Capillary Flow Dynamics in Open Triangular Grooves: From Flatland to Curvy 3D Trajectories

Capillary flow in straight open triangular grooves finds widespread use in applications such as point-of-care biomedical devices, heat pipes for cooling microelectronics and spacecraft propellant management. Advances in 3D printing and other patterning techniques can now be used to fabricate compact open curved channels in 3D. This capability introduces the potential for multi-layer and multi-functional operation of many types of microfluidic and optofluidic chips. Romero and Yost (1996) and Weislogel (1996) first elucidated how the streamwise gradient in capillary pressure due to the change in curvature of the fluid interface due to local variations in film thickness induces rapid wicking of slender films into straight and open triangular grooves. Here we present an analytic model which extends that original work to arbitrarily curved open triangular grooves in 3D. Despite the complex flow trajectories which can ensue, a first order perturbation analysis yields a compact equation for the moving interface. This finding should be of use to the design and implementation of next generation 3D fluidic devices.