# DYNAMIC STABILITY OF NON-DILUTE FIBER SHEAR SUSPENSIONS

## Main Article Content

## Abstract

Temporal stability analysis of fiber suspended shear flow is performed. After introducing the second order structure tensor to determine the Folgar-Tucker inter-fiber interactions based on the Langevin’s equation, a system governing the flow stability is derived in conjunction with the fiber orientation closure. Effect of the inter-fiber interactions on the dynamic stability is studied by solving the general eigenvalue problem. Results show that fiber interaction has significant stabilizing effects on the flow. The most unstable wave number changes with the interaction coefficient. For given interaction coefficient, wave number and other relevant parameters, there is a Re number which corresponds to the critical flow. This Re number is related to the wave number.

## Article Details

**Thermal Science**, [S.l.], v. 16, n. 5, p. 1551-1555, dec. 2016. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/863>. Date accessed: 18 nov. 2017. doi: https://doi.org/10.2298/TSCI1205551W.

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Accepted 2016-12-30

Published 2016-12-30

## References

[2] Lin, J. Z., Shen, S. H., A Theoretical Model of Turbulent Fiber Suspension and its Application to the Channel Flow, Science China, Physics, Mechanics & Astronomy, 53 (2010), 9, pp. 1659-1670

[3] Ericksen, J. L., Anisotropic Fluids, Archive for Rational Mechanics and Analysis 4 (1960), 1, pp. 231- 237

[4] Hand, G. L., A Theory of Anisotropic Fluids, Journal of Fluid Mechanics 13 (1962), 1, pp. 33-46

[5] Batchelor, G. K., Slender-Body Theory for Particles of Arbitrary Cross-Section in Stokes Flow, Journal of Fluid Mechanics 44 (1970), 3, pp. 419-440

[6] Lin, J. Z., Zhang, W. F. Yu, Z. S., Numerical Research on the Orientation Distribution of Fibers Immersed in Laminar and Turbulent Pipe Flows, Journal of Aerosol Science 35 (2004), 1, pp. 63-82

[7] Lin, J. Z., Shi, X., Yu, Z. S., The Motion of Fibers in an Evolving Nixing Layer, Int. J. Multiphase flow, 29 (2003), 8, pp. 1355-1372

[8] Nsom, B., Computation of Drag Reduction in Fiber Suspensions, Fluid Dynamics Research 14 (1994), 5, pp. 275-288

[9] Lin, J. Z., Chai, X. C., Olson, J. Z., Research on the Interaction of Three Contact Fibers in the Fiber Suspensions, Journal of Material Science, 40 (2005), 5, pp. 1183-1191

[10] Lin, J. Z., Zhang, Z. C., Yu, Z. S., Investigation of the Interactions between Two Contacting Fibers in the Fiber Suspensions, Journal of Material Science, 38 (2003), 7, pp. 1499-1505

[11] Azaiez, J., Linear Stability of Free Shear Flows of Fiber Suspensions, Journal of Fluid Mechanics, 404 (2000), 1, pp. 179-209

[12] Fan, X., Phan-Thien, N., Zheng, R., A Direct Simulation of Fiber Suspensions, Journal of Non- Newtonian Fluid Mechanics, 74 (1998), 1-3, pp. 113-135

[13] Rahnama, M., Koch, D. L., Shaqfeh, E. S. G., The Effect of Hydrodynamic Interactions on the Orientation Distribution in a Fiber Suspension Subject to Simple Shear Flow, Physics of Fluids, 7 (1995), 3, pp. 487-506

[14] Wan, Z. H., Lin, J. Z., You, Z. J., The Effects of Closure Model of Fiber Orientation Tensor on the Instability of Fiber Suspensions in the Taylor-Couette Flow, Modern Physics Letters B, 21 (2007), 24, pp. 1611-1624

[15] Gupta, V. K., Sureshkumar, R., Khomami, B., Azaiez, J., Centrifugal Instability of Semi-Dilute Non-Brownian Fiber Suspensions, Physics of Fluids, 14 (2002), 6, pp. 1958-1971

[16] Brady, J. F., Morris, J. F., Microstructure of Strongly Sheared Suspensions and Its Impact on Rheology and Diffusion, Journal of Fluid Mechanics, 348 (1997), pp. 103–139

[17] Hinch, E. J., Leal, L. G., Constitutive Equations in Suspension Mechanics, Part 2, Approximate Form for a Suspension of Rigid Particles Affected by Brownian Rotations, Journal of Fluid Mechanics, 76 (1976), pp. 187–208

[18] Yamane, Y., Kaneda, Y., Doi, M., The Effect of Interaction of Rodlike Particles in Semi-Dilute Suspensions under Shear Flow, J. of the Physical Society of Japan, 64 (1995), 9, pp. 3265-3274

[19] Folgar, F., Tucker, C. L., Orientation Behaviour of Fibers in Concentrated Suspensions, J. Reinf. Plast. Comp., 3 (1984), 2, pp. 98-119