Similar articles

Abstract: The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number, wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio, volume concentration of the fibers and the gap width of cylinders are obtained.

[1] Advani, S.G., Tucker III, C.L., 1987. The use of tensors to describe and predict fiber orientation in short fiber composites. J. Rheol., 31(8):751-784.

[2] Azaiez, J., 2000. Linear stability of free shear flows of fiber suspensions. J. Fluid Mech., 404:179-209.

[3] Batchelor, G.K., 1971. The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid Mech., 46(4):813-829.

[4] Cintra, J.S., Tucker, C.L., 1995. Orthotropic closure approximations for flow induced fiber orientation. J. Rheol., 39(6):1095-1122.

[5] Doi, M., Edwards, S.F., 1978a. Dynamics of rod-like macromolecules in concentrated solution, Part 1. J. Chem. Soc., 74:560-570.

[6] Doi, M., Edwards, S.F., 1978b. Dynamics of rod-like macromolecules in concentrated solution, Part 2. J. Chem. Soc., 74:918-932.

[7] Ericksen, J.L., 1960. Anisotropic fluids. Arch. Rat. Mech. Anal., 4:231-237.

[8] Ericksen, J.L., 1966. Instability in Couette flow of anisotropic fluids. Quart. J. Mech. and Applied. Math., 19(4):455-459.

[9] Gupta, V.K., Sureshkumar, R., Khomami, B., Azaiez, J., 2002. Centrifugal instability of semidilute non-Brownian fiber suspensions. Phys. Fluids, 14(6):1958-1971.

[10] Hand, G.L., 1962. A theory of anisotropic fluids. J. Fluid Mech., 13(1):33-46.

[11] Hinch, E.J., Leal, L.G., 1975. Constitutive equations in suspension mechanics. Part 1: General formulation. J. Fluid Mech., 71(3):481-495.

[12] Hinch, E.J., Leal, L.G., 1976. Constitutive equations in suspension mechanics. Part 2: Approximate forms for a suspension of rigid particles affected by Brownian rotations. J. Fluid Mech., 76(1):187-208.

[13] Leslie, F.M., 1964. The stability of Couette flow of certain anisotropic fluids. Proc. Camb. Phil. Soc., 60:949-955.

[14] Nsom, B., 1994. Transition from circular Couette flow to Taylor vortex flow in dilute and semi-concentrated suspensions of stiff fibers. J. Phys. II France, 4(1):9-22.

[15] Orszag, S.A., 1971. An accurate solution of the Orr-Sommerfeld equation. J. Fluid Mech., 50(4):689-703.

[16] Parsheh, M., Brown, M.L., Aidun, C.K., 2006. Investigation of closure approximations for fiber orientation distribution in contracting turbulent flow. J. Non-Newtonian Fluid Mech., 136(1):38-49.

[17] Pilipenko, V.N., Kalinichenko, N.M., Lemak, A.S., 1981. Stability of the flow of a fiber suspension in the gap between coaxial cylinders. Sov. Phys. Dokl., 26:646-648.

[18] Shaqfeh, E.S.G., Fredrickson, G.H., 1990. The hydrodynamic stress in a suspension of rods. Physics of Fluids A: Fluid Dynamics, 2(1):7-24.

[19] Trefethen, L.N., 2001. Spectral Methods in MATLAB. SIAM, Philadelphia, PA.

[20] Verma, P.D.S., 1962. Couette flow of certain anisotropic fluids. Arch. Rat. Mech. Anal., 10(1):101-107.

[21] Wan, Z.H., Lin, J.Z., You, Z.J., 2005. Non-axisymmetric instability in the Taylor-Couette flow of fiber suspension. Journal of Zhejiang University SCIENCE, 6A(Suppl. I):1-7.

[22] Wan, Z.H., Lin, J.Z., You, Z.J., 2007. Three-dimensional modes of fiber suspensions in the Taylor-Couette flow. Journal of Dong Hua University (Eng. Ed.), 23:41-47.

[23] Weideman, J.A.C., Reddy, S.C., 2000. A MATLAB differentiation matrix suite. ACM Trans. Math. Softw., 26(1):465-519.

[24] You, Z.J., Lin, J.Z., Yu, Z.S., 2004. Hydrodynamic instability of fiber suspensions in channel flows. Fluid Dyn. Res., 34(4):251-271.