Segalman

Other combinations of upper- and lower-convected time derivatives of the stress tensor are also used to construct constitutive equations for viscoelastic fluids. For example, Johnson and Segalman (1977) have proposed the following equation... 

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. 

Jang SY, Reddy P, Majumdar A, Segalman RA (2006) Nano Lett 6 2362... 

Segalman RA, Yokoyama H, Kramer EJ (2001) Graphoepitaxy of spherical domain block copolymer films. Adv Mater 13 1152... 

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... 

The use of the Gordon-Schowalter derivative, equation (36), brings some discrepancies that can be easily pointed out considering the limiting case of e = 0 [58]. This case is known as the Johnson-Segalman equation ... 

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 ... 

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. 

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). 

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