Numerical simulations of linear viscoelasticity of monodisperse emulsions of Newtonian drops in a Newtonian fluid from dilute to concentrated regime

The bulk viscoelastic properties of monodisperse emulsions of Newtonian drops in a Newtonian matrix subjected to small amplitude oscillatory shear (SAOS) flow are investigated by means of arbitrary Lagrangian Eulerian finite element method 3D numerical simulations. Volume fractions of the suspended phase from the dilute to the concentrated regime (up to 30 %), and a range of several orders of magnitude of the drops-to-matrix viscosity ratio and of the frequency of the oscillatory flow are examined; the eventual presence of slip between the two fluids is also considered. The computational results are compared with theory, yielding a quantitative agreement with Oldroyd (Proc R Soc Lond A 218:122-132, 1953) predictions in a wide range of values of the considered parameters, even well beyond the dilute regime, and also in the cases with slip.