The High Weissenberg Number Problem in Complex Fluids

• Grant number: 24/01651-0
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2024
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
• Principal Investigator: José Alberto Cuminato
• Grantee: José Alberto Cuminato
• Principal researcher abroad: Jonathan David Evans
• Institution abroad: University of Bath, England
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated researchers: Cassio Machiaveli Oishi ; Irineu Lopes Palhares Junior
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

Viscoelastic fluids have many different constitutive equations that relate stress and strain. The purpose of this project is to combine numerical and asymptotic techniques to deal with the numerical instabilities that arise for the different groups of constitutive equations in their simulation of benchmark flows.Accurately simulating the behavior of viscoelastic flows has proven to be a difficult task. The presence of the elastic properties imposes a memory aspect to the equations represented through the Weissenberg number. As the Weissenberg number increases, the elastic effects become more important, and all current numerical schemes become unstable. This computational challenge is known as the High Weissenberg Number Problem (HWNP) and is a major outstanding problem in the area of rheology.This project innovatively leverages the memory terms by formulating equations in Lagrangian formusing the generalized Lie derivative (GLD) and aligning the stress tensor along particle paths with natural stress variables. This combination of methodologies represents a unique attempt to enhance numerical stability in viscoelastic fluid simulations.Immediate beneficiaries of the work will be academics engaged in computations and experiments of viscoelastic fluids. These tend to be in the fields of chemical engineering, numerical analysis, and appliedmathematics. Others include industrial researchers who are involved in the simulation of viscoelasticfluids - this is vast, as it covers the areas of oil, chemical, food, and mineral industries.Due to the variety of models, the project sets out a direction for the long term fundamental researchof these types of complex viscoelastic fluids. The Bath PI will also lend his expertise in mathematicalmodelling to the Brazilian Study Group with Industry activities at the University of Sao Paulo. The SaoPaulo PI and co-researchers will attend the Bath doctoral centre (SAMBa) activities. (AU)