Diffusion, extensibility, flow, and orientation coupling in polymers filled with extensible and flexible fibers
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ORIGINAL CONTRIBUTION
Diffusion, extensibility, flow, and orientation coupling in polymers filled with extensible and flexible fibers Said Bentis 1 & Ali El Afif 1 Received: 30 May 2020 / Revised: 19 September 2020 / Accepted: 6 November 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract When a fiber is subjected to flow and mass transport, it deforms and swells and thus its orientation and length change accordingly. As a starting point, a semi-kinetic equation is proposed to describe the time evolution of the length and orientation of extensible fibers. Then a mesoscopic model, explicitly incorporating the coupling arising among flow, mass transport, and fibers extensibility and orientation in a mixture composed of a solvent and a fiber-reinforced polymer (FRP), is formulated. The derived governing and constitutive equations possess the GENERIC structure and are parameterized by mobility coefficients and the Helmholtz free energy density. The latter takes into account the orientational ordering of the fibers, the fiber-fiber topological interactions, and the flexible nature of the fibers. The unidirectional flow-free mass transport is thoroughly discussed via scaling analysis, numerical solutions, and comparison with sorption data selected from literature. The dynamics of the boundaries is also examined. Keywords Polymer . Fiber . Extensibility . Flexibility . Fiber tensor . Non-Fickian mass transport . GENERIC . Sorption . Permeation
Introduction Due to their numerous improved mechanical, electrical, and thermo-physical properties relative to unfilled polymer matrices, fiber-reinforced polymers (FRP) are commonly used in aeronautics, transport, civil engineering, and marine applications (Karbhari et al. 2003; Cubaud and Hamelin 1980; Hussain et al. 2006). Several key factors intervene in the improvement of the properties of these composites; the most important of which are identified to be the volume fraction of the fibers, their spatial orientation and dispersion, and their physical and mechanical properties as well. Moreover, an adequate choice of the hosting polymeric matrix appears to be of substantial importance as it controls the transfer and distribution of stresses and protects the fibers against abrasion and chemical as well as physical agents to which they might be exposed.
* Ali El Afif [email protected] 1
Department of Physics, Faculty of Sciences, Chouaib Doukkali University, Route Ben Maachou, 24000 El Jadida, Morocco
Flow dynamics of suspensions of inextensible and incompressible particles has been the subject of several investigations both on the microscopic level of description (i.e., microhydrodynamics) (Jeffrey 1922; Fan et al. 1998; Schmid et al. 2000; Joung et al. 2001) as well as on the mesoscopic level of description (i.e., meso-hydrodynamics) (Bird and DeAguir 1983; Folgar and Tucker 1984; Grmela 1985; Grmela and Carreau 1986; Doi and Edwards 1986; Bird et al. 1987a, b; Advani and Tucker 1987; Grmela and Ait Kadi 1994; Rajabian et al. 2005; Ferec et al. 2
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