Responsable: Francisco Guillén González
Tipo de Proyecto/Ayuda: Plan Nacional del 2009
Referencia: MTM2009-12927
Fecha de Inicio: 01-01-2010
Fecha de Finalización: 31-10-2013

Empresa/Organismo financiador/es:

• Ministerio de Ciencia e Innovación

Equipo:

• Investigadores:
  • José Luis Boldrini
  • Didier Bresch
  • Blanca Climent Ezquerra
  • María Ángeles Rodríguez Bellido
  • Marko Antonio Rojas Medar
• Otros Investigadores:
  • Juan Vicente Gutiérrez Santacreu
  • Giordano Tierra Chica

Resumen del proyecto:

Complex Fluids have different properties of the so-called Newtonian fluids (like water or air). Inside of Complex Fluids three different scales appear: molecular (within each fase), mesoscopic (the size of the interfaces) and macroscopic scale (for hydrodynamics). These complex materials are of great practical value because the microstructure can be manipulated to produce good mechanical, optical or thermal properties.

Liquid Crystals (LC) are particular cases of complex fluids, whose properties are intermediate between solid and liquid: they are liquid (viscous) at the macroscopic level but their microscopic molecules have the ability to maintain a certain order due to elastic properties (attribute of solids). Nematic LC have an orientational order while in Esmectic LC the order is also positional (structured by layers). This visco- elastic dynamic is modelled by coupling the Navier-Stokes equations in velocity and pressure for the macroscopic dynamics with Partial Differential Equations (PDE) for the so-called microscopic parameter of order.

Diffuse Interface Phase-Field models are being recently applied in various fields (solidification, mixtures, growth of tumors, etc.). They show many advantages over more conventional Sharp Interface models (of Stefan kind)

Modeling, theoretical and numerical analysis of Liquid Crystal and Diffuse Interface Phase-Field models is a topic of emerging research with very different applications.

The objective of this project is the mathematical study of some Complex Fluids models, like Diffuse Interface Phase-Field (multifluids and multiphases), liquid crystal (Nematic and smectics) and Nematic- Isotropic interface. Mathematical study for understanding several aspects: modeling (application of the formalism of dissipative systems in order to derive models, asymptotic behavior with respect to small parameters: penalty in Liquid Crystals or capillarity in Diffuse Interface), theoretical analysis (existence, uniqueness, regularity , asymptotic behavior in time, stability and asymptotic stability at infinite time etc..) numerical analysis (design of numerical schemes, stability and convergence towards weak solutions, error estimates, long-time stability, etc.) and effective implementation (using conventional software but with specific inputs, sensitivity to parameters, effective comparative of various schemes, etc.).