Discussion of Stokes' hypothesis through the smoothed particle hydrodynamics model

Andrea Colagrossi, Danilo Durante, Josep Bonet Avalos, and Antonio Souto-Iglesias
Phys. Rev. E 96, 023101 – Published 8 August 2017

Abstract

Stokes' hypothesis, the zeroing of the bulk viscosity in a Newtonian fluid, is discussed in this paper. To this aim, a continuum macroscopic fluid domain is initially modeled as a Hamiltonian system of discrete particles, for which the interparticle dissipative forces are required to be radial in order to conserve the angular momentum. The resulting system of particles is then reconverted to the continuum domain via the framework of the smoothed particle hydrodynamics (SPH) model. Since an SPH-consistent approximation of the Newtonian viscous term in the momentum equation incorporates interparticle radial as well as nonradial terms, it is postulated that the latter must be null. In the present work it is shown that this constraint implies that first and second viscosities are equal, resulting in a positive value for the bulk viscosity, in contradiction to the cited Stokes' hypothesis. Moreover, it is found that this postulate leads to bulk viscosity coefficients close to values found in the experimental literature for monoatomic gases and common liquids such as water.

  • Received 3 January 2017

DOI:https://doi.org/10.1103/PhysRevE.96.023101

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid Dynamics

Authors & Affiliations

Andrea Colagrossi*

  • CNR-INSEAN, Marine Technology Research Institute, Rome, Italy and Ecole Centrale Nantes, LHEEA Laboratory, Nantes, France

Danilo Durante

  • CNR-INSEAN, Marine Technology Research Institute, Rome, Italy

Josep Bonet Avalos

  • Department d'Enginyeria Química, ETSEQ, Universitat Rovira i Virgili, Tarragona, Spain

Antonio Souto-Iglesias

  • CEHINAV, DMFPA, ETSIN, Universidad Politécnica de Madrid, Madrid, Spain

  • *andrea.colagrossi@cnr.it

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 96, Iss. 2 — August 2017

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×