Seminario del Departamento de
Ecuaciones Diferenciales y Análisis Numérico

Fecha : 11 de julio de 2014
Hora  : 11:30
Lugar : Seminario del Departamento (Fac. de Matemáticas, 3a. planta, módulo 34)

Igor Pazanin

(University of Zagreb, Croacia)

Resumen

The micropolar fluid model represents an essential generalization of the wellestablished Navier-Stokes model which takes into account the microstructure of the fluid. It describes the behavior of numerous real fluids (e.g. polymeric suspensions, liquid crystals, muddy fluids, animal blood, etc.) better than the classical model. The aim of this talk is to present recent results about asymptotic approximation of the micropolar fluid flow in thin pipe-like domains. We begin by considering an incompressible micropolar fluid flowing through an undeformed straight pipe and find the effective behavior of the flow via rigorous asymptotic analysis with respect to the pipe’s thickness. Engineering practice requires extensive knowledge of fluid flows through curved pipes. Thus, in the second part of this talk we extend our analysis to the case of general curved pipe with an arbitrary central curve. Using curvilinear coordinates and two-scale asymptotic technique, we construct the approximation explicitly acknowledging the effects of fluid microstructure and pipe’s distortion.We provide the rigorous justification of the obtained effective model by proving the corresponding error estimate. Finally, in the last part of the talk we investigate the micropolar fluid flowing through a thin pipe with specific helical shape not entering in the above framework.