Fig. 1: Kinetics of liquid–liquid phase separation within fibrillar networks.

a Schematic depicting the phase separation of oil condensates within a fibrillar network. Blue represents water, tan represents ethanol, green represents agarose fibrils, and red represents decane. b Bright-field and fluorescence confocal microscopy time series showing the condensation of decane (bright-field and red) within a 0.8% w/w agarose network (green) (Supplementary Movies 1 and 2). Growth of the condensate within the fibrillar network occurs between (b_1–4), followed by network deformation (b₅), and finally fracture of the restraining element indicated by the arrow in (b₅), which leads to fluid rearrangement and expansion of a cavity within the network (b₆). c Evolution of the condensate in-plane area vs. time, where the in-plane area is determined from the bright-field images. Numbered red circles correspond to panels (b_1–3). Abrupt jumps are observed at t = 26 and 66 s, at numerals I and II. The corresponding regions are marked in (b₂) and (b₃). d Total in-plane area of all condensates in the full field-of-view movie as a function of time (Supplementary Movies 3 and 4). Area growth ceases by approximately t = 500 s, indicating that the oil solute has been fully depleted.