Dynamics of Thin Films Near Singularities Under the Influence of Non-Newtonian Rheology

Vishrut Garg, Purdue University

Abstract

Free surface flows where the shape of the interface separating two fluids is unknown apriori are an important area of interest in fluid dynamics. The study of free surface flows such as the breakup and coalescence of drops, and thinning and rupture of films lends itself to a diverse range of industrial applications, such as inkjet printing, crop spraying, foam and emulsion stability, and nanolithography, and helps develop an understanding of natural phenomena such as sea spray generation in oceans, or the dynamics of tear films in our eyes. In free surface flows, singularities are commonly observed in finite time, such as when the radius of a thread goes to zero upon pinchoff or when the thickness of a film becomes zero upon rupture. Dynamics in the vicinity of singularities usually lack a length scale and exhibit self-similarity. In such cases, universal scaling laws that govern the temporal behavior of measurable physical quantities such as the thickness of a film can be determined from asymptotic analysis and verified by high-resolution experiments and numerical simulations. These scaling laws provide deep insight into the underlying physics, and help delineate the regions of parameter space in which certain forces are dominant, while others are negligible. While the majority of previous works on singularities in free-surface flows deal with Newtonian fluids, many fluids in daily use and industry exhibit non-Newtonian rheology, such as polymer-laden, emulsion, foam, and suspension flows. The primary goal of this thesis is to investigate the thinning and rupture of thin films of non-Newtonian fluids exhibiting deformation-rate-thinning (power-law) rheology due to attractive intermolecular van der Waals forces. This is accomplished by means of intermediate asymptotic analysis and numerical simulations which utilize a robust Arbitrary Eulerian-Lagrangian (ALE) method that employs the Galerkin/Finite-Element Method for spatial discretization. For thinning of sheets of power-law fluids, a significant finding is the discovery of a previously undiscovered scaling regime where capillary, viscous and van der Waals forces due to attraction between the surfaces of the sheet, are in balance. For thinning of supported thin films, the breakdown of the lubrication approximation used almost exclusively in the past to study such systems, is shown to occur for films of power-law fluids through theory and confirmed by two dimensional simulations. The universality of scaling laws determined for rupture of supported films is shown by studying the impact of a bubble immersed in a power-law fluid with a solid wall. Emulsions, which are fine dispersions of drops of one liquid in another immiscible liquid, are commonly encountered in a variety of industries such as food, oil and gas, pharmaceuticals, and chemicals. Stability over a specified time frame is desirable in some applications, such as the shelf life of food products, while rapid separation into its constituent phases is required in others, such as when separating out brine from crude oil. The timescale over which coalescence of two drops of the dispersed phase occurs is crucial in determining emulsion stability.

Degree

Ph.D.

Advisors

Basaran, Purdue University.

Subject Area

Condensed matter physics|Fluid mechanics|Materials science|Mechanics|Physics|Polymer chemistry|Theoretical physics

COinS