Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Boundary integral simulations based on the vortex-sheet formalism for the discretization of sharp droplet interfaces in Hele-Shaw cells
Submission Author:
Rafael Menezes de Oliveira , RJ , Brazil
Co-Authors:
Rafael Menezes de Oliveira
Presenter: Rafael Menezes de Oliveira
doi://10.26678/ABCM.COBEM2023.COB2023-0963
Abstract
We track nonlinear deformations of liquid droplets confined in the parallel plates of a Hele-Shaw cell surrounded by a fluid of different viscosity. We apply an accurate boundary integral method based on the vortex-sheet formalism, which measures the jump of the tangential component of velocity as one crosses the interface. Because of Darcy’s law, the interior and exterior fluids are potential, and the bulk of both fluids is irrotational, making vorticity to be concentrated at the sharp interface between them. In addition, because of sharpness, vortex-sheet becomes a quantity better suited to access information regarding vorticity. It is defined at the interface between the fluids and is used to track the nonlinear deformations. The plane curve that describes the interface is constrained by surface tension and evolves according to its normal velocity, which depends on the vortex-sheet distribution. So, the vortex-sheet is used to describe the morphology of the interfacial patterns and needs to be calculated in every time step. In the current work, we discuss this methodology and present results of different Hele-Shaw flow configurations, including (i) Growth of viscous fingers by radial injection; (ii) Fingering formation driven by centrifugal effects in rotating Hele-Shaw cells; (iii) Deformations of magnetic droplets subjected to different external magnetic fields.
Keywords
Hele-Shaw cell, viscous fingering, Boundary integral method, surface tension
