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Liquid pumping induced by transverse forced vibrations of an elastic beam: A lubrication approach

: Borcia, Rodica; Bestehorn, Michael; Uhlig, Sebastian; Gaudet, Matthieu; Schenk, Harald


Physical review fluids 3 (2018), No.8, Art. 084202, 17 pp.
ISSN: 2469-990X
ISSN: 2469-9918
Journal Article
Fraunhofer IPMS ()

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.