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

  • 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 aTwo 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.show moreshow less

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Metadaten
Author: Rodica Borcia, Michael BestehornGND, Sebastian Uhlig, Matthieu Gaudet, Harald SchenkORCiD
URL:https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.3.084202
DOI:https://doi.org/10.1103/PhysRevFluids.3.084202
ISSN:2469-990X
Title of the source (English):Physical Review Fluids
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2018
Tag:Microfluidic devices; Thin fluid films
Volume/Year:3
Issue number:8
Article number:084202
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Statistische Physik und Nichtlineare Dynamik
Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Mikro- und Nanosysteme
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