A motion of freely oscillating droplet of a yield stress fluid: analysis and numerical studies
type: CreativeWork
description: This dissertation studies the problem of free small-amplitude oscillations of a droplet of a yield stress fluid under the action of surface tension forces. The problem is treated both analytically and numerically. In particular, we address the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. In this thesis, a variational inequality formulation is deduced for the problem of yield stress fluid dynamics with a free surface. The free surface is assumed to evolve with a normal velocity of the flow. We also consider capillary forces acting along the free surface. Based on the variational inequality formulation an energy equality is obtained, where kinetic and free energy rate of change is in balance with the internal energy viscoplastic dissipation and the work of external forces. Further, we consider free small-amplitude oscillations of a droplet of Herschel-Bulkley fluid under the action of surface tension forces. Under certain assumptions it is shown that the finite stopping time $T_f$ of oscillations exists once the yield stress parameter is positive and the flow index $\alpha$ satisfies $\alpha\ge1$. Results of several numerical experiments illustrate the analysis, reveal the dependence of $T_f$ on problem parameters and suggest an instantaneous transition of the whole drop from yielding state to the rigid one. In Charpter 1, we review the Navier-Stokes equations for motion of incompressible viscous fluid and consider different boundary conditions. We also discuss several approaches to recover the evolution of free interface. In Charpter 2, we derive a variational inequality formulation for the problem of yield stress fluid dynamics with a free surface. An energy balance follows from the variational inequality. In this chapter, we also describe a numerical method to simulate a non-Newtonian fluid flow with free surface. In Charpter 3, we apply the method of viscous velocity potentials to study the probl…
abstract: This dissertation studies the problem of free small-amplitude oscillations of a droplet of a yield stress fluid under the action of surface tension forces. The problem is treated both analytically and numerically. In particular, we address the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. In this thesis, a variational inequality formulation is deduced for the problem of yield stress fluid dynamics with a free surface. The free surface is assumed to evolve with a normal velocity of the flow. We also consider capillary forces acting along the free surface. Based on the variational inequality formulation an energy equality is obtained, where kinetic and free energy rate of change is in balance with the internal energy viscoplastic dissipation and the work of external forces. Further, we consider free small-amplitude oscillations of a droplet of Herschel-Bulkley fluid under the action of surface tension forces. Under certain assumptions it is shown that the finite stopping time $T_f$ of oscillations exists once the yield stress parameter is positive and the flow index $\alpha$ satisfies $\alpha\ge1$. Results of several numerical experiments illustrate the analysis, reveal the dependence of $T_f$ on problem parameters and suggest an instantaneous transition of the whole drop from yielding state to the rigid one. In Charpter 1, we review the Navier-Stokes equations for motion of incompressible viscous fluid and consider different boundary conditions. We also discuss several approaches to recover the evolution of free interface. In Charpter 2, we derive a variational inequality formulation for the problem of yield stress fluid dynamics with a free surface. An energy balance follows from the variational inequality. In this chapter, we also describe a numerical method to simulate a non-Newtonian fluid flow with free surface. In Charpter 3, we apply the method of viscous velocity potentials to study the probl…
author: Cheng, Wanli 1987-
language: eng
keywords: Free surface flows, Viscoplastic fluid, Herschel-Bulkley model, Oscillating drop, Finite stopping time
date published: 2017-12
date modified: 2026-07-24T02:31:52Z
provider: University of Houston
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Houston

PropertyValue
property ID: Handle
value: https://hdl.handle.net/10657/5684