Capillary pumps with constant flow rate

This paper unambiguously derives, ab initio starting from the Navier-Stokes and Laplace equations, the geometric parameters defining capillary pumps (CPs) with rectangular cross section with constant volumetric flow rate and steady velocity profile. The parametric formulation of the channel shape is derived using Taylor series approximations of the capillary pressure and the hydrodynamic flow resistance with negligible error. First, the design parameters are derived for a CP consisting of a single channel and illustrated with an example. Thereafter, the design parameters for multichannel and for micropillar array CPs are derived. Finally, the design of CPs for multistep constant flow rates derived and those for arbitrarily varying flow rates are discussed.