TY - GEN A1 - Borcia, Rodica A1 - Bestehorn, Michael A1 - Uhlig, Sebastian A1 - Gaudet, Matthieu A1 - Schenk, Harald T1 - Liquid pumping induced by transverse forced vibrations of an elastic beam: A lubrication approach T2 - Physical Review Fluids N2 - Two liquid pumps are investigated theoretically and numerically: a single thin liquid layer actuated by a periodic force at an elastic beam and a two-layer geometry actuated by an elastic beam. For the second geometry, the beam actuates the liquid from both sides. For both pumps, the liquid film thickness is small compared to the lateral characteristic length of the system. A lubrication theory is developed. The Euler-Bernoulli equation for transverse deformations of an elastic beam is coupled to the fundamental hydrodynamic equations: the Navier-Stokes equation and a continuity equation in the long-wave approximation. In this way, one connects the transverse displacement of the beam with the hydrodynamic quantities (pressure, velocity fields, and flow rates). Appropriate boundary conditions incorporate the function of the valves. The derivation of the theoretical model is followed by numerical simulations. We estimate flow rates (in two and three spatial dimensions) for different system parameters and we compute the efficiency of a well-designed liquid pump. KW - Microfluidic devices KW - Thin fluid films Y1 - 2018 UR - https://opus4.kobv.de/opus4-UBICO/frontdoor/index/index/docId/22219 UR - https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.3.084202 SN - 2469-990X VL - 3 IS - 8 ER -