I. Dynamics of flowing polymer solutions. II. The measurement of velocity gradients by homodyne light scattering spectroscopy

Citation

Fuller, Gerald Gendall (1980) I. Dynamics of flowing polymer solutions. II. The measurement of velocity gradients by homodyne light scattering spectroscopy. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5PPN-JZ62. https://resolver.caltech.edu/CaltechETD:etd-12112006-152815

Abstract

This thesis is presented in two parts. In the first part the results of flow birefringence experiments and modelling efforts on both concentrated and dilute polymer solutions are discussed. The second part presents theoretical developments and complementary experiments which demonstrate the utility of the technique of homodyne light scattering spectroscopy to the measurement of velocity gradients in laminar flow fields.

The flow birefringence experiments were performed using a four roll mill which was designed in order to allow the simulation of a wide range of two dimensional flows ranging from purely extensional flows to purely rotational flows. Flow visualization and homodyne light scattering spectroscopy experiments were used to characterize the flow fields.

Using this device the flow birefringence of concentrated polyethylene/water and polystyrene/tricresyl phosphate solutions was measured. Birefringence measurements of the Polyox solutions over a wide range of flow types indicated that the birefringence could be well correlated against the eigenvalue of the velocity gradient tensor, in agreement with model calculations. Transient experiments were performed in which the birefringence was measured as purely extensional flows were started from rest. Both polymer/solvent systems showed a pronounced overshoot in the birefringence. Turbidity measurements were also performed on the polyox solutions and a 30% increase in the turbidity was measured which persisted for many hours after the cessation of flow (whereas the birefringence decayed to zero in a fraction of a second). This increased turbidity and its persistence with time suggests the occurence of flow induced crystallization of the polymer.

These experiments involving concentrated polymer systems were compared to model calculations using the Yamamoto network theory. Several choices of the polymer entanglements creation and destruction functions were analyzed and it is demonstrated that analytical results can be obtained using these choices. A variety of nonlinear phenomena can be predicted including the correlation of the of purely extensional flows. The predicted response of the stress tensor is also presented and discussed.

Flow birefringence experiments were also carried out in the dilute concentration range. Measurements were taken on three molecular weight samples (2-8x10^6 MW, MW/MN=1.14-1.3) in a viscous polychlorinated biphenyl solvent in the range of 50-100 ppm subjected to a wide range of two dimensional flows. The birefringence was again found to be well correlated against the eigenvalue of the velocity gradient tensor. The normalized birefringence, corrected for concentration, ([delta]n/nc), was observed to approach a saturation value at high velocity gradients in purely extensional flow. This saturation value was independent of both the molecular weight and the concentration c, in agreement with theory. In addition, the magnitude of the saturation value is consistent with nearly fully extended chains and suggests extensions in the range of 20-50 times the rest state size. The experiments were complemented by simple dumbbell model calculations which incorporated the nonlinear spring, internal viscosity and variable hydrodynamic friction. The model was found to simulate the experimental data very well if the effects of molecular weight distribution and finite transit times in the flow were taken into account.

The results of a detailed investigation of the dumbbell model used to analyze the dilute solution experiments is also included. The effects of the nonlinear spring, variable friction factor and internal viscosity to the response of the dumbbell to steady state and transient two dimensional flows are exposed. A perturbation solution for the dumbbell with a small amount of internal viscosity is presented and it is demonstrated that this problem can be solved analytically.

The technique of homodyne light scattering spectroscopy applied to suspensions in laminar flow is investigated. It is demonstrated both theoretically and experimentally that use of this method allows direct measurement of velocity gradients without the need for differentiating velocity data which is the normal method used. This technique was used to characterize the spatial distribution of velocity gradients existing in the four roll mill simulating purely extensional flow.

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