  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.
