## Flow-driven orientation dynamics in two classes of fibre suspensions

• In this dissertation we consider mesoscale based models for flow driven fibre orientation dynamics in suspensions. Models for fibre orientation dynamics are derived for two classes of suspensions. For concentrated suspensions of rigid fibres the Folgar-Tucker model is generalized by incorporating the excluded volume effect. For dilute semi-flexible fibre suspensions a novel moments based description of fibre orientation state is introduced and a model for the flow-driven evolution of the corresponding variables is derived together with several closure approximations. The equation system describing fibre suspension flows, consisting of the incompressible Navier-Stokes equation with an orientation state dependent non-Newtonian constitutive relation and a linear first order hyperbolic system for the fibre orientation variables, has been analyzed, allowing rather general fibre orientation evolution models and constitutive relations. The existence and uniqueness of a solution has been demonstrated locally in time for sufficiently small data. The closure relations for the semiflexible fibre suspension model are studied numerically. A finite volume based discretization of the suspension flow is given and the numerical results for several two and three dimensional domains with different parameter values are presented and discussed.

Author: Uldis Strautins urn:nbn:de:hbz:386-kluedo-22461 Oleg Iliev Doctoral Thesis English 2008 2008 Technische Universität Kaiserslautern Technische Universität Kaiserslautern 2008/05/21 2008/07/03 Fiber suspension flow; closure approximation; finite volume method; rheology; well-posedness Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q35 PDEs in connection withfluid mechanics 76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Axx Foundations, constitutive equations, rheology / 76A05 Non-Newtonian fluids Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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