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When a globule with a complete symmetry (such as simple spherical droplets and concentric double emulsions) is transiting in a constriction tube, there is only one pattern of the transition. However, for a multiple-emulsion globule with asymmetric internal structures, there are many possible patterns with different pressure drops Δp due to various initial orientations of the inner droplets. In this paper, a boundary integral method developed recently is employed to investigate numerically the possible oriented transition of a globule with two unequal inner droplets in an axisymmetric microfluidic constriction. The transition is driven by an axisymmetric Poiseuille flow with a fixed volume flow rate, and the rheological behaviors of the globule are observed carefully. When the big inner droplet is initially located in the front of the globule, the maximum pressure drop during the transition is always lower than that when it is initially placed in the rear. Thus, a tropism-whereby a globule more easily gets through the constriction when its bigger inner droplet locates in its front initially-might exist, in which the orientating stimulus is the required pressure drops. The physical explanation of this phenomenon has also been analyzed in this paper.

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