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Title: Flow of “stress power-law” fluids between parallel rotating discs with distinct axes

Abstract

The problem of flow between parallel rotating discs with distinct axes corresponds to the case of flow in an orthogonal rheometer and has been studied extensively for different fluids since the instrument's inception. All the prior studies presume a constitutive prescription of the fluid stress in terms of the kinematical variables. In this paper, we approach the problem from a different perspective, i.e., a constitutive specification of the symmetric part of the velocity gradient in terms of the Cauchy stress. Such an approach ensures that the boundary conditions can be incorporated in a manner quite faithful to real world experiments with the instrument. Interestingly, the choice of the boundary condition is critical to the solvability of the problem for the case of creeping/Stokes flow. Furthermore, when the no-slip condition is enforced at the boundaries, depending on the model parameters and axes offset, the fluid response can show non-uniqueness or unsolvability, features which are absent in a conventional constitutive specification. In case of creeping/Stokes flow with prescribed values of the stress, the fluid response is indeterminate. We also record the response of a particular case of the given “stress power-law” fluid; one that cannot be attained by the conventional power-law fluids.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Univ. of Alberta, Edmonton, AB (Canada). Dept. of Statistical and Mathematical Sciences
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). EES-16: Computational Earth Science Group
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1375865
Report Number(s):
LA-UR-15-21025
Journal ID: ISSN 0020-7462
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
International Journal of Non-Linear Mechanics
Additional Journal Information:
Journal Volume: 74; Journal Issue: C; Journal ID: ISSN 0020-7462
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Stress power-law fluids; Power law fluids; Non-Newtonian fluids; Orthogonal rheometer; Implicit constitutive theory

Citation Formats

Srinivasan, Shriram, and Karra, Satish. Flow of “stress power-law” fluids between parallel rotating discs with distinct axes. United States: N. p., 2015. Web. doi:10.1016/j.ijnonlinmec.2015.04.004.
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Srinivasan, Shriram, & Karra, Satish. Flow of “stress power-law” fluids between parallel rotating discs with distinct axes. United States. https://doi.org/10.1016/j.ijnonlinmec.2015.04.004
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Srinivasan, Shriram, and Karra, Satish. Thu . "Flow of “stress power-law” fluids between parallel rotating discs with distinct axes". United States. https://doi.org/10.1016/j.ijnonlinmec.2015.04.004. https://www.osti.gov/servlets/purl/1375865.
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@article{osti_1375865,
title = {Flow of “stress power-law” fluids between parallel rotating discs with distinct axes},
author = {Srinivasan, Shriram and Karra, Satish},
abstractNote = {The problem of flow between parallel rotating discs with distinct axes corresponds to the case of flow in an orthogonal rheometer and has been studied extensively for different fluids since the instrument's inception. All the prior studies presume a constitutive prescription of the fluid stress in terms of the kinematical variables. In this paper, we approach the problem from a different perspective, i.e., a constitutive specification of the symmetric part of the velocity gradient in terms of the Cauchy stress. Such an approach ensures that the boundary conditions can be incorporated in a manner quite faithful to real world experiments with the instrument. Interestingly, the choice of the boundary condition is critical to the solvability of the problem for the case of creeping/Stokes flow. Furthermore, when the no-slip condition is enforced at the boundaries, depending on the model parameters and axes offset, the fluid response can show non-uniqueness or unsolvability, features which are absent in a conventional constitutive specification. In case of creeping/Stokes flow with prescribed values of the stress, the fluid response is indeterminate. We also record the response of a particular case of the given “stress power-law” fluid; one that cannot be attained by the conventional power-law fluids.},
doi = {10.1016/j.ijnonlinmec.2015.04.004},
journal = {International Journal of Non-Linear Mechanics},
number = C,
volume = 74,
place = {United States},
year = {Thu Apr 16 00:00:00 EDT 2015},
month = {Thu Apr 16 00:00:00 EDT 2015}
}
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https://doi.org/10.1016/j.ijnonlinmec.2015.04.004
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    Works referencing / citing this record:

    Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non-Fourier heat flux model: SHAMSHUDDIN et al.
    journal, October 2018

    • Shamshuddin, Md; Mishra, S. R.; Bég, O. Anwar
    • Heat Transfer-Asian Research, Vol. 48, Issue 1
    • DOI: 10.1002/htj.21392
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