Fig. 2: Cluster position becomes off-centered as the droplet size decreases.
a Typical examples of the droplet size dependence. Stable position of the cluster became off-centered in small droplets. Images were acquired 1 h after encapsulation. b Quantification of the cluster positioning symmetry. The polarity parameter DC-ratio is defined as the ratio of d to Rdroplet, where d is the distance from the droplet center to the cluster centroid, and Rdroplet is the radius of the droplet. DC-ratio is classified into two distinct regimes: larger than 0.5 is the “edge” and smaller than 0.2 is in the “center”. c–h Typical examples of the c–e inwardly and f–h outwardly directed motion of clusters after their formation (Supplementary Movies 10 and 11). The time point at which clusters started to move (typically  ~1 min after the cluster formation) is defined as 0 min. The clusters either rested near their initial positions or moved away from the initial positions. Only the clusters that moved are shown. Different colors in e and h indicate different clusters. i–k Droplet size dependence of cluster position. i Raw data of DC-ratio showing two-state positioning. The stable position depends on the droplet diameter. We analyzed bright-field images acquired more than 1 h after encapsulation. We performed two independent experiments (n = 176 droplets). j Histogram of DC-ratio for each 50 μm bins summarized from i. DC-ratio >  0.5, 0.5 ≥ DC-ratio ≥ 0.2, and 0.2 >  DC-ratio are colored in red, gray, and green, respectively. k Edge-positioned probability calculated from j. Filled circles and the solid curve represent experimental values and model fitting of Eq. (2), respectively. Experimental data were fitted by Eq. (2) using L = 6.1 μm and τ = 0.46 s. Transition diameter Dc = 85 μm at which edge-probability becomes 0.5 was estimated from the fitting curve. Scale bars, 100 μm.
