Dynamics of yield stress fluids: Drops, bubbles and foams
Abstract
Yield stress fluids, or as often referred to as "viscoplastic fluids", combine the behavior of solids and non-Newtonian viscous liquids depending on level of stress in material. Motivated by numerous fascinating applications of yield stress fluids in both industries and scientific researches, this thesis is focused on numerically and experimentally studying the dynamics of yield stress fluids. A computational program is developed based on Galerkin Finite Element method (G/FEM) and the elliptic mesh generation technique for solving dynamics of complex flows with yield stress fluids. Flow problems with Newtonian fluids, including the Drop-On-Demand drop formation with a square wave inflow condition and the slow dripping from a nozzle, are simulated by using this computational tool with 2D models and a robust remeshing algorithm developed by Suryo. A widely accepted mathematical model for yield stress fluids, Bingham fluid model, is incorporated in the G/FEM algorithm in order to extend the numerical algorithm to Bingham fluids. Due to the computational difficulty rooted from the discontinuity in original Bingham model. A regularized model, Panpanastasiou model, is thus applied in the computational code to avoid this issue. A numerical analysis of uni-directional flow with Bingham fluid in a slot is carried out to verify the numerical algorithm and the constitutive model by comparing simulation results with analytical solutions. This tool is used to analyse a more complex flow problem with free surface, which is the steady dripping with Bingham fluids. The co-existence of solid (unyielded) and liquid (yielded) regions in the fluids are predicted by simulations, and the evolution of and transition between solid and liquid regions determines the dynamics of drop formation. The elastic response of liquid foams which is particular type of yield stress fluid is experimentally studied by using a modern experimental technique, Stokes experiment technique. The elastic modulus of a liquid foam can be deduced from the measurements of the elastic force exerted on a solid sphere by the creeping foam flows past the sphere and the displacement of the sphere in foams. A thorough investigation on the effects of various experimental conditions, including the bead size and material, the translation velocity, the wall effect, and so on, are carried out in order to verify the success of this technique under various conditions. Furthermore, Stokes experiment technique is used as a tool to probe the effect of solid walls on the elastic modulus. The investigation shows that the foam near solid boundaries exhibits a smaller elastic modulus than foams far away from the boundary. In addition, Stokes experiment results also reveals that this technique can also be used to probe the viscous response of liquid foams by conducting experiments with a very fine foams and a large solid sphere. In order to generate and characterize foams for stokes experiment, an investigation of foam generation and characterization under various foaming conditions are carried out in this thesis.
Degree
Ph.D.
Advisors
Harris, Purdue University.
Subject Area
Chemical engineering
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