Nonlinear stationary viscosity

Whenever its dependence on the shear rate is studied,(y) is referred to as the nonlinear stationary viscosity. The CGS unit of the viscosity [g cm s ] is called poise. Its MKS unit is [kgms ]= [Pas]. 

Fig. 9.7 Deviation from the Cox-Merz rule. The frequency-dependent linear viscosity r](co) (solid lines) is compared to the nonlinear stationary viscosity rjsiiy) (broken lines). The quadratic /3(r) is assumed. The parameter /3q is varied from curve to curve. (Reprinted with permission from Ref. [17].)...

Fig. 9.14 Concepts of strain hardening, stress overshoot, and nonlinear stationary viscosity shown by...

Chapter 9 presents the transient network theory of associating polymer solutions, which is the other one of the two major theories treated in this book. It studies the dynamic and rheological flow properties of structured solutions from a molecular point of view. Thus, linear complex modulus, nonlinear stationary viscosity, start-up flows, and stress relaxation in reversible polymer networks are studied in detail. 

Figure 9.14(a) schematically shows the relation between strain hardening, stress overshoot, and the steady nonlinear viscosity in a shear-thinning regime. For a sufficiently high shear rate, the viscosity first shows an upward deviation due to strain hardening, followed by an overshoot peak, and then asymptotically decreases to the stationary value. The stationary viscosity is plotted in Figure 9.14(b). 

This chapter is devoted to the molecular rheology of transient networks made up of associating polymers in which the network junctions break and recombine. After an introduction to theoretical description of the model networks, the linear response of the network to oscillatory deformations is studied in detail. The analysis is then developed to the nonlinear regime. Stationary nonhnear viscosity, and first and second normal stresses, are calculated and compared with the experiments. The criterion for thickening and thinning of the flows is presented in terms of the molecular parameters. Transient flows such as nonhnear relaxation, start-up flow, etc., are studied within the same theoretical framework. Macroscopic properties such as strain hardening and stress overshoot are related to the tension-elongation curve of the constituent network polymers. 

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