We numerically investigate the rheological response of a noncoalescing multiple emulsion under a symmetric shear flow. We find that the dynamics significantly depends on the magnitude of the shear rate and on the number of the encapsulated droplets, two key parameters whose control is fundamental to accurately select the resulting nonequilibrium steady states. The double emulsion, for instance, attains a static steady state in which the external droplet stretches under flow and achieves an elliptical shape (closely resembling the one observed in a sheared isolated fluid droplet), while the internal one remains essentially unaffected. Novel nonequilibrium steady states arise in a multiple emulsion. Under low/moderate shear rates, for instance, the encapsulated droplets display a nontrivial planetarylike motion that considerably affects the shape of the external droplet. Some features of this dynamic behavior are partially captured by the Taylor deformation parameter and the stress tensor. Besides a theoretical interest on its own, our results can potentially stimulate further experiments, as most of the predictions could be tested in the lab by monitoring droplets’ shapes and position over time.
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