Figure 4
From: Flow coupling between active and passive fluids across water–oil interfaces
Intradroplet circulatory flows were accompanied by the formation of a weak nematic layer in the microtubule network structure near the water–oil interface. A droplet (radius = 2.4 mm; height = 1 mm) was immersed in an oil layer of thickness (Δ) 2.4 mm and developed an intradroplet circulatory flow. (a) Microtubule network structures were imaged with a confocal microscope at three locations: the water–oil interface (blue), ~ 400 µm from the interface (red), and the droplet center (green). (b) Confocal image of the microtubule network at the droplet midplane. (c) Corresponding network structure extracted with the snake algorithm41. (d) Orientational distributions of microtubule bundles when intradroplet flows were circulating (solid, Δ ≈ 2.4 mm) and not circulating (dashed, Δ ≈ 1.1 mm). Blue, red, and green curves represent the locations within the droplet indicated in panel a. In circulating flows, most microtubule bundles near the interface were aligned at angles of ~ 15° from the interface (solid blue curve), and most microtubule bundles 400 µm from the interface were aligned at angles of ~ 45° (solid red curve). In noncirculating flows, the bundles were oriented isotropically (dotted curves). (e–j) Time-averaged velocity fields and vorticity maps of microtubule flows (panels e and h, plotted as in Fig. 1c), director fields and nematic order parameter (NOP) maps of microtubule bundles (panels f and i), and \(\sqrt {\user2{D}:\user2{D}}\) maps of microtubule network (panels g and j) near the water–oil interface. D is bundle orientational tensor defined as \(\user2{D} \equiv \langle\user2{pp}\rangle\) where p represents the orientation of a bundle segment. In Gao et al.’s model26, \(\sqrt {\user2{D}:\user2{D}}\) is proportional to magnitude of active stress \(\user2{\sigma }_{a}\) so \(\sqrt {\user2{D}:\user2{D}}\) maps can be interpreted as active stress maps. The first row (panels e–g) represents a droplet immersed in a 2.4-mm-thick oil layer, and the second row (panels h–j) represents a droplet immersed in a 1.1-mm-thick oil layer.
