A study of the Saffman-Taylor instability in viscoplastic fluids
department or school: Science, Faculty of
department or school: Mathematics, Department of
data provider: DSpace
degree campus: UBCV
creator: Dufresne, Ariel
issued: 2022-08-30T19:04:32Z
issued: 2022
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: This thesis aims to explore and understand the Saffman-Taylor instability at the interface of a Hershel-Bulkley fluid and air. We describe the flow in a Hele-Shaw cell theoretically and experimentally. For our theoretical analysis, we follow the usual Hele-Shaw approximations for incompressible flows with a Herschel-Bulkley constitutive law. We extend this model by allowing the fluid to slip on the smooth walls of the cell. We conduct a linear stability analysis for both planar and circular geometries and predict that effective slip stabilizes the interface. We also use numerical computations to examine the non-linear regime of a single finger in the planar geometry. We find that slip generates wider fingers and makes the plugged-up area at the roots of the fingers smaller and appear at later times. We conduct experiments using corn syrup as a control case and aqueous suspensions of Carbopol as a model Herschel-Bulkley fluid. The fluids are pumped into a Hele-Shaw cell through a circular vent, forming an initial disk in the cell. Then, we either pump air into the center of the disk, creating an expanding annulus, or we withdraw the disk through the vent. In both cases, the interface is in an unstable Saffman-Taylor configuration causing fingers to appear. We look at the effect of the type of cell wall, the gap size, the flux and the size of the initial disk. The instability and the observed patterns are very different between a cell with smooth or rough walls, confirming our theoretical prediction on the influence of effective slip. The trends with the other parameter variations are in reasonable agreement with the theoretical predictions.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/82596
note: A study of the Saffman-Taylorinstability in viscoplastic fluidsbyAriel DufresneB. Sc., University of British Columbia, 2020a thesis submitted in partial fulfillmentof the requirements for the degree ofMaster of Scienceinthe faculty of graduate and postdoctoralstudies(Mathematics)The University of British Columbia(Vancouver)August 2022© Ariel Dufresne, 2022The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:A study of the Saffman-Taylor instability in viscoplastic fluidssubmitted by Ariel Dufresne in partial fulfillment of the requirements forthe degree of Master of Science in Mathematics.Examining Committee:Neil Balmforth, Professor, Mathematics, UBCSupervisorMark Martinez, Professor, Chemical and Biological Engineering, UBCSupervisory Committee MemberiiAbstractThis thesis aims to explore and understand the Saffman-Taylor instabilityat the interface of a Hershel-Bulkley fluid and air. We describe the flowin a Hele-Shaw cell theoretically and experimentally. For our theoreticalanalysis, we follow the usual Hele-Shaw approximations for incompressibleflows with a Herschel-Bulkley constitutive law. We extend this model byallowing the fluid to slip on the smooth walls of the cell. We conduct a linearstability analysis for both planar and circular geometries and predict thateffective slip stabilizes the interface. We also use numerical computationsto examine the non-linear regime of a single finger in the planar geometry.We find that slip generates wider fingers and makes the plugged-up areaat the roots of the fingers smaller and appear at later times. We conductexperiments using corn syrup as a control case and aqueous suspensions ofCarbopol as a model Herschel-Bulkley fluid. The fluids are pumped into aHele-Shaw cell through a circular vent, forming an initial disk in the cell.Then, we either pump air into the center of the disk, creating an expandingannulus, or we wit…
has type: Thesis/Dissertation
date issued: 2022-11
is shown at: 10.14288/1.0418435
language: eng
degree discipline: Mathematics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Balmforth, Neil J.
type: Text
identifier URI: http://hdl.handle.net/2429/82596