  We numerically study the dynamic behavior under a symmetric shear flow of
selected examples of concentrated phase emulsions with multi-core morphology
confined within a microfluidic channel. A variety of new nonequilibrium steady
states is reported. Under low shear rates, the emulsion is found to exhibit a
solid-like behavior, in which cores display a periodic planetary-like motion
with approximately equal angular velocity. At higher shear rates two steady
states emerge, one in which all inner cores align along the flow and become
essentially motionless and a further one in which some cores accumulate near
the outer interface and produce a dynamical elliptical-shaped ring chain,
reminiscent of a treadmilling-like structure, while others occupy the center of
the emulsion. A quantitative description in terms of i) motion of the cores,
ii) rate of deformation of the emulsion and iii) structure of the fluid flow
within the channel is also provided.
