Ratcheting fluid pumps: Using generalized polynomial chaos expansions to assess pumping performance and sensitivity

A large diversity of fluid pumps is found throughout nature. The study of these pumps has provided insights into fundamental fluid dynamic processes and inspiration for the development of micro-fluid devices. Recent work by Thiria and Zhang [Appl. Phys. Lett. 106, 054106 (2015)] demonstrated how a reciprocal, valveless pump with a geometric asymmetry could drive net fluid flow due to an impedance mismatch when the fluid moves in different directions. Their pump's geometry is reminiscent of the asymmetries seen in the chains of contractile chambers that form the insect heart and mammalian lymphangions. Inspired by these similarities, we further explored the role of such geometric asymmetry in driving bulk flow in a preferred direction. We used an open-source implementation of the immersed boundary method to solve the fluid-structure interaction problem of a viscous fluid moving through a sawtooth channel whose walls move up and down with a reciprocal motion. Using a machine learning approach based on generalized polynomial chaos expansions, we fully described the model's behavior over the target 3-dimensional design space, composed of input Reynolds numbers (Rein), pumping frequencies, and duty cycles. Scaling studies showed that the pump is more effective at higher intermediate Rein. Moreover, greater volumetric flow rates were observed for near extremal duty cycles, with higher duty cycles (longer contraction and shorter expansion phases) resulting in the highest bulk flow rates.