Capillary Flow in V-Shaped Grooves: From Flatland to Curved 3D Trajectories

Capillary flow in rectilinear V-shaped grooves inscribed on planar domains is finding 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 microfabrication can now be used to extend simple rectilinear trajectories in 2D to arbitrarily curved compact trajectories in 3D. This 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) elucidated how the streamwise gradient in capillary pressure due to the change in radius of curvature of the circular fluid interface caused by differences in local film thickness leads to rapid wicking of Newtonian films in slender rectilinear V-grooves. We present an analytic model which extends that original work to arbitrarily curved V-grooves in 3D. Despite the complex flow trajectories allowed, a first order perturbation analysis yields a compact equation for the moving interface. This advance should be of use to the design and implementation of next generation 3D fluidic devices.