Capillary filling of active liquids

In this paper, we provide a theory for probing the horizontal and vertical circular capillary filling of an active liquid. The active liquid is characterized by the presence of active particles demonstrating vortex defects: such particles give rise to a circular polarization field, which induces a pressure gradient and a pressure-driven flow in the presence of an axial gradient of the activity (or the concentration of the active particles). For the present problem, there is a finite activity and a finite pressure inside the reservoir from where the capillary starts, and zero (or constant) activity and pressure at the migrating air–liquid interface of the filling column. Under such circumstances, there occurs a combined activity-gradient-driven and an imposed pressure-gradient-driven flow: the resulting wall-induced drag force (and the force due to gravity for vertical capillary filling) balances the driving capillary force, and one obtains the time variation of the filling length, characterizing the filling dynamics. In horizontal (vertical) capillary filling, the filling length is found to vary linearly (parabolically) with filling time and the filling rate is found to decrease with an increase in the relative contributions (dictated by the corresponding dimensionless groups) of the activity and the strength of the pressure-gradient (these two factors lead to a greater flow strength and hence a larger drag force on the filling column), and gravitational effects (for vertical capillary filling; gravitational effects also lead to a larger retarding force on the rising filling column in vertical capillary filling).