Transient response of velocity fluctuations in inertialess channel flows of viscoelastic fluids

Mihailo Jovanovic, Satish Kumar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We examine transient responses of velocity fluctuations in inertialess channel flows of viscoelastic fluids. Such fluids have broad applications in modern technology including the design and control of polymer processing operations and the development of strategies to efficiently mix fluids in microfluidic devices. For streamwise-constant three-dimensional fluctuations, we demonstrate analytically the existence of initial conditions that lead to quadratic scaling of the kinetic energy density with the Weissenberg number, We. This illustrates that in strongly elastic channel flows of viscoelastic fluids, velocity fluctuations can exhibit significant transient growth even in the absence of inertia. Furthermore, we show that the fluctuations in streamwise velocity achieve O(We) growth over a time scale O(We) before eventual asymptotic decay. We also demonstrate that the large transient responses originate from the stretching of polymer stress fluctuations by a background shear and draw parallels between streamwise-constant inertial flows of Newtonian fluids and streamwise-constant inertialess flows of viscoelastic fluids.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 American Control Conference, ACC 2010
Pages5682-5687
Number of pages6
StatePublished - Oct 15 2010
Event2010 American Control Conference, ACC 2010 - Baltimore, MD, United States
Duration: Jun 30 2010Jul 2 2010

Publication series

NameProceedings of the 2010 American Control Conference, ACC 2010

Other

Other2010 American Control Conference, ACC 2010
CountryUnited States
CityBaltimore, MD
Period6/30/107/2/10

Keywords

  • Elastic turbulence
  • Inertialess flows
  • Microfluidic mixing
  • Polymers
  • Transient response
  • Viscoelastic fluids

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  • Cite this

    Jovanovic, M., & Kumar, S. (2010). Transient response of velocity fluctuations in inertialess channel flows of viscoelastic fluids. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 5682-5687). [5531134] (Proceedings of the 2010 American Control Conference, ACC 2010).