A boundary-only approach to the deformation of a shear-thinning drop in extensional Newtonian flow

The influence of shear thinning on drop deformation is examined through a n umerical simulation. A two-dimensional formulation within the scope of the boundary element method (BEM) is proposed for a drop driven by the ambient flow inside a channel of a general shape, with emphasis on a convergent-div ergent channel. The drop is assumed to be shear thinning, obeying the Carre au-Bird model and the suspending fluid is Newtonian. The viscosity of the d rop at any time is estimated on the basis of a rate-of-strain averaged over the region occupied by the drop. The viscosity thus changes from one time step to the next, and it is strongly influenced by drop deformation. It is found that small drops, flowing on the axis, elongate in the convergent par t of the channel, then regain their spherical form in the divergent part; t hus confirming experimental observations. Newtonian drops placed off-axis a re found to rotate during the flow with the period related to the initial e xtension, i.e. to the drop aspect ratio. This rotation is strongly prohibit ed by shear thinning. The formulation is validated by monitoring the local change of viscosity along the interface between the drop and the suspending fluid. It is found that the viscosity averaged over the drop compares, gen erally to within a few per cent, with the exact viscosity along the interfa ce. Copyright (C) 2000 John Wiley & Sons, Ltd.