On the transient motion of ordered suspensions of liquid drops

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Abstract
The transient motion of ordered suspensions of liquid drops, initially arranged on a cubic lattice, is studied as a model of suspension rheology. An asymptotic three-term expansion for the effective stress tensor of a dilute suspension of spherical drops is derived based on the Faxén law for the stresslet. Comparisons with available exact results for cubic lattices suggests that the expansion is remarkably accurate even at concentrations close to maximum packing. The behaviour of suspensions with recurrent structure evolving under the influence of a simple shear flow is investigated, and the results show that the time-averaged behaviour may differ substantially from the instantaneous behaviour. Transient normal stress differences may vanish in the mean, but make appreciable contributions to the instantaneous dynamics. The effect of particle deformation is assessed by numerically computing the motion of initially spherical drops arranged on a cubic lattice. At large times, the suspension is shown to exhibit periodic motions in which the drops oscillate about a mean shape with a phase shift which depends on the geometry of the lattice and the physical properties of the fluids. It is shown that drop deformations cause shear thinning and some type of elastic behaviour, and may lower the effective viscosity of the suspension below that corresponding to the dilute limit.