Advances in Hele-Shaw flows

• Ano de defesa: 2026
• Autor(a) principal: ABREU, Írio Menezes Rodrigues Coutinho
• Orientador(a): MIRANDA NETO, José Américo
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Pernambuco
• Programa de Pós-Graduação: Programa de Pos Graduacao em Fisica
• País: Brasil
• Palavras-chave em Português: Fluxo de Hele-Shaw; Extração de petróleo; Simulações numéricas; Fluidos Complexos; Dinâmica não linear
• Link de acesso: https://repositorio.ufpe.br/handle/123456789/68344

The Hele-Shaw cell is an experimental apparatus consisting of two parallel plates separated by anarrow gap, and is central to research in pattern formation, enhanced oil recovery, car bon capture,and storage due to its simplicity and controllability.When two immiscible fluids flow within this confined geometry, the interface often becomes unstable, producing intri cate, branchingpatterns.This thesis investigates abroad range of Hele-Shaw flow configura tions, examining how distinct physical mechanisms,forcing conditions,and fluid properties shape interfacial dynamics. This is performed by employing an analytical approach, based on perturbation theory, and a numerical one, with a novel, two-phase, sharp interface level set scheme. As interfacial instabilities can be detrimental to industrial applications, we pro posetwonewstrategiesforsuppressingtheirgrowth.Thefirstaimstostabilizetheinjection driven Saffman-Taylor instability, by rotating the entire Hele-Shaw cell. The second involves envelopingthecentralviscousdropletinaliftingHele-Shawcellconfigurationwithafluidof intermediate viscosity. We demonstrate that both schemes effectively suppress instabilities at the fluid-fluid interface. Beyond suppression, we explore ferrohydrodynamic flow, specif ically the pattern formation of a magnetorheological fluid annular structure under crossed magnetic fields, and the effects of misalignment between a ferrofluid droplet and the cen ter of an applied radial magnetic field. These studies suggest the possibility of controlling a magnetic fluid drop both rotationally and translationally. Additionally, we investigate the displacement of an off-centered dense fluid droplet in a centrifugally driven cell, produc ing translational motion of the droplet, and leading to a preferential growth direction of the emerging fingers. The thesis also addresses the impact of interfacial rheology on the finger ing patterns in rotating and lifting Hele-Shaw setups, showing that interfacial perturbations are stabilized in rotating flows, but promoted in lifting flows. We also incorporate the ef fects of normal stresses into the mathematical framework of Hele-Shaw flow by performing a proper gap-averaged calculation.Finally,we inspect the saturation profile of one-and two phase flows in the radial viscous fingering problem