Johnson-Segalman model

The connection between the double value of the slip parameter obtained from the viscometric functions and the violation of the Lodge-Meissner rule becomes more evident when the time-strain separability of the model is considered. For this purpose, the Johnson-Segalman model can be rewritten under the form of a single integral equation, cancelling the Cauchy term, which gives the following form in simple shear flows ... 

Problem 3.14 (Worked Example) Derive expressions for the shear viscosity and first and second normal stress coefficients in steady-state shearing of the Johnson-Segalman model, given by Eqs. (3-80) and (3-8 la). 

Radulescu O, Olmsted PD (2000) Matched asymptotic solutions for the steady banded flow of the diffusive johnson-segalman model in various geometries. J Non-Newt Fluid Mech 91(2-3) 143-164... 

A. Arsac, C. Carrot, J.Guillet, P.Revenu, Problems originating from the use of the Gordon-Schowalter derivative in the Johnson Segalman and related models in various shear flow situations, J. Non-Newt. Fluid Mech. 55 (1994), 21-36. 

Johnson, M. W. and Segalman, D., 1977. A model for viscoelastic fluid behaviour which allows non-affine deformation. J. Non-Newtonian Fluid Mech. 2, 255-270. 

Using this derivative in the former UCM model, Johnson and Segalman proposed a model [48] that improves the predictions especially in shear, leading to normal stress differences and shear viscosity which are now shear rate dependent. Unfortunately, although it appears to be attractive in shear, the use of such a derivative can lead to some physical paradoxes that will be discussed... 

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