Arrested segregative phase separation in capillary tubes

Abstract

Phase separation in a capillary tube with one of the phases fully wetting the capillary wall is arrested when the typical size of the phase domains reaches the value of the diameter of the tube. The arrested state consists of an alternating sequence of concave-capped and convex-capped cylindrical domains, called "plugs," "bridges," or "lenses," of wetting and nonwetting phase, respectively. A description of this arrested plug state for an aqueous mixture of two polymer solutions is the subject of this work. A phase separating system consisting of two incompatible polymers dissolved in water was studied. The phase volume ratio was close to unity. The initial state from which plugs evolve is characterized by droplets of wetting phase in a continuous nonwetting phase. Experiments show the formation of plugs by a pathway that differs from the theoretically well-described instabilities in the thickness of a fluid thread inside a confined fluid cylinder. Plugs appear to form after the wetting layer (the confined fluid cylinder) has become unstable after merging of droplet with the wetting layer. The relative density of the phases could be set by the addition of salt, enabling density matching. As a consequence, the capillary length can in principle be made infinitely large and the Bond number (which represents the force of gravity relative to the capillary force) zero, without considerably changing the interfacial tension. Using the possibility of density matching, the relations among capillary length and capillary diameter on the one hand, and the presence of plugs and their average size on the other were studied. It was found that stable plugs are present when the capillary radius does not exceed a certain value, which is probably smaller than the capillary length. However, the average plug size is independent of capillary length. At constant capillary length, average plug size was found to scale with the capillary diameter to a power 1.3, significantly higher than the expected value of 1. Plug sizes had a polydispersity between 1.1 and 1.2 for all capillary radii for which this number could be reliably determined, suggesting a universal plug size distribution. Within plug sequences, size correlations were found between plugs with one to three plugs in between. This suggests the presence of an additional length scale.