a b s t r a c tThe influence of matrix and droplet viscoelasticity on the steady deformation and orientation of a single droplet subjected to simple shear is investigated microscopically. Experimental data are obtained in the velocity-vorticity and velocity-velocity gradient plane. A constant viscosity Boger fluid is used, as well as a shear-thinning viscoelastic fluid. These materials are described by means of an Oldroyd-B, Giesekus, Ellis, or multi-mode Giesekus constitutive equation. The drop-to-matrix viscosity ratio is 1.5. The numerical simulations in 3D are performed with a volume-of-fluid algorithm and focus on capillary numbers 0.15 and 0.35. In the case of a viscoelastic matrix, viscoelastic stress fields, computed at varying Deborah numbers, show maxima slightly above the drop tip at the back and below the tip at the front. At both capillary numbers, the simulations with the Oldroyd-B constitutive equation predict the experimentally observed phenomena that matrix viscoelasticity significantly suppresses droplet deformation and promotes droplet orientation. These two effects saturate experimentally at high Deborah numbers. Experimentally, the high Deborah numbers are achieved by decreasing the droplet radius with other parameters unchanged. At the higher capillary and Deborah numbers, the use of the Giesekus model with a small amount of shear-thinning dampens the stationary state deformation slightly and increases the angle of orientation. Droplet viscoelasticity on the other hand hardly affects the steady droplet deformation and orientation, both experimentally and numerically, even at moderate to high capillary and Deborah numbers.

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An experimental study of drop dynamics under shear is conducted for five fluid pairs: a reference Newtonian system, two systems with a viscoelastic drop in a Newtonian matrix, one with a Newtonian drop in a viscoelastic matrix, all at drop to matrix viscosity ratio λ = 1.5, and a separate case at λ = 0.75. The viscoelastic liquids are either a Boger fluid or a shear-thinning viscoelastic fluid satisfying an Ellis model. Deborah numbers in the range 1 to 2 and a range of capillary numbers from low to above breakup conditions are addressed. The results focus on three aspects: relaxation after cessation of shear, a new viscoelastic drop breakup scenario, and the effect of shear flow history on drop breakup. Numerical simulations with the 3D volume-of-fluid PROST method complement the experimental results.

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