Biaxial nematic liquid crystals and their numerical solution

• Grant number: 19/04133-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: November 25, 2019
• End date: December 09, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Agreement: CONFAP ; Newton Fund, with FAPESP as a partner institution in Brazil ; UK Academies
• Principal Investigator: José Alberto Cuminato
• Grantee: José Alberto Cuminato
• Visiting researcher: James Clark St. Claire Sean McKee
• Visiting researcher institution: University of Strathclyde, Scotland
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

This project is concerned with the development of a numerical method for solving biaxial nematic liquid crystals subject to a strong magnetic field. The director is fixed by this field and is described by two angles. The first task is not difficult but extremely tedious: to derive the components of the stress tensor. A code will be constructed/extended from an existing code for uniaxial nematics. An analytic solution of simple shear flow between two plates will be constructed as a means of verifying the code. The question that we wish to answer in the three weeks available is what effect changing the direction of the magnetic field can have on the flow field. (AU)