Why Capillary Flows in Slender Triangular Grooves Are So Stable Against Disturbances

Abstract

Ongoing development of fuel storage and delivery systems for space probes, interplanetary vehicles, satellites and orbital platforms continues to drive interest in propellant management systems that utilize surface tension to retain, channel and control flow in microgravity environments. Although it has been known for decades that capillary flows offer an ideal method of fuel management, there has been little research devoted to the general stability properties of such flows. In this work, we demonstrate theoretically why capillary flows which channel wetting liquids in slender open triangular channels tend to be very stable against disturbances. By utilizing the gradient flow form of the governing fluid interface equation, we first prove that stationary interfaces in the presence of steady flow are asymptotically nonlinearly and exponentially stable in the Lyapunov sense. We then demonstrate that fluid interfaces exhibiting self-similar Washburn dynamics are transiently and asymptotically linearly stable to small perturbations. This second finding relies on a generalized non-modal stability analysis due to the non-normality of the governing disturbance operator. Taken together, these findings reveal the robust nature of transient and steady capillary flows in open grooved channels and likely explains the prevalent use of capillary flow management systems in many emerging technologies ranging from cubesats to point-of-care microfluidic diagnostic systems.