheological behavior of a dilute emulsion composed of two Newtonian phases. It is shown that the bulk behavior is non-Newtonian because of the deformation of the drops. The effect of vorticity on the components of bulk stress was investigated. It is shown that, as a rheometer, the orthogonal rheometer does not give a unique correspondence between stress and shear rate because of the contribution of vorticity. For instance, at any fixed value of the shear rate, the bulk stress may have multiple values, depending on the magnitude of the vorticity.