Numerical simulations of two-phase electroosmotic viscoelastic flows on hierarchical grids

Author(s)

Daniel Garcia Leal Raymundo

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2024-12-20

Examining board members

Antonio Castelo Filho; Wesley de Souza Bezerra; Luis Jorge Lima Ferras; Leandro Franco de Souza

• Advisor: Antonio Castelo Filho

Abstract

This work investigates the numerical modeling and two-dimensional simulation of electroosmotic singlephase and two-phase flows involving complex fluids in rectangular channels with no pressure difference. We explore and implement partial differential equation systems considering various viscoelastic regimes and fluid permittivity configurations. We encompass both the Poisson-Nernst-Planck (PNP) and the Poisson-Boltzmann (PB) models for charge distribution, coupled to the Navier-Stokes equations, to constitutive models for viscoelastic fluids, and to the interface transport by Volume-of-Fluid with Piecewise-Linear Interface Construction. The numerical framework is implemented in the HiG-Flow system, which simulates incompressible flows in hierarchical cartesian meshes of arbitrary refinement represented by generalized trees with interpolations by a robust meshless moving least squares method. Results demonstrate distinct temporal evolution patterns between the PNP and PB approaches, and reveal significant effects of viscoelasticity on flow development, particularly for high Debye parameters. In two-phase systems, we analyze droplet deformation under both neutral and electroosmotic shear, exploring the impact of permittivity variations between matrix and droplet fluids. Our results suggest that the Korteweg-Helmholtz force may play a crucial role in interface deformation patterns, while viscoelasticity demonstrates itself capable of moderating surface tension effects and stabilizing deformations in uniform and non-uniform permittivity cases. This work intends to contribute to the understanding of electrokinetic phenomena in complex multiphase systems and provides a step for future applications in microfluidic devices. (AU)

• FAPESP's process: 22/07717-7 - Numerical simulations of biphasic viscoelastic electro-osmotic flows on hierarchical grids
• Grantee: Daniel Garcia Leal Raymundo
• Support Opportunities: Scholarships in Brazil - Master