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The stress-microstructure relationship in an evolving mixing layer of fiber suspensions. (English) Zbl 1200.76198

Summary: The equations for fiber suspensions in an evolving mixing layer were solved by the spectral method, and the trajectory and orientation of fibers were calculated based on the slender body theory. The calculated spatial and orientation distributions of fibers are consistent with the experimental ones that were performed in this paper. The relationship between the microstructure of fibers and additional stress was examined. The results show that the spatial and orientation distributions of fibers are heterogeneous because of the influence of coherent vortices in the flow, which leads to the heterogeneity of the additional stress. The degree of heterogeneity increases with the increasing of St number and fiber aspect ratio. The fibers in the flow make the momentum loss thickness of the mixing layer thicker and accelerate the vorticity dispersion.

MSC:

76T20 Suspensions
Full Text: DOI

References:

[1] Petrie, C.J.S.: The rheology of fiber suspensions. J. Non-Newtonian Fluid Mech. 87, 369-402 (1999) · Zbl 0948.76079
[2] Stover, C.A, Koch, D.L, Cohen, C.: Observations of fiber orientation in simple shear-flow of semi-dilute suspensions. J. Fluid Mech. 62, 277-296 (1992)
[3] Iso, Y., Koch, D.L., Cohen, C.: Orientation in simple shear flow of semi-dilute fiber suspensions. 1, Weakly elastic fluids. J. Non-Newtonian Fluid Mech. 62, 115-134 (1996)
[4] Iso, Y., Koch, D.L., Cohen, C.: Orientation in simple shear flow of semi-dilute fiber suspensions. 2, Highly elastic fluids. J. Non-Newtonian Fluid Mech. 62, 135-153 (1996)
[5] Petrich, M.P., Koch, D.L., Cohen, C.: An experimental determination of the stress-microstructure relationship in semi-concentrated fiber suspension. J. Non-Newtonian Fluid Mech. 95, 101-133 (2000)
[6] Mackaplow, M.B., Shaqfeh, E.S.G.: A numerical study of the sedimentation of fiber suspension. J. Fluid Mech. 376 149-182 (1998) · Zbl 0937.76068
[7] Raiskinmaki, P., Shakib-Manesh, A., Koponen, A. et al.: Simulations of non-spherical particles suspended in a shear flow. Compute Phys. Commun. 129, 185-195 (2000) · Zbl 0987.76097
[8] Sundararajakumar, R.R., Koch, D.L.: Structure and properties of sheared fiber suspensions with mechanical contacts. J. Non-Newtonian Fluid Mech. 73, 205-239 (1997)
[9] Chaouche, M., Koch, D.: Rheology of non-Brownian rigid fiber suspensions with adhesive contacts. J. Rheol. 45, 369-382 (2001)
[10] Lin, J.Z., Zhang, Z.C., YU, Z.S.: Investigation of the interactions between two contacting fibers in the fiber suspensions. J. Mater. Sci. 38(7) 1499-1505 (2003)
[11] Lin, J.Z., Lin, J., Shao, X.M. et al.: Research on particle dispersion in a plane mixing layer with coherent structure. Acta Mechanica Sinica 19(6), 535-542 (2003)
[12] Lin, J.Z., Shi, X., You, Z.J.: Effects of the aspect ratio on the sedimentation of a fiber in Newtonian fluids. J. Aerosol Sci. 34(7), 909-921 (2003)
[13] Batchelor, G.K.: Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419-440 (1970) · Zbl 0216.52401
[14] Rogers, M.M., Moser, R.D.: The three-dimensional evolution of a plane mixing layer: The Kelvin-Helmoholtz roll-up. J. Fluid Mech. 243, 183-226 (1992) · Zbl 0825.76311
[15] Michalke, A.: On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543-556 (1964) · Zbl 0129.20302
[16] Crowe, C.T., Gore, R.A., Troutt, T.R.: Particle dispersion by coherent structures in free shear flows. Particle Science and Tech. 3, 149-158 (1985)
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