Low Reynolds number flows of active liquids in permeable, long, and thin capillaries

In this Letter, we develop an analytical theory to study the transport of active liquids, which contain active and self-propelling particles (with vortex defects), inside a long and thin permeable capillary tube. This transport is triggered by a pressure gradient induced by an imposed gradient in the activity (or the particle concentration). Our results show a clear distinction in the radial and axial velocity profiles between the pressure-driven transport of active (with either extensile or contractile activity) and non-active liquids inside such permeable capillaries. We also identify the stream function characterizing the active liquid velocity field inside such permeable tubes.