Studies of Flow Modification and Polymer Conformation in Extensional Flows of Dilute Polymer Solutions
<p>This is a study of the coil-stretch transition of macromolecules in dilute solutions which are subjected to extensional flows and of the effects of the polymer molecules on the flow fields. The flow fields are produced in a four-roll mill, two-roll mills of several different gap width to ro...
| Summary: | <p>This is a study of the coil-stretch transition of macromolecules in dilute solutions which are subjected to extensional flows and of the effects of the polymer molecules on the flow fields. The flow fields are produced in a four-roll mill, two-roll mills of several different gap width to roller radius ratios, and a cylindrical Couette device. These flows are laminar, and approximately two-dimensional linear flows covering the range of flow types with different amounts of extension and vorticity from pure extension to simple shear flow. The two-roll mills were constructed to extend the previously accessible range of flow types to those with only slightly more extension than vorticity, <i>i.e.</i>, much nearer to simple shear flow. The flows are characterized by using homodyne light scattering spectroscopy to directly measure velocity gradients fields. The degree of polymer extension is monitored using flow birefringence measurements.</p>
<p>Studies using 100 ppm polystyrene in viscous solvents show that the flow birefringence data for all the different strong flows (simple shear is a weak flow) correlate with the eigenvalue of the velocity gradient tensor. Extensional flow birefringence data for the same polymer in different solvents correlate with the Zimm relaxation time based on the intrinsic viscosity. When the polymers are sufficiently extended there is a distinct onset of measurable decreases in the velocity gradients. A necessary condition for this to occur is a very high level of domain overlap between the extended molecules. If we estimate this by the volume concentration of circumscribed spheres, φ<sub>eff</sub> (i.e., the sphere diameter equals the extended length of the polymer), the onset of an effect of polymer on the flow does not occur until φ<sub>eff</sub> ~ 4000-6000. Nevertheless, our measurements show that dilute polymer solutions do inhibit the development of large strain rates in regions of persistent extensional flow.</p>
<p>Studies using sodium polystyrenesulfonate in glycerol with various amounts of added sodium chloride show the range of coil-stretch behavior that can occur as a function of the equilibrium conformation of the polyelectrolyte. With high ionic strength solutions, the polyelectrolyte behavior is the same as that of nonionic polymers. As the ionic strength decreases and the equilibrium dimensions increase, the onset of the coil-stretch transition shifts to much lower shear rates. With no added salt, the expanded coil approaches free-draining behavior with a monotonic increase of flow birefringence with increasing shear rate instead of the distinct onset point usually observed. These low ionic-strength solutions also exhibit overshoots in the birefringence on startup of simple shear flow.</p>
<p>The flow birefringence data have been compared with predictions of the nonlinear elastic dumbbell model with various combinations of constant or conformation-dependent friction laws, internal viscosity, strain-inefficient rotation, and Coulombic charges on the beads. It seems that <i>all</i> of the models studied work well in pure extension where the coil-stretch process largely governed by the limited amount of total strain (or finite residence time) in the flow. However, in flows with considerable vorticity, the details of the hydrodynamic interaction between beads and solvent and the rotational motion of the deforming dumbbell become very important in determining the behavior of the model. Thus the birefringence data in the flows near simple shear flow provide more stringent tests of the models than flows with no vorticity. In flows slightly more extensional than simple shear flow, none of the more advanced models gives entirely satisfactory comparisons with the data. In this flow regime, the best comparisons with data are obtained with the simple FENE dumbbell. Some evidence that the current modeling approach (and conformation-dependent hydrodynamic friction) is basically sound was found. The charged dumbbell model is able to describe the large difference in behavior between highly charged polyelectrolytes and those with excess added salt only if a conformation-dependent friction law is included.</p> |
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