Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

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

Journal Article · · International Journal of Non-Linear Mechanics
 [1];  [2]
  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
+ Show Author Affiliations
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.
Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC52-06NA25396
OSTI ID:
1375865
Report Number(s):
LA-UR--15-21025
Journal Information:
International Journal of Non-Linear Mechanics, Journal Name: International Journal of Non-Linear Mechanics Journal Issue: C Vol. 74; ISSN 0020-7462
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (22)

Analysis of steady state shearing and stress relaxation in the Maxwell orthogonal rheometer journal September 1968
Analysis of the Maxwell orthogonal rheometer journal January 1967
Kinematical concepts with applications in the mechanics and thermodynamics of incompressible viscoelastic fluids journal January 1962
Flow of viscoelastic fluids between rotating disks journal February 1992
On the flow of a simple fluid in an orthogonal rheometer journal July 1982
Flow and stability of a second grade fluid between two parallel plates rotating about noncoincident axes journal January 1981
An exact solution of the navier-stokes equation the vortex with curvilinear axis journal January 1982
Flow of K-BKZ fluids between parallel plates rotating about distinct axes: shear thinning and inertial effects journal January 1987
The flow of a second order fluid between rotating parallel plates journal January 1981
Unsteady flows of a class of novel generalizations of the Navier–Stokes fluid journal June 2013
A note on the flow of a Burgers’ fluid in an orthogonal rheometer journal November 2004
Generalizations of the Navier–Stokes fluid from a new perspective journal December 2010
Tensorial implicit constitutive relations in mechanics of incompressible non-Newtonian fluids journal February 2015
On implicit constitutive theories for fluids journal February 2006
Rheometrical flow systems Part 2. Theory for the orthogonal rheometer, including an exact solution of the Navier-Stokes equations journal January 1970
On Implicit Constitutive Theories journal August 2003
On a Class of Deformations of a Material with Nonconvex Stored Energy Function∗ journal January 1984
A class of motions with constant stretch history journal January 1971
On thermomechanical restrictions of continua
  • Rajagopal, K. R.; Srinivasa, A. R.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 460, Issue 2042 https://doi.org/10.1098/rspa.2002.1111
journal February 2004
Substantially Stagnant Motions journal March 1962
Studies of a Polymer Melt in an Orthogonal Rheometer journal March 1965
On the Properties of the Motion With Constant Stretch History Occurring in the Maxwell Rheometer journal December 1969

Cited By (3)

Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor journal February 2019
Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids journal March 2021
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

Similar Records

Stokes flow through a system of parallel infinite cylinders with axes oriented at an angle to the direction of mean flow
Technical Report · Fri Jul 18 00:00:00 EDT 1986 · OSTI ID:5521916
Helical screw rheometer: a new concept in rotational rheometry
Conference · Sat Dec 31 23:00:00 EST 1983 · OSTI ID:5330315
A viscoplastic constitutive theory for monolithic ceramics. 1
Journal Article · Wed Dec 31 23:00:00 EST 1997 · Journal of Engineering for Gas Turbines and Power · OSTI ID:290095

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Implicit constitutive theory
Non-Newtonian fluids
Orthogonal rheometer
Power law fluids
Stress power-law fluids