A general approach for modelling complex fluids: its application to concentrated emulsions under shear

Abstract

We present a general Lagrangian–Eulerian approach for modelling complex fluid flows. Our method can track the microstructure evolution of complex fluids under flow in a natural physical way. It is especially useful for mesoscopic modelling of complex fluids in which the characteristic time and length scales are usually several orders of magnitude higher than those for simple fluids. The method is illustrated by studying hydrodynamically interacting two-dimensional concentrated emulsions under Couette flow. We have carried out the simulations of concentrated emulsions under shear over a range of capillary number (0.1≤Ca≤0.6) with a fixed area fraction φ=0.4 and viscosity ratio λ=1. The results show that concentrated emulsions exhibit the characteristics of viscoelastic fluids: strong shear thinning of shear stress and non-zero of first normal stress difference. Deformable drops can glide past each other with less resistance than in the case of hard suspensions and hence reduce shear stress. We have found that the dependence of the first normal stress difference on shear rate changes from quadratic to linear as the shear rate increases. In the regime of larger capillary numbers, highly inhomogeneous behaviour of drops and the dumbbell shape of drops can be clearly observed.