Geodesic
Analysis of a nonlinear dynamic model of the Couette flow for structured liquid in a flat gap
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 85-92.

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Parametric investigation of structured liquid Couette flow in a plain gap is presented. Bifurcation conditions of steady non-uniform solutions are defined from unsteady uniform ones in the nonmonotonic region of rheological curve. Relevant bifurcation diagrams are plotted. The coincidence between the steady-state solution and the solution of unstable problem is noted.
Mots-clés : Couette flow, bifurcation
Keywords: structed liquid, nonmonotonic region of rheological curve, parametric investigation. 
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N. A. Belyaeva; K. P. Kuznetsov. Analysis of a nonlinear dynamic model of the Couette flow for  structured liquid in a flat gap. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 85-92. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a9/

[1] Bulgin D., Wratten R., “Measurements of steady flow characteristics of rubber at high rates of shear”, Proceedings of the Second international Congress of Rheology, ed. V. Q. W. Harrison, London, 1954

[2] Belkin I. M., Vinogradov G. V., Leonov A. I., Rotary Instruments. Measurement of Viscosity and Physicomechanical Characteristics of Materials, Mashinostroenie, Moscow, 1968, 272 pp.

[3] Lifshits A. E., Rybnikov G. L., “Dissipative structures and Couette flow of a non-Newtonian fluid”, Dokl. Akad. Nauk SSSR, 281:5 (1985), 1088–1093 | MR

[4] Buchatskii L. M., Manelis G. B., Stolin A. M., Khudyaev S. I., “Theory of structural transformations in flowing systems”, J. Eng. Phys. Thermophys., 41:6 (1981), 1321–1327 | DOI

[5] Stolin A. M., Khudyaev S. I., “Formation of spatially inhomogeneous states of a structured fluid accompanying a superanomaly in the viscosity”, Dokl. Akad. Nauk SSSR, 260:5 (1981), 1180–1184

[6] Khudyaev S. I., Ushakovskiy O. V., “Space nonuniformity and auto-oscillations in the structured liquid flow”, Matem. Mod., 14:7 (2002), 53–73 | MR

[7] Belyaeva N. A., “Spatially inhomogeneous flow of structured liquid in a flat gap”, Nonlinear Problems in Mechanics and Physics of Deformable Solid Body. Issue 8, SPbGU, St. Petersburg, 2005, 151–156

[8] Belyaeva N. A., Khudyaev S. I., Gorst. D. L., “The inhomogeneous Couette flow of structured liquid”, Vestn. Syktyvk. Un-ta. Ser. 1, 2003, no. 5, 43–48

[9] Belyaeva N. A., Deformation of viscoelastic structured systems (Russian), Lambert Academic Publishing, Germany, 2011, 200 pp.

[10] Belyaeva N. A., Kuznetsov K. P., “Bifurcation analysis of Couette flow of structured liquid accompanying a superanomaly”, The 2nd International Conference “Mathematical Physics and its Applications”, Book of Abstracts and Conference Materials, eds. I. V. Volovich and Yu. N. Radayev, Kniga, Samara, 2010, 51–52

[11] Kuznetsov K. P., Bifurcation of stationary inhomogeneous structures in a superanomaly domain of Couette flow of structured liquid in a flat gap

[12] Kuznetsov K. P., Belyaeva N. A., “The dissipative structure and superanomaly domain of of Couette flow of structured liquid in a flat gap”, Vestn. Syktyvk. Un-ta. Ser. 1, 2011, no. 13, 61–74

[13] Holodniok M., Klíč A., Kubíček M., Marek M., Methods of Analysis of Nonlinear Dynamical Models (Czech), Academia, Prague, 1986; Kholodniok M., Klich A., Kubichek M., Marek M., Metody analiza nelineinykh dinamicheskikh modelei, Mir, M., 1991, 386 pp.

[14] Moler C., Kahaner D., Nash S., Numerical Methods and Software, Prentice Hall, Englewood Cliffs, NJ, 1988, 384 pp.; Kakhaner D., Mouler K., Nesh S., Chislennye metody i programmnoe obespechenie, Mir, M., 1998, 575 pp.

[15] Iooss G., Joseph D. D., Elementary Stability and Bifurcation Theory, second ed., Springer-Verlag, New York, 356 pp. ; Ioss Zh., Dzhozef D., Elementarnaya teoriya ustoichivosti i bifurkatsii, Mir, M., 1983, 301 pp. | MR | MR