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

Rodica Borcia, Michael Bestehorn, Sebastian Uhlig, Matthieu Gaudet, and Harald Schenk
Phys. Rev. Fluids 3, 084202 – Published 20 August 2018

Abstract

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.

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  • Received 31 January 2018
  • Corrected 19 February 2019

DOI:https://doi.org/10.1103/PhysRevFluids.3.084202

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Fluid Dynamics

Corrections

19 February 2019

Correction: Minor errors in Eqs. (28) and (31) have been fixed.

Authors & Affiliations

Rodica Borcia* and Michael Bestehorn

  • Chair of Statistical Physics and Nonlinear Dynamics, Brandenburg University of Technology, Cottbus-Senftenberg, 03046 Cottbus, Germany

Sebastian Uhlig, Matthieu Gaudet, and Harald Schenk

  • Chair Micro- and Nanosystems, Brandenburg University of Technology, Cottbus-Senftenberg, 03046 Cottbus, Germany and Fraunhofer Institute for Photonic Microsystems, ISS, Cottbus, 03046 Cottbus, Germany

  • *borciar@b-tu.de

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Issue

Vol. 3, Iss. 8 — August 2018

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