Department of Mathematics

Applied Mathematics

  •  Giordano Tierra, Temple University
  •  Numerical methods for energy-based models and its applicability to mixtures of isotropic and nematic flows with anchoring and stretching effects
  •  04/21/2017
  •  4:10 PM - 5:00 PM
  •  1502 Engineering Building

The study of interfacial dynamics between two different components has become the key role to understand the behavior of many interesting systems. Indeed, two-phase flows composed of fluids exhibiting different microscopic structures are an important class of engineering materials. The dynamics of these flows are determined by the coupling among three different length scales: microscopic inside each component, mesoscopic interfacial morphology and macroscopic hydrodynamics. Moreover, in the case of complex fluids composed by the mixture between isotropic (newtonian fluid) and nematic (liquid crystal) flows, its interfaces exhibit novel dynamics due anchoring effects of the liquid crystal molecules on the interface. In this talk I will introduce a PDE system to model mixtures composed by isotropic fluids and nematic liquid crystals, taking into account viscous, mixing, nematic, stretching and anchoring effects and reformulating the corre- sponding stress tensors in order to derive a dissipative energy law. Then, I will present new linear unconditionally energy-stable splitting schemes that allows us to split the computation of the three pairs of unknowns (velocity- pres- sure, phase field-chemical potential and director vector-equilibrium) in three different steps. The fact of being able to decouple the computations in different linear sub-steps maintaining the discrete energy law is crucial to carry out relevant numerical experiments under a feasible computational cost and assuring the accuracy of the computed results. Finally, I will present several numerical simulations in order to show the efficiency of the proposed numerical schemes, the influence of the shape of the nematic molecules (stretching effects) in the dynamics and the importance of the interfacial interactions (anchoring effects) in the equilibrium configurations achieved by the system. This contribution is based on joint work with Francisco Guill´ en-Gonzal´ ez (Universidad de Sevilla, Spain) and Mar´ıa ´ Angeles Rodr´ıguez-Bellido (Universidad de Sevilla, Spain)



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