Transient flow, birefringence

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

Optical measurements often have a greater sensitivity compared with mechanical measurements. Semidilute polymers, for example, may not be sufficiently viscous to permit reliable transient stress measurements or steady state normal stress measurements. Chow and coworkers [113] used two-color flow birefringence to study semidilute solutions of the semirigid biopolymer, collagen, and used the results to test the Doi and Edwards model discussed in section 7.1.6.4. That work concluded that the model could successfully account for the observed birefringence and orientation angles if modifications to the model proposed by Marrucci and Grizzuti [114] that account for polydispersity, were used. 

J. A. van Aken and H. Janeschitz-Kriegl, Rheol. Acta, Simultaneous measurement of transient stress and flow birefringence in one sided compression (biaxial extension) of a polymer melt, Rheol. Acta, 20,419 (1981). 

A.W. Chow, and G.G. Fuller, The rheo-optical response of rod-like chains subject to transient shear flow. Part I Model calculations on the effects of polydispersity, Macromolecules 18, 786 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like chains subject to transient shear flow. Part II. Two-color flow birefringence measurements, Macromolecules 18,793 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like shortened collagen protein to transient shear flow, Macromolecules, 18, 805 (1985). 

J.S. Lee and G.G. Fuller, The spatial development of transient couette flow and shear wave propagation in polymeric liquids by flow birefringence, J. of Non Newt. Fluid Mech., 26, 57 (1987). 

We have seen that flow birefringence is a powerful tool for studying steady and transient flows of molten polymers. This technique can also be used to assess local flow conditions during flow instabilities. These problems are specifically treated in Chapter III-4. We would just like to present here the potential of birefiingence techniques for such stupes. 

Extensional flow and structure-property relationships may also be studied by birefiringence. A particularly interesting application from transient flow is presented in Figure 2, where phenomena such as overshoot and ringing are observed (3). In this example we see results for 1.5% polyethylene oxide solution for three different velocity gradients. Birefringence detects the presence of an overshoot,... 

A. Chow, G. Fuller, D. Wallace, and J. Madri, Rheo-optical response of rod-like chains subject to transient shear flow 2. Two-color flow birefringence measurements on collagen protein. Macromolecules, 18,793-804,1985. 

In Section 10.8.1 it was noted that molecular orientation results in flow birefringence in a polarizable polymer, and if the melt is transparent, optical techniques can be used to determine the three components of the stress tensor in uniform, shear flows [91-93]. To determine the transient normal stress differences, the phase-modulated polarization technique was developed by Frattini and Fuller [ 126]. Kalogrianitis and van Egmond [ 127] used this technique to determine the shear stress and both the normal stress differences as functions of time in start-up of steady simple shear. Optical techniques are particularly attractive for measurements of normal stress differences, since such methods do not require the use of a mechanical transducer, whose compliance plagues measurements of normal stress differences by mechanical rheometry. 

The birefringence and isoclinic angles may be determined using the above methods. However, the rheologist usually desires the stresses. To do this, the stress-optic relation must be applied, as discussed in Section 20.2. The above discussion deals with steady flow situations. Transient flows (except those with very slow changes) need other methods and recently a number of new ideas have emerged. 

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

S. J. Johnson, P. L. Frattini and G. G. Fuller, Simultaneous dichroism and birefringence measurements of dilute colloidal suspensions in transient shear flow, J. Colloid Interface Sci., 104,440 (1985) S. J. Johnson and G. G. Fuller, Flowing colloidal suspensions in non-Newtonian suspending fluids decoupling the composite birefringence, Rheol. Acta, 25, 405 (1986). 

D. S. Pearson, A. D. Kiss, L. J. Fetters, andM. Doi, Flow-induced birefringence of concentrated polyisoprene solutions, J. Rheol., 33, 517 (1989) D. S. Pearson, E. Herbolzheimer, N. Grizzuti, and G. Marrucci, Transient behavior of entangled polymers at high shear rates, J. Polym. Sci., Part B, 29,1589 (1991). 

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