The motion of macromolecules and immiscible drops in creeping flow

Citation

Olbricht, William Lee (1981) The motion of macromolecules and immiscible drops in creeping flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/jnx5-8786. https://resolver.caltech.edu/CaltechETD:etd-10052006-091257

Abstract

Experimental studies were conducted on the creeping motion of immiscible drops of a Newtonian liquid through a circular tube. The mobility of the drop, the additional pressure gradient owing to the presence of the suspended drop, and the deformation and breakup of the drop were determined as a function of the drop size, flow rate and viscosity ratio, for both Newtonian and viscoelastic suspending fluids. Two tube geometries were employed to generate kinematically distinct flows. First, the effects of density differences between the fluids were studied in a tube of constant diameter for comparison with available results for neutrally buoyant drops. Surprisingly small density differences produced highly eccentric drop positions, and the data, including the steady shape of the drop, were correlated with the gap width between the drop and the tube wall using simple lubrication approximations. The results suggest the presence of both viscometric and time-dependent non-Newtonian effects for the viscoelastic suspending fluid. Experiments were then conducted for the case where the diameter of the tube varies periodically with axial position. The conformation of the drop depends strongly on the value of the inverse capillary number. For small values of this parameter, the shape of the drop, and hence, the measured quantities were periodic and in-phase with the drop's passage through the oscillatory tube. When the inverse capillary number was large, a drop suspended in a Newtonian fluid became highly elongated and eventually broke into several fragments. Under the same conditions, a drop suspended in a viscoelastic fluid did not elongate, but instead, developed tails which issued satellite drops. The effect of increasing the polymer concentration in the suspending fluid was to stabilize the tails. The different conformations of the drop produced qualitatively different behavior for the additional pressure gradient and drop mobility. The observed dispersion processes appeared as onset phenomena at critical values of the material parameters.

The dynamics of fluid systems which are comprised of a suspended material in a Newtonian continuous phase were investigated theoretically. Important dynamical phenomena for such fluids are often a consequence of significant flow-induced deformation and/or orientation of the suspended elements. Hence, conditions under which large-scale distortion of the microstructure occurs were predicted via criteria for the flow strength, which is a measure of the form and magnitude of the velocity gradient tensor. The form of the criteria depends on the model chosen to describe the microstructure, but the properties which describe the specific fluid system enter only as parameters. Thus, the theoretical framework encompasses a wide class of fluids including macromolecular solutions and particulate suspension. Two examples illustrate the approach: the macromolecular stretching induced by a turbulent flow and the breakup of immiscible liquid drops in a shear field.

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