Abstract
Linear stability analysis of a fiber suspension flow in a channel domain is performed using a modified Folgar-Tucker equation. Two kinds of potential instability are identified: one is associated with overcritical Reynolds number and another is associated with certain perturbations in fiber orientation field and is present for any Reynolds numbers. The second type of instability leads to initially growing transient perturbations in the microstructure. It is shown that both types of instability lead to instability of the bulk velocity field. As for the perturbed Orr-Sommerfeld eigenvalues, the presence of fibers increases the stability region; the stability region increases with growing C i and decreases with growing S 0 in the modified Folgar-Tucker model.
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Acknowledgements
This work was supported by ESF research project 2009/0223/1DP/1.1.1.2.0/ 09/APIA/VIAA/008.
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Strautins, U. (2014). On Stability of a Concentrated Fiber Suspension Flow. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_17
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DOI: https://doi.org/10.1007/978-3-319-05365-3_17
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