Transient shear viscosity, defined

Figure 4 shows the transient evolution of the extensional viscosity at varying strain rates for PHA Sample I. The plots follow the start-up to reach a steady state plateau value. At short times, the curves fall on top of one another. At high strain rates, we observe a slight decrease in the steady state extensional viscosity for both PHA samples. This could indicate that the two PHA samples are strain-rate thinning, as predicted by the Doi-Edwards tube model [9]. The Trouton Ratio (Tr), defined as the ratio of the extensional viscosity to the zero-shear viscosity of the polymer, was also investigated for the two PHA samples. For both PHA samples, the Trouton Ratio maintained the Newtonian value of Tr=3 at low strain rates. 

The superscript indicates that the shear rate was increased from zero at time t = 0. This definition is only meaningful if the fluid at time r = 0 is in a well-defined state, usually a stress-free state, and if this starting state and the transient viscosity are reproducible from one run to the next. The superscript -p is sometimes omitted. Measurements of t) give information about rates of structural rearrangement within a deforming complex fluid. 

In the United Kingdom the Ministry of Defence (MOD) has issued specifications DTD 5628-5633, which cover test procedures and performance requirements for a range of products. Five strength bands and four viscosities, from penetrating to thixotropic, are defined. The torque strengths are tested on M8 nuts and bolts and the shear strength in 12-mm pins and collars. The development of these specifications and the test procedures have been described by C. L. Brett at the MOD. The breakloose torque on nuts and bolts requires particular attention to a transient measurement where the first torsional motion is detected. Other products show somewhat different behavior, with no distinct breakloose, and the torque at which the sealant begins to yield is not easily detected [77]. British Standard BS 5292 relates to the use of anaerobic sealants on gas appliances. 

To is a terminal relaxation time describing chain motions. Other global relaxation times can be defined experimentally, for example as the inverse of the frequency of the maximum in the terminal dispersion in the loss modulus, Tmax from the time for equilibration following cessation of nonlinear shear flow, XR rj, measured by recovery of the overshoot in the transient viscosity the corresponding time for recovery of the overshoot in the second normal... 

Equation (10) cannot be applied until A, the equivalent relaxation time for the fluid, is known. However, A is defined by the linear Maxwell model, and actual polymer solutions exhibit marked nonlinear viscoelastic properties [5,6,7]. For both fresh and shear degraded solutions of Separan AP 30 polyacrylamide, which exhibit pronounced drag reduction in turbulent flow, Chang and Darby [8] have measured the nonlinear viscosity and first normal stress functions, and Tsai and Darby [6] have reported transient elastic properties of similar solutions, A nonlinear hereditary integral function containing six parameters has been proposed to represent the measured properties [8], The apparent viscosity function predicted by this model is ... 

Just as the Deborah number is often used to plot data or predictions for transient tests at finit rates, the Weissenberg number (Wi) is used for a similar purpose for representing stresses that are independent of time. This is defined as the product of a time scale governing the onset of nonlinearity, let s call it /I, and the rate of strain of the experiment. We will see in the next section that a fluid that has a shear-rate dependent viscosity must have at least one material constant with units of time. For example, one might select the reciprocal of the shear rate at which the viscosity falls to 60% of its zero-shear value. This time then characterizes the nonlinearity of the behavior for this flow. Obviously, the degree to which a melt deviates from Newtonian behavior depends on how this time constant compares with the rate of the deformation. Thus, the Weissenberg number in simple shear flow is defined as ... 

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