Nonlinear Interface Equation For Capillary Driven Flow in 3D Open Curved Trajectories

Capillary driven flow of wetting liquids in open V-grooves and interior corners is known to be an especially robust and rapid means of fluid transport in gravity free environments and in small scale systems where gravity plays a negligible role. Nowadays, such flows are routinely used for propellant management in space based systems, lab-on-a-chip devices and high performance chip with micro heat pipes. The low-order inertia-free model developed by Romero and Yost (1996) and Weislogel (1996) first elucidated the flow behavior of an incompressible Newtonian liquid in a straight V-groove whose length far exceeds the film thickness. Here we present an extension of this classic work to flow in 3D open and curved channels in which the trajectory radius of curvature is larger than the film thickness. Despite the complexity of trajectories allowed by this model, a first-order perturbation analysis of the governing conservation equation yields a surprisingly simple form of the nonlinear equation governing the behavior of the moving interface. This thin film equation can now be used to design determininistic flow trajectories for ultracompact microfluidic systems featuring arbitrarily curved 3D channel flows.