Abstract
A model of polymer composition material that is composed of a unidirectional fiber and binder has been considered. The space between two neighboring filaments of fibers is considered as a capillary along which the binder propagates during impregnation. In order to describe the flow process, a gradient generalization of the Navier–Stokes equation has been suggested. A corrected model of the flow of binder in the capillary-porous space of a unidirectional fiber material is developed on its basis. In particular cases, the found solution coincides with the Navier–Stokes–Darcy equations and conventional Navier–Stokes equation. The model that has been developed allows the refinement of the nonclassical effect of the existence of two boundary layers that appear during flow and may prevent it.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. S. Borodulin, “Investigation of properties of polymer composition materials around a geterogeneous matrix,” Polym. Sci., Ser. D 6 (3), 256–259 (2013).
B. A. Nelyub, “Technologies of production of components of electric transmission line supports from epoxy binders by the winding method,” Polym. Sci., Ser. D 6 (1), 44–47 (2013).
N. I. Baurova, “Microstructural investigations of surfaces of destruction of carbon plastic,” Polym. Sci., Ser. D 6 (3), 246–249 (2013).
G. V. Malysheva, E. Sh. Akhmetova, and Yu. Yu. Shimina, “Evaluation of phase transition temperatures of polymer binders by differential scanning calorimetry,” Klei, Germetiki, Tekhnol., No. 6, 29–33 (2014).
T. A. Guzeva, “Microwave heating as a way to intensify curing processes in binders,” Klei, Germetiki, Tekhnol., No. 12, 41–43 (2013).
A. S. Borodulin, “Plasticizers for epoxy adhesives and binders,” Klei, Germetiki, Tekhnol., No. 7, 31–35 (2012).
G. V. Malysheva, “Predicting the endurance of adhesive joints,” Polym. Sci., Ser. D 7 (2), 145–147 (2014).
L. G. Loitsyanskii, Fluid and Gas Mechanics (Drofa, Moscow, 2003) [in Russian].
P. A. Belov, L. P. Kobets, and A. S. Borodulin, “Kinetics of impregnation of fibers with fluids. Modeling in the framework of classical Navier–Stokes equations,” Klei, Germetiki, Tekhnol., No. 12, 36–40 (2013).
P. A. Belov, L. P. Kobets, and A. S. Borodulin, “Kinetics of impregnation of fibers with fluids. Modeling in the framework of classical Navier–Stokes equations,” Materialovedenie, No. 3, 29–33 (2014).
P. A. Belov and S. A. Lur’e, “The theory of ideal adhesion interactions,” Mekh. Kompoz. Mater. Konstr. 13 (4), 519–529 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © P.A. Belov, A.S. Borodulin, L.P. Kobets, G.V. Malysheva, 2015, published in Vse Materialy. Entsiklopedicheskii Spravochnik, 2015, No. 12, pp. 2–6.
Rights and permissions
About this article
Cite this article
Belov, P.A., Borodulin, A.S., Kobets, L.P. et al. Kinetics of fiber impregnation by a binder. Gradient generalization of Navier–Stokes–Darcy equations. Polym. Sci. Ser. D 9, 205–208 (2016). https://doi.org/10.1134/S1995421216020039
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995421216020039