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

We present a general Lagrangian-Eulerian approach for modelling complex flu id Bows. Our method can track the microstructure evolution of complex fluid s under flow in a natural physical way. It is especially useful for mesosco pic modelling of complex fluids in which the characteristic time and length scales are usually several orders of magnitude higher than those for simpl e fluids. The method is illustrated by studying hydrodynamically interactin g two-dimensional concentrated emulsions under Couette flow. We have carrie d out the simulations of concentrated emulsions under shear over a range of capillary number (0.1 less than or equal to Ca less than or equal to 0.6) with a tired area fraction phi =0.4 and viscosity ratio, lambda = 1. The re sults show that concentrated emulsions exhibit the characteristics of visco elastic fluids, strong shear thinning of shear stress and tron-zero of firs t normal stress difference, Deformable drops can Elide past each other with less resistance than in the case of hard suspensions and hence reduce shea r stress. We have found that the dependence of the first normal stress diff erence on shear rate changes from quadratic to linear as the shear rate inc reases. In the regime of larger capillary numbers, highly inhomogeneous beh aviour of drops and the dumbbell shape of drops can be clearly observed, (C ) 1998 Elsevier Science B.V. All rights reserved.