Semi-dilute polymer solutions in strong flows. Part I: Birefringence and flow modification in extensional flows. Part II: Chaotic mixing in time-periodic flows

Citation

Ng, Ricky Chiu-Yin (1990) Semi-dilute polymer solutions in strong flows. Part I: Birefringence and flow modification in extensional flows. Part II: Chaotic mixing in time-periodic flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/z6wv-9136. https://resolver.caltech.edu/CaltechETD:etd-05172007-154209

Abstract

Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

The non-Newtonian effects of semi-dilute polymer solutions in laminar two-dimensional steady and time-periodic strong flows are examined separately in two parts of this thesis. Strong flows are flows that can induce large deformation of the polymer molecules. The first part of this thesis is the study of flow-induced stretching of macromolecules in semi-dilute solutions and the subsequent modification to extensional flows in a two-roll and a four-roll mill. Experimental results are presented for flow birefringence, which provides a measure of the degree of polymer extension. In addition, we report on velocity gradient measurements via the technique of homodyne light scattering for solutions of various polymer concentrations in the dilute to semi-dilute regime. Model predictions are also discussed using an interacting dumbbell model. In the second part of the thesis, we examine fluid mixing and transport in two-dimensional time-periodic Stokes flows produced in a blinking two-roll mill (BTRM) for both Newtonian and polymer solutions. Here, we report experimental data obtained by the technique of flow visualization using dye tracer, as well as quantitative measurements using a digital imaging technique.

The flow birefringence results for 100, 1500, and 4500 ppm polystyrene in viscous solvents indicate that increasing concentration will inhibit stretching of polymer molecules due to strong intermolecular interactions. The birefringence data for all three solutions correlate with the eigenvalue of the velocity gradient tensor for different extensional flows in the 2-roll and the 4-roll mill. Inception and cessation of steady extensional flows show distinctive overshoots in birefringence for the semi-dilute (1500 and 4500 ppm) solutions. Complementary velocity gradient measurements show a significant inhibition of large strain rates when a sufficient amount of extended polymer is present (the dilute 100 ppm solution shows no flow effect). The onset of polymer-induced changes in the flow (flow modification) occurs at a critical effective volume concentration, [...] ~ 175, based upon the volume of spheres that circumscribe the extended polymer chain, for both semi-dilute solutions. The magnitude of flow modification is larger in the less concentrated 1500 ppm solution due to the competing effects of increasing concentration and the inhibition of polymer extension which tends to lower the effective volume concentration, [...]. The correlation of the magnitude of flow modification with [...] is revealed by the local (pointwise) velocity gradient measurements for different concentration polymer solutions.

Various molecular models for non-dilute polymer solutions are discussed. The best comparison with the present flow birefringence data is obtained from the predictions of an interacting nonlinear elastic dumbbell (FENE-IDB) model. The FENE-IDB model predictions show a smooth transition of dilute solution behavior to semi-dilute solution behavior. In dilute solutions, the birefringence normalized with polymer concentration (or specific birefringence) is independent of concentration, c. However, the specific birefringence is proportional to c(-1) when plotted versus the dimensionless eigenvalue of the velocity gradient tensor, [...], for semi-dilute solutions. We also noted that the relaxation time of polymer, [...], is dependent on c for semi-dilute solutions.

Studies of mixing and fluid transport properties in time-periodic laminar BTRM flows are first performed for Newtonian solutions. Fluid mixing is shown to be either regular or chaotic depending on the characteristic period of oscillation, µ. Chaotic (efficient) mixing is achieved globally in the flow device when µ >= 0.5. The results in the mixing study can be compared qualitatively with dynamical systems theory predictions of chaos in time-periodic vortex-pair flows. The effect of polymer (a 1500 ppm solution of polystyrene in viscous solvent) on chaotic mixing and fluid transport in the BTRM flows is an O(1) decrease in both the area of mixing and the rate of fluid transport between different regions of the flow when compared with the corresponding Newtonian data. The onset of the polymer effect on the flow occurs at a critical Deborah number of (De)c ~ 2. This high De effect may be related to polymer-induced changes to both the weak and strong flow regions in the BTRM since the time-periodic flow is alternatively strong and mostly weak in the Lagrangian frame of reference.

Thesis Files