×

Hydrodynamical and computational aspects and stability problems for viscoplastic flows. (English. Russian original) Zbl 1273.76423

J. Math. Sci., New York 189, No. 2, 223-256 (2013); translation from Sovrem. Mat. Prilozh. 78 (2012).
Summary: This survey is devoted to some typical problems modeling technological processes of treatment of materials, rolling of a rigid body on a lubricated surface, the behavior of layers of the Earth’s crust for continuous loading, and dynamical interaction of elements of viscoplastic constructions.

MSC:

76U05 General theory of rotating fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. A. Aganin, R. I. Nigmatulin, M. A. Ilgamov, and I. Sh. Akhatov, ”Dynamics of a gas bubble at the center of a spherical volume of a fluid,” Dokl. Ross Akad. Nauk, 369, No. 2, 182–185 (1999). · Zbl 1033.76500
[2] L. D. Akulenlo, D. V. Georgievskii, D. M. Klimov, S. A. Kumakshev, and S. V. Nesterov, ”Squeeze flow of a viscous-plastic material with small yield stress from a planar confuser,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 183–197 (2003).
[3] L. D. Akulenlo, D. V. Georgievskii, D. M. Klimov, S. A. Kumakshev, and S. V. Nesterov, ”Deformation of a viscoplastic Bingham medium in a planar confuser,” Prikl. Mekh., 42, No. 4, 3–45 (2006).
[4] L. D. Akulenko, D. V. Georgievskii, D. M. Klimov, S. A. Kumakshev, and S. V. Nesterov, ”Stationary flow of a viscoplastic medium with small yield stress in a plane confuser,” Russ. J. Math. Phys., 10, No. 4, 381–398 (2003). · Zbl 1105.76302
[5] A. N. Alexandrou, E. Duca, and V. Entov, ”Inertial, viscous and yield stress effects in Bingham fluid filling of a 2D cavity,” J. Non-Newton. Fluid Mech., 96, No. 3, 383–403 (2001). · Zbl 0961.76510 · doi:10.1016/S0377-0257(00)00199-3
[6] S. Alexandru, ”Caracterizarea tranzit,iei de la regimul laminar la cel turbulent de curgere pentru fluide nenewtoniene,” Rev. Chim., 44, No. 7, 676–682 (1993).
[7] L. Anand, K. H. Kim, and T. G. Shawki, ”Onset of shear localization in viscoplastic solids,” J. Mech. Phys. Solids, 35, No. 4, 407–429 (1987). · Zbl 0612.73046 · doi:10.1016/0022-5096(87)90045-7
[8] C. Ancey, ”Plasticity and geophysical flows: a review,” J. Non-Newton. Fluid Mech., 142, No. 2–3, 4–35 (2007). · Zbl 1143.76315 · doi:10.1016/j.jnnfm.2006.05.005
[9] B. D. Annin, V. O. Bytev, and S. I. Senashov, Group Properties of Equations of Elasticity and Plasticity [in Russian], Izd. Sib. Otd. Akad. Nauk USSR, Novosibirsk, 1985. · Zbl 0603.73018
[10] N. N. Aref’ev, ”An axial flow of a viscous-plastic fluid in a ring gap with hydrolubricant of both walls,” Vestn. Ross. Gos. Akad. Vodn. Transp., 20, 116–124 (2006).
[11] K. Arrow, L. Hurwicz, and H. Uzawa, Studies in Nonlinear Programming, Stanford Univ. Press, Stanford (1958). · Zbl 0091.16002
[12] I. M. Astrahan, ”Stability of the rotating motion of a viscous-plastic fluid between two coaxial cylinders,” Zh. Prikl. Mekh. Tekh. Fiz., 2, 47–53 (1961).
[13] C. Atkinson and K. El-Ali, ”Some boundary value problem for the Bingham model,” J. Non-Newton. Fluid Mech., 41, No. 3, 339–363 (1992). · Zbl 0747.76012 · doi:10.1016/0377-0257(92)87006-W
[14] N. J. Balmforth, R. V. Craster, A. C. Rust, and R. Sassi, ”Viscoplastic flow over an inclined surface,” J. Non-Newton. Fluid Mech., 139, No. 1–2, 103–127 (2006). · Zbl 1195.76009 · doi:10.1016/j.jnnfm.2006.07.010
[15] N. J. Balmforth, R. V. Craster, R. Sassi, ”Shallow viscoplastic flow on an inclined plane,” J. Fluid Mech., 470, 1–29 (2002). · Zbl 1026.76002
[16] I. V. Basov, ”Estimate of the width of rigid zones of a flow of a compressible Bingham fluid at the equilibrium loss,” Dynam. Solid Medium, 120, 8–15, (2002). · Zbl 1022.35043
[17] I. V. Basov and V. V. Shelukhin, ”Generalized solutions to the equations of compressible Bingham flows,” ZAMM (Z. Angew. Math. Mech.), 79, No. 3, 185–192, (1999). · Zbl 0928.76009 · doi:10.1002/(SICI)1521-4001(199903)79:3<185::AID-ZAMM185>3.0.CO;2-N
[18] I. V. Basov and V. V. Shelukhin, ”Nonhomogeneous incompressible Bingham viscoplastic as a limit of nonlinear fluids,” J. Non-Newton. Fluid Mech., 142, No. 1–3, 95–103, (2007). · Zbl 1107.76005 · doi:10.1016/j.jnnfm.2006.05.004
[19] J. Bejda and T. Wierzbicki, ”Dispersion of small amplitude stress waves in pre-stressed elastic, visco-plastic cylindrical bars,” Quart. Appl. Math., 24, No. 1, 63–71 (1966).
[20] V. P. Belomytsev and N. N. Gvozdikov, ”On the loss of heat stability of the motion of a viscousplastic material,” Dokl. Akad. Nauk SSSR, 170, No. 2, 305–307 (1966).
[21] M. Bercovier and M. Engelman, ”A finite element method for incompressible non-Newtonian flows,” J. Comput. Phys., 36, No. 2, 313–326 (1980). · Zbl 0457.76005 · doi:10.1016/0021-9991(80)90163-1
[22] R. Betchov and W. O. Criminale, Stability of Parallel Flows, Academic Press, New York-London (1967). · Zbl 0248.76018
[23] C. R. Beverly and R. I. Tanner, Numerical analysis of three-dimensional Bingham plastic flow, J. Non-Newton. Fluid Mech., 42, No. 1–2, 85–115 (1992). · doi:10.1016/0377-0257(92)80006-J
[24] E. Bingham, Fluidity and Plasticity, New York (1922).
[25] R. B. Bird, G. C. Dai, and B. J. Yarusso, ”The rheology and flow of viscoplastic materials,” Rev. Chem. Eng., 1, No. 1, 1–70 (1982).
[26] S. H. Bittleston and O. Hassager, ”Flow of viscoplastic fluids in a rotating concentric annulus,” J. Non-Newton. Fluid Mech., 42, No. 1–2, 19–36 (1992). · Zbl 0748.76015 · doi:10.1016/0377-0257(92)80002-F
[27] A. Borrelli, M. C. Patria, E. Piras, ”Spatial decay estimates in the problem of entry flow for a Bingham fluid filling a pipe,” Math. Comput. Model., 40, No. 1–2, 23–42 (2004). · Zbl 1112.76301 · doi:10.1016/j.mcm.2003.12.001
[28] M. Bostan and P. Hild, ”Starting flow analysis for Bingham fluids,” Nonlinear Anal., 64, No. 5, 1119–1139 (2006). · Zbl 1094.76003 · doi:10.1016/j.na.2005.05.058
[29] S. A. Bostandjyan and A. M. Stolin, ”Complex shear of a viscous-plastic fluid between two parallel plates,” In: Theor. Instrum. Rheology [in Russian], Minsk (1970), pp. 107–118.
[30] M. A. Brutyan and P. L. Krapivskii, ”Hydrodynamics of non-Newtonian fluids,” In: Progress in Science and Technology, Series on Complex and Special Sections of Mechanics [in Russian], 4, All-Russian Institute for Scientific and Technical Information, Russian Academy of Sciences, Moscow (1991), pp. 3–98.
[31] R. Bukowski and W. Wojewòdzki, ”Dynamic buckling of viscoplastic spherical shell,” Int. J. Solids Struct., 20, No. 8, 761–776 (1984). · Zbl 0546.73037 · doi:10.1016/0020-7683(84)90064-7
[32] R. Bunoiu and S. Kesavan, ”Asymptotic behavior of a Bingham fluid in thin layers,” J. Math. Anal. Appl., 293, No. 2, 405–418 (2004). · Zbl 1059.76004 · doi:10.1016/j.jmaa.2003.10.049
[33] S. L. Burgess and S. D. R. Wilson, ”Spin-coating of a viscoplastic material,” Phys. Fluids, 8, No. 9, 2291–2297 (1996). · Zbl 1027.76501 · doi:10.1063/1.869016
[34] T. J. Burns, ”Similarity and bifurcation in unstable viscoplastic solids,” SIAM J. Appl. Math., 49, No. 1, 314–329 (1989). · Zbl 0663.73023 · doi:10.1137/0149019
[35] G. Camenschi and N. Cristescu, and N. Şandru, ”Development in high-speed viscoplastic flow through conical converging dies,” Trans. ASME. J. Appl. Mech., 50, No. 3, 566–570 (1983). · Zbl 0524.73045 · doi:10.1115/1.3167092
[36] F. Caton, ”Linear stability of circular Couette flow of inelastic viscoplastic fluids,” J. Non-Newton. Fluid Mech., 134, No. 1–3, 148–154 (2006). · Zbl 1123.76328 · doi:10.1016/j.jnnfm.2006.02.003
[37] O. Cazacu and I. R. Ionescu, ”Compressible rigid viscoplastic fluids,” J. Mech. Phys. Solids, 54, No. 8, 1640–1667 (2006). · Zbl 1120.74364 · doi:10.1016/j.jmps.2006.02.001
[38] O. Cazacu, I. R. Ionescu, and T. Perrot, ”Steady-state flow of compressible rigid-viscoplastic media,” Int. J. Eng. Sci., 44, No. 15–16, 1082–1097 (2006). · Zbl 1213.76119 · doi:10.1016/j.ijengsci.2006.05.011
[39] M. Chatzimina, G. C. Georgiou, I. Argyropaidas, E. Mitsoulis, and R. R. Huilgol, ”Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times,” J. Non-Newton. Fluid Mech., 129, No. 3, 117–127 (2005). · Zbl 1195.76012 · doi:10.1016/j.jnnfm.2005.07.001
[40] M. Chatzimina, C. Xenophontos, G. C. Georgiou, I. Argyropaidas, E. Mitsoulis, ”Cessation of annular Poiseuille flows of Bingham plastics,” J. Non-Newton. Fluid Mech., 142, 135–142 (2007). · Zbl 1113.76014 · doi:10.1016/j.jnnfm.2006.07.002
[41] E. A. Cheblakova, ”Modeling of convection in domains with free boundaries,” Vychisl. Tekhnol., 5, No. 6, 87–98 (2000). · Zbl 0965.80005
[42] A. D. Chernyshov, ”On flows of a viscous-plastic medium with nonlinear viscosity in a wedge,” Zh. Prikl. Mekh. Tekh. Fiz., 4, 152–154 (1966).
[43] A. D. Chernyshov, ”Steady-state flows of a viscous-plastic medium between two coaxial cones and inside a dihedral angle,” Zh. Prikl. Mekh. Tekh. Fiz., 5, 93–99 (1970).
[44] A. D. Chernyshov, ”On the motion of a viscous-plastic medium inside a dihedral angle,” Prikl. Mekh., 7, No. 1, 120–124 (1971).
[45] R. P. Chhabra and P. H. T. Uhlherr, ”Static equilibrium and motion of spheres in viscoplastic liquids,” In: Encyclopedia of Fluid Mechanics. Rheology and Non-Newtonian Flows, 7, Gulf. Publ., Houston (1988), pp. 611–633.
[46] E. V. Chizhonkov, Relaxation Methods for Solving Saddle Problems [in Russian], Izd. Inst. Vychisl. Mat. Ross. Akad. Nauk, Moscow (2002). · Zbl 1058.65037
[47] D. Cioranescu, ”On the flow of a Bingham fluid passing through an electric field,” Internat. J. Non-Linear Mech., 38, No. 3, 287–304 (2003). · Zbl 1346.76004 · doi:10.1016/S0020-7462(01)00061-0
[48] S. Cochard and C. Ancey, ”Experimental investigation of the spreading of viscoplastic fluids on inclined planes,” J. Non-Newton. Fluid Mech., 158, No. 1–3, 73–84 (2009). · Zbl 1274.76008 · doi:10.1016/j.jnnfm.2008.08.007
[49] P. L. Dai and J. Z. Dai, ”The Gal”erkin finite element method for Bingham-fluid,” Numer. Math. J. Chinese Univ., 24, No. 1, 31–36 (2002). · Zbl 1112.76386
[50] I. Daprà and G. Scarpi, ”Start-up of channel-flow of a Bingham fluid initially at rest,” Math. Appl., 15, No. 2, 125–135 (2004). · Zbl 1104.76031
[51] I. Daprà and G. Scarpi, ”Start-up flow of a Bingham fluid in a pipe,” Meccanica, 40, No. 1, 49–63 (2005). · Zbl 1098.76005 · doi:10.1007/s11012-004-4997-7
[52] M. R. Davidson, N. H. Khan, and Y. L. Yeow, ”Collapse of a cylinder of Bingham fluid,” In: Proc. Internat. Conf. on Computat. Techniques and Applications, Canberra, Aust. Math. Soc., 499–517 (2000). · Zbl 1012.76058
[53] E. J. Dean and R. Glowinski, ”Operator-splitting methods for the simulation of Bingham viscoplastic flow,” Chinese Ann. Math. Ser. B, 23, No. 2, 187–204 (2002). · Zbl 1002.35100 · doi:10.1142/S0252959902000183
[54] E. J. Dean, R. Glowinski, and G. Guidoboni, ”On the numerical simulation of Bingham viscoplastic flow: old and new results,” J. Non-Newton. Fluid Mech., 142, No. 2–3, 36–62 (2007). · Zbl 1107.76061 · doi:10.1016/j.jnnfm.2006.09.002
[55] N. Dubash, N. J. Balmforth, A. C. Slim, S. Cochard, ”What is the final shape of a viscoplastic slump?,” J. Non-Newton. Fluid Mech., 158, No. 1–3, 91–100 (2009). · Zbl 1274.76019 · doi:10.1016/j.jnnfm.2008.08.004
[56] Z. Dursunkaya and S. Nair, ”Solidification of a finite medium subject to a periodic variation of boundary temperature,” Trans. ASME. J. Appl. Mech., 70, No. 5, 633–637 (2003). · Zbl 1110.74425 · doi:10.1115/1.1604836
[57] H. C. Elman and G. H. Golub, ”Inexact and preconditioned Uzawa algorithms for saddle point problems,” SIAM J. Numer. Anal., 31, 1645–1661 (1994). · Zbl 0815.65041 · doi:10.1137/0731085
[58] J. D. Evans and J. R. King, ”Asymptotic results for the Stefan problem with kinetic undercooling,” Quart. J. Mech. Appl. Math., 53, No. 3, 449–473 (2000). · Zbl 0998.80004 · doi:10.1093/qjmam/53.3.449
[59] J. D. Evans and J. R. King, ”The Stefan problem with nonlinear kinetic undercooling,” Quart. J. Mech. Appl. Math., 56. No 1, 139–161 (2003). · Zbl 1050.35152 · doi:10.1093/qjmam/56.1.139
[60] Chun Fan, ”Flow of viscoplastic fluid on a rotating disk,” Appl. Math. Mech., 15, No. 5, 447–453 (1994). · Zbl 0804.73031 · doi:10.1007/BF02451494
[61] A. Fasano and M. Primicerio, ”Viscoplastic impact of a rod on a wall,” Bol. Unione Mat. Ital., 11, No. 3, 531–553 (1975). · Zbl 0356.73037
[62] Z. C. Feng and L. G. Leal, ”Nonlinear bubble dynamics,” Annu. Rev. Fluid Mech., 29, 201–243 (1997). · doi:10.1146/annurev.fluid.29.1.201
[63] B. Finzi, ”Rotazioni plastiche,” Atti Reale Accad. Naz. dei Lincei, 23, No. 9, 676–681 (1936). · JFM 62.0985.04
[64] B. Finzi, ”Dispersione di un vortice in un mezzo plastico,” Atti Reale Accad. Naz. dei Lincei, 23, No. 10, 733–739 (1936). · JFM 62.0985.05
[65] A. L. Florence, ”Buckling of viscoplastic cylindrical shells due to impulsive loading,” AIAA J., 6, No. 3, 532–537 (1968). · doi:10.2514/3.4530
[66] A. L. Florence and G. R. Abrahamson, ”Critical velocity for collapse of viscoplastic cylindrical shells without buckling,” Trans. ASME. J. Appl. Mech., 44, No. 1, 89–94 (1977). · Zbl 0396.73091 · doi:10.1115/1.3424021
[67] L. Formaggia, D. Lamponi, and A. Quarteroni, ”One-dimensional models for blood flow in arteries,” J. Eng. Math., 47, No. 3–4, 251–276 (2003). · Zbl 1070.76059 · doi:10.1023/B:ENGI.0000007980.01347.29
[68] M. Fortin and R. Glowinski, Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, North-Holland, Amsterdam (1983). · Zbl 0525.65045
[69] G. B. Freustehter, A. I. Nakorchevskii, V. V. Sinitsin, and E. I. Tsetsoho, ”Loss of stability of the laminar form of motion in flows of plastic lubricants in capillaries,” Prikl. Reol., 2, 135–146 (1970).
[70] I. A. Frigaard, S. D. Howison, and I. J. Sobey, ”On the stability of Poiseuille flow of a Bingham fluids,” J. Fluid Mech., 263, 133–150 (1994). · Zbl 0804.76036 · doi:10.1017/S0022112094004052
[71] I. A. Frigaard and C. Nouar, ”On three-dimensional linear stability of Poiseuille flow of Bingham fluids,” Phys. Fluids, 15, No. 10, 2843–2851 (2003). · Zbl 1186.76181 · doi:10.1063/1.1602451
[72] I. A. Frigaard and C. Nouar, ”On the usage of viscosity regularization methods for visco-plastic fluids flow computation,” J. Non-Newton. Fluid Mech., 127, No. 1, 1–26 (2005). · Zbl 1187.76716 · doi:10.1016/j.jnnfm.2005.01.003
[73] I. A. Frigaard and O. Scherzer, ”The effects of yield stress variation on uniaxial exchange flows of two Bingham fluids in a pipe,” SIAM J. Appl. Math., 60, No. 6, 1950–1976 (2000). · Zbl 0988.35007 · doi:10.1137/S0036139998335165
[74] I. A. Frigaard, O. Scherzer, and G. Sona, ”Uniqueness and non-uniqueness in the steady displacement of two visco-plastic fluids,” ZAMM (Z. Angew. Math. Mech.), 81, No. 2, 99–118 (2001). · Zbl 0972.35004 · doi:10.1002/1521-4001(200102)81:2<99::AID-ZAMM99>3.0.CO;2-Q
[75] L. Fusi and A. Farina, ”An extension of the Bingham model to the case of an elastic core,” Adv. Math. Sci. Appl., 13, No. 1, 113–163 (2003). · Zbl 1038.76003
[76] L. Fusi and A. Farina, ”Modeling of Bingham-like fluids with deformable core,” Comput. Math. Appl., 53, No. 3–4, 583–594 (2007). · Zbl 1121.76005 · doi:10.1016/j.camwa.2006.02.033
[77] A. N. Gaipova, ”Finite-difference method of solving the problem on the impact of a viscousplastic rod against a rigid barrier,” Inzh. Zh. Mekh. Tverd. Tela, 1, 128–130 (1968).
[78] H. M. Gamsaev, ”Modeling of the motion of a single particle in an ascending flow of a viscousplastic fluid,” Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 26, No. 2, 148–153 (2006).
[79] F. A. Garifullin and K. Z. Halimov, ”On the hydrodynamical stability of non-Newtonian media,” Prikl. Mekh., 10, No. 8, 3–25 (1974).
[80] G. T. Gasanov, N. A. Gasanzade, and A. H. Mirzadjanzade, ”Squeezing out of a viscous-plastic layer by circular plates,” Zh. Prikl. Mekh. Tekh. Fiz., 5, 88–90 (1961).
[81] D. V. Georgievskii, ”A linearized problem on the stability of viscous-plastic bodies with an arbitrary inner relation,” Vestn. MGU, Ser. 1. Mat. Mekh., 6, 65–67 (1992).
[82] D. V. Georgievskii, ”Stability of two- and three-dimensional viscous-plastic flows and the generalized Squire theorem,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 117–123 (1993).
[83] D. V. Georgievskii, ”The collapse of a cavitational bubble in a nonlinearly viscous and viscousplastic media,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 2, 181–184 (1994).
[84] D. V. Georgievskii, ”Sufficient integral estimates of the stability of the viscous-plastic shear,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 124–131 (1994).
[85] D. V. Georgievskii, ”Viscous-Plastic Couette–Taylor flows: Distribution of rigid zones and stability,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 6, 101–106 (1994).
[86] D. V. Georgievskii, ”Stability of nonstationary shear of a viscous-plastic half-plane with a tangential break along the boundary,” Vestn. MGU, Ser. 1. Mat. Mekh., 3, 65–72 (1996).
[87] D. V. Georgievskii, ”Estimates of the stability of a nonstationary deformation of viscous-plastic bodies in planar domains,” Dokl. Ross Akad. Nauk, 346, No. 4, 471–473 (1996).
[88] D. V. Georgievskii, ”Integral estimates of the stability of nonstationary deformation of threedimensional bodies with complex rheology,” Dokl. Ross Akad. Nauk, 356, No. 2, 196–198 (1997).
[89] D. V. Georgievskii, ”The method of integral relations in stability problems for nonlinear flows with kinematics defined at the boundary,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 102–113 (1997).
[90] D. V. Georgievskii, ”Stability of deformation processes according to measure sets with respect to given perturbations classes,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 69–92 (1997).
[91] D. V. Georgievskii, ”General estimates of development of perturbations in three-dimensional nonhomogeneous scalar nonlinear flows,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 6, 90–97 (1998).
[92] D. V. Georgievskii, Stability of Deformation Processes of Viscous-Plastic Bodies [in Russian], URSS, Moscow (1998).
[93] D. V. Georgievskii, ”Stability problem for quasilinear flows with respect to perturbations of the strengthening function,” Zh. Prikl. Mat. Mekh., 63, Issue 5, 826–832 (1999). · Zbl 1019.74005
[94] D. V. Georgievskii, ”Some non-one-dimensional problems of viscous-plasticity: Rigid zones and stability (review),” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 61–78 (2001).
[95] D. V. Georgievskii, ”Tensor nonlinear effects in the isothermal deformation of continuous media,” Usp. Mech., 1, No. 2, 150–176 (2002).
[96] D. V. Georgievskii, ”Small perturbations of nondeformed states in media with yield stress,” Dokl. Ross Akad. Nauk, 392, No. 5, 634–637 (2003).
[97] D. V. Georgievskii, ”Diffusion of the break of the tangential stress at the boundary of a viscousplastic half-plane,” Zh. Prikl. Mat. Mekh., 70, No. 5, 884–892 (2006).
[98] D. V. Georgievskii, ”Perturbations of material functions in defining relations of ideal- and viscous-plastic media,” In: Elasticity and Nonelasticity [in Russian], URSS, Moscow (2006), pp. 35–43.
[99] D. V. Georgievskii, ”Perturbations of flows of noncompressible nonlinearly viscous and viscousplastic fluids generated by variations of material functions,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 3, 55–62 (2007).
[100] D. V. Georgievskii, ”Generalized diffusion of the vortices: Self-similarity and the Stefan problem,” Contemp. Math. Appl., 62, 28–46 (2009). · Zbl 1186.35160
[101] D. V. Georgievskii, ”Viscoplastic stratified composites: shear flows and stability,” In: Proc. NATO ASI ”Mechanics of Composite Materials and Structures”. III. Troia (Portugal), 1998, NATO ASI, Lisboa (1998), pp. 315–324.
[102] D. V. Georgievskii, ”Isotropic nonlinear tensor functions in the theory of constitutive relations,” J. Math. Sci., 112, No. 5, 4498–4516 (2002). · Zbl 1161.74304 · doi:10.1023/A:1020522321721
[103] D. V. Georgievskii, ”Perturbation of constitutive relations in tensor nonlinear materials,” Mech. Adv. Mater. Struct., 15, No. 6, 528–532 (2008). · doi:10.1080/15376490802142759
[104] D. V. Georgievskii, ”Applicability of the Squire transformation in linearized problems on shear stability,” Russian J. Math. Phys., 16, No. 4, 478–483 (2009). · Zbl 1186.35159 · doi:10.1134/S1061920809040025
[105] D. V. Georgievskii and A. V. Zhdanova, ”Asymptotics in the problem of starting of deformation and complete filling of a gas bubble,” Dokl. Ross Akad. Nauk, 399, No. 2, 188–191 (2004).
[106] D. V. Georgievskii and A. V. Zhdanova, ”On starting of deformation and complete filling of a spherical gas bubble in media with yield stress,” Vestn. MGU, Ser. 1. Mat. Mekh., 4, 39–45 (2005).
[107] D. V. Georgievskii and D. M. Klimov, ”Energy analysis of the development of kinematic perturbations in weakly nonhomogeneous viscous fluids,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 2, 56–67 (2000). · Zbl 0984.76031
[108] D. V. Georgievskii, D. M. Klimov, and A. G. Petrov, ” Problems of inertialess flows of weakly nonhomogeneous viscous media,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 3, 17–25 (2003).
[109] D. V. Georgievskii and N. N. Okulova, ”On viscous-plastic von Karman flows,” Vestn. MGU, Ser. 1. Mat. Mekh., 5, 45–49 (2002). · Zbl 1119.76309
[110] G. Z. Gershuni and E. M. Zhukhovitskii, ”On the convective stability of a Bingham fluid,” Dokl. Akad. Nauk SSSR, 208, No. 2, 63–65 (1973).
[111] R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer-Verlag, New York (1984). · Zbl 0536.65054
[112] A. V. Gnoevoi, D. M. Klimov, A. G. Petrov, and V. M. Chesnokov, ”Flows of viscous-plastic media between parallel circular plates at their coming together and receding,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 1, 9–17 (1996).
[113] A. V. Gnoevoi, D. M. Klimov, A. G. Petrov, and V. M. Chesnokov, ”Planar flows of viscousplastic media in narrow channels with deformable walls,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 2, 23–31 (1996).
[114] A. V. Gnoevoi, D. M. Klimov, A. G. Petrov, and V. M. Chesnokov, ”On a method of the investigation of spatial flows of viscous-plastic media,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 4, 150–158 (1993).
[115] A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, Flows of Viscous-Plastic Media in Channels and Cavities with Changing Forms of Their Walls (Elements of Theory and Technical Application) [in Russian], Poligrafservis, Moscow (1995).
[116] A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, ”On the theory of flows of Bingham media,” Preprint IPM RAN No. 626, Moscow (1998).
[117] A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, ”On a planar flow of Bingham media,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 5, 63–73 (2001).
[118] A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, ”On flow equations for Bingham media,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 6, 108–114 (2001).
[119] A. V. Gnoevoi, D. M. Klimov, and V. M. Chesnokov, Foundations of the Theory of Flows of Bingham Media [in Russian], Fizmatlit, Moscow (2004).
[120] R. V. Goldshtein and V. M. Entov, Qualitative Methods in Mechanics of Continuous Media [in Russian], Nauka, Moscow (1989).
[121] A. L. Gonor and S. N. Kutsaev, ”Collisions of a viscous-plastic body against a rigid barrier at an arbitrary contact angle,” Nauch. Tr. Vsesoyuz. Zaoch. Mash. Inst., 38, 62–70 (1976).
[122] H. R. W. Gottlieb, ”Exact solution of a Stefan problem in a nonhomogeneous cylinder,” Appl. Math. Lett., 15, No. 2, 176–172 (2002). · Zbl 0999.80008
[123] T. B. Grankina, ”Numerical methods of solving the one-phase Stefan problem,” Dynam. Contin. Media, 118, 16–20, (2001). · Zbl 1002.80020
[124] V. G. Grigoriev, S. Z. Dunin, and V. V. Surkov, ”Closing of a spherical pore in a viscous-plastic material,” Izv. Akad. Nauk SSSR, Mekh. Tv. Tela, No. 1, 199–201 (1981).
[125] P. P. Grinevich and M. A. Olshanskii, ”An iterative method for the Stokes-type problem with variable viscosity,” SIAM J. Sci. Comput., 31, No. 5, 3959–3978 (2009). · Zbl 1410.76290 · doi:10.1137/08744803
[126] Yu. V. Gurkov and A. G. Petrova, ”Numerical solution of the Stefan problem with nonconstant temperature of phase transition,” Zh. Prikl. Mekh. Tekh. Fiz., 22, 105–112 (1996). · Zbl 0935.80004
[127] A. M. Gutkin, ”Flow of a viscous-plastic disperse system on a rotating disk,” Kolloid. Zh., 22, No. 5, 573–575 (1960).
[128] A. M. Gutkin, ”Slow flow of a viscous-plastic disperse medium in conic and planar diffusers at small aperture,” Kolloid. Zh., 23, No. 3, 352 (1961).
[129] A. M. Gutkin, ”Flow of a viscous-plastic disperse system on a rotating cone,” Kolloid. Zh., 24, No. 3, 283–288 (1962).
[130] O. N. Dementiev and E. V. Karas’, ”Stability of extension of a restangular plate,” Vestn. Chelyabinsk. Univ. Ser. Mat. Mekh., No. 1, 121–128 (1991).
[131] A. G. Dzhafarli, ”Nonlinear viscous-plastic waves in threads in their spatial motion,” Dokl. Akad. Nauk AzSSR, 42, No. 1, 16–19 (1986). · Zbl 0631.73023
[132] A. S. Dudko, ”Influence of a finite-size sink on the rotation of a linear viscous-plastic medium,” In: Hydromechanics [in Russian], Naukova Dumka, Kiev (1989), 59, pp. 44–49.
[133] D. V. Evdokimov and A. A. Kochubey, ”Application of boundary-element methods for solving the Stefan problem in the case of slow phase transitions,” Vestn. Khar’kov. Univ., 590, 26–31 (2003).
[134] G. S. Erganov and A. K. Egorov, ”The stability of the viscous-plastic flow of thick-walled ball,” Izv. Akad. Nauk KazSSR, Ser. Fiz. Mat., No. 1, 17–23 (1984).
[135] G. S. Erzhanov, A. K. Egorov, and G. Sh. Zhantaev, ”Stability of a viscous-plastic flow of a heavy stratified medium,” Izv. Akad. Nauk KazSSR, Ser. Fiz. Mat., No. 1, 17–23 (1981). · Zbl 0465.73024
[136] R. W. Hanks, ”The laminar-turbulent transition for fluids with a yield stress,” AIChE J., 9, No. 3, 306–309 (1963). · doi:10.1002/aic.690090307
[137] R. W. Hanks and B. L. Ricks, ”Laminar-turbulent transition in flow of pseudoplastic fluids with yield stresses,” J. Hydronaut., 8, No. 4, 163–166 (1974). · doi:10.2514/3.62992
[138] J. W. He and R. Glowinski, ”Steady Bingham fluid flow in cylindrical pipes: a time-dependent approach to the iterative solution,” Numer. Linear Algebra Appl., 7, No. 6, 381–428 (2000). · Zbl 1050.76031 · doi:10.1002/1099-1506(200009)7:6<381::AID-NLA203>3.0.CO;2-W
[139] P. Hild, ”The mortar finite element method for Bingham fluids,” M2AN Math. Model. Numer. Anal., 35, No. 1, 153–164 (2001). · Zbl 0990.76042 · doi:10.1051/m2an:2001110
[140] P. Hild, I. R. Ionescu, T. Lachand-Robert, and I. Roşca, ”The blocking of an inhomogeneous Bingham fluid. Applications to landslides,” M2AN Math. Model. Numer. Anal., 36, No. 6, 1013–1026 (2002). · Zbl 1057.76004 · doi:10.1051/m2an:2003003
[141] A. J. Hogg and G. P. Matson, ”Slumps of viscoplastic fluids on slopes,” J. Non-Newton. Fluid Mech., 158, No. 1–3, 101–112 (2009). · Zbl 1274.76028 · doi:10.1016/j.jnnfm.2008.07.003
[142] C. K. Hsieh, ”Exact solution of a Stefan problems related to a moving line heat source in a quasi-stationary state,” Trans. ASME. J. Heat Transfer., 117, No. 4, 1076–1078 (1995). · doi:10.1115/1.2836288
[143] C. K. Huen, I. A. Frigaard, and D. M. Martinez, ”Experimental studies of multi-layer flows using a visco-plastic lubricant,” J. Non-Newton. Fluid Mech., 142, No. 1–3, 150–161 (2007). · Zbl 1143.76332 · doi:10.1016/j.jnnfm.2006.08.001
[144] R. R. Huilgol, ”On kinematic conditions affecting the existence and nonexistence of a moving yield surface in unsteady unidirectional flows of Bingham fluids,” J. Non-Newton. Fluid Mech., 123, No. 2–3, 215–221 (2004). · Zbl 1084.76007 · doi:10.1016/j.jnnfm.2004.08.009
[145] R. R. Huilgol, ”A systematic procedure to determine the minimum pressure gradient required for the flow of viscoplastic fluids in pipes of symmetric cross-sections,” J. Non-Newton. Fluid Mech., 136, No. 2–3, 140–146 (2006). · Zbl 1195.76023 · doi:10.1016/j.jnnfm.2006.04.001
[146] R. R. Huilgol and Z. You, ”Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel–Bulkley fluids,” J. Non-Newton. Fluid Mech., 128, No. 2–3, 126–143 (2005). · Zbl 1195.76024 · doi:10.1016/j.jnnfm.2005.04.004
[147] R. R. Huilgol and Z. You, ”Prolegomena to variational inequalities and numerical schemes for compressible viscoplastic fluids,” J. Non-Newton. Fluid Mech., 158, No. 2, 113–126 (2009). · Zbl 1274.76031 · doi:10.1016/j.jnnfm.2008.07.005
[148] I. R. Ionescu and M. Sofonea, Functional and Numerical Methods in Viscoplasticity, Clarendon Press; Oxford Univ. Press, New York (1993). · Zbl 0787.73005
[149] A. A. Il’yushin, ”Deformation of viscous-plastic bodies,” Uch. Zap. MGU. Mech., No. 39, 3–81 (1940).
[150] A. A. Il’yushin, ”Stability of plates and shells over the elasticity limit,” Zh. Prikl. Mat. Mekh., 8, Issue 5, 337–360 (1944).
[151] A. A. Il’yushin, Plasticity. Elastoplastic Deformations [in Russian], Gostekhizdat, Moscow–Leningrad, (1944).
[152] A. A. Il’yushin, Plasticity. Fundamentals of General Mathematical Theory [in Russian], Izd. Akad. Nauk. SSSR, Moscow, (1963).
[153] A. A. Il’yushin, Mechanics of Continuous Media [in Russian], MGU, Moscow, (1990).
[154] A. A. Il’yushin, ”Dynamics,” Vestn. MGU, Ser. 1. Mat. Mekh., 3, 79–87 (1994).
[155] A. A. Il’yushin, ”On the problem on viscous-plastic flows of materials,” In: Collected Papers. Vol. 1 [in Russian], Fizmatlit, Moscow (2003), pp. 115–131.
[156] A. Yu. Ishlinskii, ”On the stability of a viscous-plastic flow of a circular plate,” Zh. Prikl. Mat. Mekh., 7, No. 6, 405–412 (1943).
[157] A. Yu. Ishlinskii, ”On the stability of a viscous-plastic flow of a band and a circular rod,” Zh. Prikl. Mat. Mekh., 7, No. 2, 109–130 (1943).
[158] A. Yu. Ishlinskii and G. I. Barenblatt, ”On the impact of a viscous-plastic rod against a rigid barrier,” Dokl. Akad. Nauk SSSR, 144, No. 4, 734–737 (1962).
[159] A. Yu. Ishlinskii and G. P. Sleptsova, ”On the impact of a viscous-plastic rod against a rigid barrier,” Prikl. Mekh., 1, No. 2, 1–9 (1965).
[160] S. A. Jenekhe and S. B. Schuldt, ”Flow and film thickness of Bingham plastic liquids on a rotating disk,” Chem. Eng. Commun., 33, No. 1–4, 135–147 (1985). · doi:10.1080/00986448508911165
[161] P. Jie and K. Q. Zhu, ”Drag force of interacting coaxial spheres in viscoplastic fluids,” J. Non-Newton. Fluid Mech., 135, No. 2–3, 83–91 (2006). · Zbl 1195.76028 · doi:10.1016/j.jnnfm.2006.01.006
[162] L. Jossic and A. Magnin, ”Drag of an isolated cylinder and interactions between two cylinders in yield stress fluids,” J. Non-Newton. Fluid Mech., 164, No. 1–3, 9–16 (2009). · Zbl 1274.76035 · doi:10.1016/j.jnnfm.2009.07.002
[163] I. A. Kaliev, ”Global solvability of one problem that models a phase transition gas–rigid solid,” Dynam. Contin. Media, 116, 36–41, (2000). · Zbl 1055.76571
[164] J. M. Kelly and T. Wierzbicki, ”Motion of a circular viscoplastic plate subject to projectile impact,” ZAMP, 18, No. 2, 236–246 (1967). · Zbl 0154.22904 · doi:10.1007/BF01596915
[165] I. V. Keppen and S. Yu. Rodionov, Extension and Compression of Plates made of Nonlinear Viscous-Plastic Materials. Elasticity and Inelasticity [in Russian], MGU, Moscow (1987).
[166] S. Kesavan, ”On the asymptotic behavior of a Bingham fluid in thin layer,” In: Analysis and Applications, Allied Publ., New Delhi (2004), pp. 57–70.
[167] Inwon C. Kin, ”Uniqueness and existence results on the Hele-Shaw and the Stefan problems,” Arch. Ration. Mech. Anal., 168, No. 4, 299–328 (2003). · Zbl 1044.76019 · doi:10.1007/s00205-003-0251-z
[168] L. P. Kholpanov, S. E. Zakiev, and V. A. Fedotov, ”Neumann–Lam’e–Clapeyron–Stefan problem and the solution by the method of fractional differentiation,” Teor. Fundam. Khim. Tehnol., 37, No. 2, 128–137 (2003).
[169] I. A. Kiyko, Theory of Viscous-Plastic Flows. Elasticity and Inelasticity [in Russian], URSS, Moscow (2006).
[170] A. H. Kim and M. P. Volarovich, ”Planar problem on the motion of a viscous-plastic disperse system between two planes with an acute angle between them,” Kolloid. Zh., 22, No. 2, 186–194 (1960).
[171] D. M. Klimov and D. V. Georgievskii, ”Evolution of a weak initial inhomogeneity (start of mixing) in a continuous medium,” In: Actual Problems of Mechanics. Mechanics of Deformable Rigid Bodies [in Russian], Nauka, Moscow (2009), pp. 352–370.
[172] D. M. Klimov and A. G. Petrov, ”Analytical solutions of the boundary-value problem of nonstationary flow of viscoplastic medium between two plates,” Arch. Appl. Mech., 70, No. 1, 3–16 (2000). · Zbl 0981.74006 · doi:10.1007/s004199900027
[173] D. M. Klimov, S. V. Nesterov, L. D. Akulenlo, D. V. Georgievskii, and S. A. Kumakshev, ”Flows of viscous-plastic media with small yield stress in planar confusers,” Dokl. Ross. Akad. Nauk, 375, No. 4, 37–41 (2000).
[174] D. M. Klimov, S. V. Nesterov, L. D. Akulenlo, D. V. Georgievskii, and S. A. Kumakshev, ”Viscous-plastic flows in confusers,” Izv. Vuzov. Sev.-Kavk. Reg. Estestv. Nauki, Special Issue, 89–92 (2001).
[175] D. M. Klimov, A. G. Petrov, and D. V. Georgievskii, Viscous-Plastic Flows: Dynamical Chaos, Stability, and Confusion [in Russian], Nauka, Moscow (2005).
[176] O. R. Kozyrev and Yu. A. Stepaniants, ”Method of integral relations in the linear theory of hydrodynamical stability,” In: Progress in Science and Technology, Series on Mechanics of Fluid and Gas [in Russian], 25, All-Russian Institute for Scientific and Technical Information, Russian Academy of Sciences, Moscow (1991), pp. 3–89.
[177] Yu. Ya. Kolbovskii, N. P. Shanin, and V. N. Khranin, ”On flows of non-Newtonian fluids in conic and planar diffusers,” Nauch. Tr. Yaroslav. Tekhnol. Inst., 31, 102–106 (1972).
[178] V. L. Kolmogorov and G. L. Kolmogorov, ”Flows of viscous-plastic lubricants for draging in the regime of hydrodynamical friction,” Izv. Vuzov. Black Metal., No. 2, 67–72 (1968).
[179] S. V. Konev, ”The hydrodynamical isothermal problem of rolling of cylindrical surfaces with sliding under plastic lubricants,” In: Friction and Wear Problems [in Russian], Tekhnika, Kiev, 30, (1986), pp. 16–18
[180] L. I. Kotova, ”The theory of rolling of a cylinder along a surface covered by a layer of viscousplastic lubricant,” Zh. Tekh. Fiz., 27, No. 7, 1540–1557 (1957).
[181] L. I. Kotova and B. V. Deryagin, ”The theory of rolling of a cylinder along a surface covered by a layer of plastic lubricant,” Zh. Tekh. Fiz., 27, No. 6, 1261–1271 (1957).
[182] N. V. Krasnoshchek, ”Stefan problem for a degenerate system of equations,” Dopov. Nats. Akad. Nauk Ukr., 4, 29–32 (1999).
[183] S. N. Kruzhkov, ”On some problems with unknown boundaries for the heat equation,” Zh. Prikl. Mat. Mekh., 31, No. 6, 1009–1020 (1967). · Zbl 0159.39604
[184] S. N. Krugkov, ”On one class of problems with the unknown boundary for the heat conductivity equation,” Dokl. Akad. Nauk SSSR, 178, No. 5, 1036–1038 (1968).
[185] P. A. Kuzin, ”The longitudinal impact of a viscous-plastic rod,” Inzh. Zh. Mekh. Tverd. Tela, 5, 94–97 (1968).
[186] A. A. Lacey and L. A. Herraiz, ”Macroscopic models for melting derived from averaging microscopic Stefan problems. I. Simple geometries with kinetic undercooling of surface tension,” Eur. J. Appl. Math., 11, No. 2, 153–169 (2000). · Zbl 0954.35155 · doi:10.1017/S0956792599004027
[187] O. A. Ladyzhenskaya and G. A. Seregin, ”On global stability of the two-dimensional viscoplastic flows,” In: Jyv”askyl”a – St. Petersburg Seminar on Partial Differ. Equat. and Numer. Meth. Rept., 56, Univ. Jyväskylä (1993), pp. 43–52. · Zbl 0790.73027
[188] O. A. Ladyzhenskaya and G. A. Seregin, ”On semigroups generated by initial-boundary value problems describing two-dimensional viscoplastic flows,” Nonlinear Evolution Equations, Amer. Math. Soc. Transl. Ser. 2, 164, 99–123 (1995). · Zbl 0846.35068
[189] M. P. Landry, I. A. Frigaard, and D. M. Martinez, ”Stability and instability of Taylor–Couette flows of a Bingham fluid,” J. Fluid Mech., 560, 321–353 (2006). · Zbl 1161.76473 · doi:10.1017/S0022112006000620
[190] C. Lanos and A. Dustens, ”Rhéométrie des écoulements entre plateaux parallèeles: Réflexions,” Eur. J. Mech. Engng., 39, No. 2, 77–89 (1994).
[191] B. I. Lapushina and A. Kh. Kim, ”Approximate solution of the problem on a stationary isothermal flow of a viscous-plastic medium in a planar parabolic diffuser by the variational method,” Teor. Prikl. Mekh, 1, 17–20 (1975).
[192] N. V. Lazovskaya, ”The study of kinematics of flows of disperse systems (peat, consistent lubricants, etc.) in conic nozzles,” Kolloid. Zh., 11, No. 2, 77–83 (1949).
[193] E. V. Lenskii, ”On group properties of equations of motion of nonlinear viscous-plastic media,” Vestn. MGU, Ser. 1. Mat. Mekh., 5, 116–125 (1966).
[194] E. A. Leonova, ”Group classification and invariant solutions of flow equations and heat-change equations for viscous-plastic media,” Zh. Prikl. Mekh. Tekh. Fiz., 4, 3–18 (1966).
[195] E. A. Leonova, ”Invariant properties of equations of termoviscoplasticity with incomplete information on proprties of the medium,” In: Elasticity and Nonelasticity [in Russian], 1, MGU, Moscow (1993), pp. 35–43.
[196] Y. M. Leroy and A. Molinari, ”Stability of steady states in shear zones,” J. Mech. Phys. Solids, 40, No. 1, 181–212 (1992). · doi:10.1016/0022-5096(92)90310-X
[197] N. P. Leshchii, ”Transition from laminar to turbulent regimes in flows of nonlinear viscous-plastic fluids,” In: Hydraulics and hydrotechnics [in Russian], 31, Tekhnika, Kiev (1981), pp. 81–86.
[198] A. I. Litvinov, ”Semiempirical description of turbulence of viscous-plastic fluids,” Izv. Acad. Nauk UzSSR, Ser. Tekh., No. 5, 46–50 (1975).
[199] V. V. Lokhin and L. I. Sedov, ”Nonlinear tensor functions of some tensor arguments,” Zh. Prikl. Mat. Mekh., 27, No. 3, 393–417 (1975).
[200] O. B. Magomedov and B. E. Pobedrya, ”Some problems of viscoelasticplastic flows,” In: Elasticity and Nonelasticity [in Russian], 4, MGU, Moscow (1993), pp. 152–169.
[201] A. A. Mamakov, N. V. Tyabin, and G. V. Vinogradov, ”Application of the similarity theory to calculation of flows of plastic lubricants in pipes,” Kolloid. Zh., 21, No. 2, 208–215 (1959).
[202] A. E. Mamontov, ”Existence of global solutions of multi-dimensional equations of compressible Bingham fluids,” Mat. Zametki, 82, No. 4, 560–577 (2007). · doi:10.4213/mzm3825
[203] S. Matsumoto, Y. Takashima, T. Kamlya, A. Kayano, and Y. Ohta, ”Film thickness of a Bingham liquid on a rotating disk,” Industr. Eng. Chem. Fundam., 21, No. 3, 198–202 (1982). · doi:10.1021/i100007a002
[204] R. M. Matveevskii, V. L. Lahshi, and I. A. Buyanovskii, Lubricants: Antifriction and Antiwear Properties. Tests Methods [in Russian], Mashinostroenie, Moscow (1989).
[205] A. K. Mekhtiev, ”On compression of a cylindrical pattern by impact under nonlinear dependence of the stress on the deformation velocity,” In: Static and Dynamic Problems of Theory of Elasticity and Plasticity [in Russian], Izd. AzSSR, Baku (1968), pp. 90–95.
[206] P. R. Mendes, M. F. Naccache, P. R. Varges, and F. H. Marchesini, ”Flow of viscoplastic liquids through axisymmetric expansions – contractions,” J. Non-Newton. Fluid Mech., 142, No. 1–3, 207–217 (2007). · Zbl 1113.76015 · doi:10.1016/j.jnnfm.2006.09.007
[207] O. Merkak, L. Jossic, and A. Magnin, ”Spheres and interactions between spheres moving at very low velocities in a yield stress fluid,” J. Non-Newton. Fluid Mech., 133, No. 2–3, 99–108 (2006). · Zbl 1195.76037 · doi:10.1016/j.jnnfm.2005.10.012
[208] C. Métivier and C. Nouar, ”On linear stability of Rayleigh–Bénard Poiseuille flow of viscoplastic fluids,” Phys. Fluids, 20, No. 10, 104101/1–104101/14 (2008). · Zbl 1182.76511
[209] C. Métivier and C. Nouar, ”Linear stability of the Rayleigh–Bénard Poiseuille flow for thermodependent viscoplastic fluids,” J. Non-Newton. Fluid Mech., 163, No. 1–3, 1–8 (2009). · Zbl 1274.76208 · doi:10.1016/j.jnnfm.2009.06.001
[210] C. Métivier, C. Nouar, and J.-P. Brancher, ”Linear stability involving the Bingham model when the yield stress approaches zero,” Phys. Fluids, 17, No. 10, 104106/1–104106/7 (2005). · Zbl 1188.76095
[211] S. V. Milyutin, ”On the calculation of flows of Bingham fluids,” In: Finite-Difference Methods for Boundary-Value Problems and Applications [in Russian], Proceedings of VII All-Russian Seminar, Izd. Kazan. Gos. Univ., Kazan (2007), pp. 200–205.
[212] S. V. Milyutin, ”Practical optimization of the three-parametric iteration method for the calculation of flows of Bingham fluids,” Vychisl. Met. Prilozh., 9, 38–43 (2008).
[213] S. V. Milyutin, ”On an algorithm of the calculation of flows of a generalized Newtonian fluid,” Vestn. MGU, Ser. 1. Mat. Mekh., 5, 63–65 (2009). · Zbl 1304.76030
[214] N. V. Mikhailov and P. A. Rebinder, ”On structural-mechanical properties of disperse and high molecular systems,” Kolloid. Zh., 17, No. 2, 107–119 (1955).
[215] E. Mitsoulis, ”Fountain flow of pseudoplastic and viscoplastic fluids,” J. Non-Newton. Fluid Mech., 165, No. 1–2, 45–55 (2010). · Zbl 1274.76043 · doi:10.1016/j.jnnfm.2009.09.001
[216] E. Mitsoulis and Th. Zisis, ”Flow of Bingham plastics in a lid-driven cavity,” J. Non-Newton. Fluid Mech., 101, No. 3, 173–180 (2001). · Zbl 1079.76506 · doi:10.1016/S0377-0257(01)00147-1
[217] A.Molinari and R. J. Clifton, ”Analytical characterization of shear localization in thermoviscoplastic materials,” Trans. ASME. J. Appl. Mech., 54, No. 4, 806–812 (1987). · Zbl 0633.73118 · doi:10.1115/1.3173121
[218] A. A. Movchan, ”On the direct Lyapunov method in problems of stability of elastic systems,” Zh. Prikl. Mat. Mekh., 23, No. 3, 483–493 (1959).
[219] A. A. Movchan, ”Stability of processes by two metrics,” Zh. Prikl. Mat. Mekh., 24, No. 6, 988–1001 (1960).
[220] A. A. Movchan, ”On the stability of deformation processes of continuous media,” Arch. Mech. Stosow, 15, 659–682 (1963).
[221] P. P. Mosolov and V. P. Myasnikov, Variational Methods in the Theory of Flows of Rigid-Viscous-Plastic Media [in Russian], MGU, Moscow (1971). · Zbl 0248.52011
[222] M. A. Moyers-Gonzalez and I. A. Frigaard, ”Numerical solution of duct flows of multiple viscoplastic fluids,” J. Non-Newton. Fluid Mech., 122, No. 1–3, 227–241 (2004). · Zbl 1143.76343 · doi:10.1016/j.jnnfm.2003.12.010
[223] E. A. Muravleva, ”Finite-difference schemes for the calculation of flows of viscous-plastic media in channels,” Mat. Model., 12, 64–76 (2008). · Zbl 1164.76300
[224] E. A. Muravleva, ”The problem on the termination of flow of a viscous-plastic medium in a channel,” Vestn. MGU, Ser. 1. Mat. Mekh., 1, 68–71 (2009).
[225] E. A. Muravleva and L. V. Muravleva, ”Nonstationary flows of viscous-plastic media in channels,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 5, 164–188 (2009). · Zbl 1404.76182
[226] L. V. Muravleva and E. A. Muravleva, ”Uzawa method on semi-staggered grids for unsteady Bingham media flows, Russ. J. Numer. Anal. Math. Model., 24, No. 6, 543–563 (2009). · Zbl 1404.76182
[227] E. A. Muravleva and M. A. Olshanskii, ”Two finite-difference schemes for calculation of Bingham fluid flows in a cavity,” Russ. J. Numer. Anal. Math. Model., 23, No. 6, 615–634 (2008). · Zbl 1151.76539
[228] V. P. Myasnikov, ”Flows of viscous-plastic media under a complex shear,” Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 76–87 (1961).
[229] M. Nakamura and T. Sawada, ”Theoretical study on turbulence transition of Bingham plastic fluid in a pipe,” Trans. Jpn. Soc. Mech. Eng., B51, No. 465, 1642–1647 (1985). · doi:10.1299/kikaib.51.1642
[230] M. Nakamura and T. Sawada, ”A k {\(\epsilon\)} model for the turbulent analysis of Bingham plastic fluid,” Trans. Jpn. Soc. Mech. Eng., B52, No. 479, 2544–2551 (1986). · doi:10.1299/kikaib.52.2544
[231] G. A. Nesenenko, Mathematical Modeling of Nonlinear Singularly Perturbed Nonstationary Processes of Heat and Mass Transition, Doctoral thesis, Moscow (2003). · Zbl 1050.35010
[232] D. W. Nicholson, ”Adiabatic temperature rise in a viscoplastic rod under impact,” Mech. Res. Commun., 11, No. 5, 317–327 (1984). · Zbl 0575.73028 · doi:10.1016/0093-6413(84)90077-6
[233] R. I. Nigmatulin, I. Sh. Akhatov, N. K. Vakhitova, and R. T. Lahey, ”On the forced oscillations of a small gas bubble in a spherical liquid-filled flask,” J. Fluid Mech., 414, 47–73 (2000). · Zbl 0997.76076 · doi:10.1017/S0022112000008338
[234] L. V. Nikitin and D. B. Tokbergenov, ”Interaction of a viscous-plastic, dynamically deformable thread with a matrix,” Izv. Akad. Nauk KazSSR, Ser. Fiz. Mat., No. 3, 58–61 (1974).
[235] B. R. Nuriev, ”Transverse impact of the cone against a viscous-plastic thread with large speed,” Izv. Akad. Nauk AzSSR, Ser. Fiz.-Khim. Mat., 7, No. 3, 58–63 (1986).
[236] C. Nouar, N. Kabouya, J. Dusek, and M. Mamou, ”Modal and non-modal linear stability of the plane Bingham–Poiseuille flow,” J. Fluid Mech., 577, 211–239 (2007). · Zbl 1110.76017 · doi:10.1017/S0022112006004514
[237] P. M. Ogibalov and A. H. Mirzadjanzade, Nonstationary Motions of Viscous-Plastic Media [in Russian], Nauka, Moscow (1977).
[238] N. A. Okulov and N. N. Okulova, ”Tests of version methods,” Uch. Zap. RGSU, 7, 236–241 (2009).
[239] N. N. Okulova, ”On a method for solution of the problem on the diffusion of a vortex layer in a viscous-plastic half-plane,” Vestn. MGU, Ser. 1. Mat. Mekh., 4 (2004). · Zbl 1164.74371
[240] N. N. Okulova, ”Numerical-analytical simulation of the problem on the distribution of stresses in a viscous-plastic band,” Vestn. Samar. Univ. Estestv.-Nauch. Ser., 6, 78–84 (2007).
[241] M. A. Olshanskii, ”Analysis of semi-staggered finite-difference method with application to Bingham flows,” Comput. Methods Appl. Mech. Engrg., 198, 975–985 (2009). · Zbl 1229.76067 · doi:10.1016/j.cma.2008.11.010
[242] F. K. Oppong and J. R. de Bruyn, ”Diffusion of microscopic tracer particles in a yield-stress fluid,” J. Non-Newton. Fluid Mech., 142, No. 1–3, 104–111 (2007). · Zbl 1116.76003 · doi:10.1016/j.jnnfm.2006.05.008
[243] J. F. Osterle, A. Charnes, and E. Saibel, ”The rheodynamic squeeze film,” Lubricat. Eng., 12, No. 1, 33–36 (1956).
[244] Ya. G. Panovko, Mechanics of Deformable Rigid Bodies. Modern Conceptions, Errors, and Paradoxes [in Russian], Nauka, Moscow (1985).
[245] T. C. Papanastasiou, ”Flows of materials with yield,” J. Rheol., 31, No. 3, 385–404 (1987). · Zbl 0666.76022 · doi:10.1122/1.549926
[246] P. R. Paslay and A. Slibar, ”Laminar flow of drilling mud due to axial pressure gradient and external torque,” J. Petrol. Technol., 9, No. 11, 310–317 (1957).
[247] P. R. Paslay and A. Slibar, ”Criterion for flow of a Bingham plastic between two cylinders loaded by torque and pressure gradient,” J. Appl. Mech., 25, No. 2, 284–285 (1958). · Zbl 0102.17801
[248] K. B. Pavlov, A. S. Romanov, and S. L. Simhovich, ”Hydrodynamical unstability of Poiseuille flows of a non-Newtonian viscous-plastic fluid,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 6, 152–154 (1974).
[249] K. B. Pavlov, A. S. Romanov, and S. L. Simhovich, ”Hydrodynamical stability of Hartman flows of a non-Newtonian viscous-plastic fluid,” Magn. Gidrodinam., 4, 43–46 (1974).
[250] K. B. Pavlov, A. S. Romanov, and S. L. Simhovich, ”Stability of Poiseuille flows of a viscousplastic fluid with respect to perturbations of finite amplitude,” Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, No. 5, 166–169 (1975).
[251] J. Peixinho, C. Nouar, C. Desaubry, and B. Thèron, ”Laminar transitional and turbulent flow of yield stress fluid in a pipe,” J. Non-Newton. Fluid Mech., 128, No. 2–3, 172–184 (2005). · doi:10.1016/j.jnnfm.2005.03.008
[252] P. Perzyna, Fundamental Problems in Viscoplasticity, Academic Press, New York (1966).
[253] A. G. Petrov, ”On the optimization of control processes for viscous-plastic flows in thin layers with varying forms of boundaries,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 127–132 (1997).
[254] A. G. Petrov, ”The planar problem on displacement of a viscous-plastic medium by two parallel plates under the action of constant force,” Zh. Prikl. Mat. Mekh., 62, No. 4, 608–617 (1998).
[255] A. G. Petrov, ”Exact solutions of the boundary-value problem on nonstationary flows of a viscous-plastic medium between two plates,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 2, 3–13 (1999).
[256] A. G. Petrov, ”Flows of viscous and viscous-plastic media between two parallel plates,” Zh. Prikl. Mat. Mekh., 64, No. 1, 127–136 (2000). · Zbl 1050.74551
[257] A. G. Petrov, ”Method of Poincar’e mappings in hydrodynamical systems. Dynamical chaos in the liquid layer between eccentrically rotating cylinders,” Zh. Prikl. Mekh. Tekh. Fiz., 44, No. 1, 3–21 (2003).
[258] A. G. Petrov, ”On mixing of a viscous fluid in the layer between eccentrically rotating cylinders,” Zh. Prikl. Mat. Mekh., 72, No. 5, 741–758 (2008). · Zbl 1183.74063
[259] A. G. Petrov, Analytical Hydrodynamics [in Russian], Fizmatlit, Moscow (2009).
[260] A. G. Petrov and L. V. Cherepanov, ”Exact solutions of the problem on nonstationary flows of a viscous-plastic medium in a circular pipe,” Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, No. 2, 13–24 (2003). · Zbl 1161.76393
[261] M. Piau and J. M. Piau, ”Plane Couette flow of viscoplastic materials along a slippery vibrating wall,” J. Non-Newton. Fluid Mech., 125, No. 1, 71–85 (2005). · Zbl 1143.76361 · doi:10.1016/j.jnnfm.2004.10.003
[262] A. Pinarbasi and A. Liakopoulos, ”Stability of two-layer Poiseuille flow of Carreau-Yasuda and Bingham-like fluids,” J. Non-Newton. Fluid Mech., 57, No. 2–3, 227–241 (1995). · Zbl 1027.76568 · doi:10.1016/0377-0257(94)01330-K
[263] B. E. Pobedrya, ”On quasilinear tensor operators,” Vestn. MGU, Ser. 1. Mat. Mekh., 5, 97–100 (1971).
[264] B. E. Pobedrya, Mechanics of Composite Materials [in Russian], Izd. MGU, Moscow (1984). · Zbl 0555.73069
[265] B. E. Pobedrya, Lectures on Tensor Analysis [in Russian], Izd. MGU, Moscow (1986). · Zbl 0616.53001
[266] H. Poritsky, ”The collapse or growth of a spherical bubble in a viscous fluid,” In: Proc. 1st U.S. Nat. Congr. Appl. Mech., 1951, Ann Arbor, Mich. (1951), pp. 812–821.
[267] G. P. Prikazchikov, ”On the stability of flows of a viscous-plastic medium between planes with a gap,” Vestn. MGU, Ser. 1. Mat. Mekh., 3, 51–55 (1964).
[268] T. M. Rasulov, ”Solution of the mixed problem for the linearized equations of motion for a viscous-plastic medium motion,” Differ. Uravn., 27, No. 9, 1610–1617 (1991). · Zbl 0737.73047
[269] N. Roquet, R. Michel, and P. Saramito, ”Estimations d’erreur pour un fluide viscoplastique par èléments finis Pk et maillages adaptés,” C. R. Acad. Sci. Paris. Sér. I. Math., 331, No. 7, 563–568 (2000). · Zbl 1011.76047 · doi:10.1016/S0764-4442(00)01619-0
[270] N. Roquet and P. Saramito, ”An adaptive finite element method for viscoplastic fluid flows in pipes,” Comput. Methods Appl. Mech. Eng., 190, No. 41, 5391–5412 (2001). · Zbl 1002.76071 · doi:10.1016/S0045-7825(01)00175-X
[271] N. Roquet and P. Saramito, ”An adaptive finite element method for Bingham fluid flows around a cylinder,” Comput. Methods Appl. Mech. Eng., 192, No. 31–32, 3317–3341 (2003). · Zbl 1054.76053 · doi:10.1016/S0045-7825(03)00262-7
[272] N. Roussel, C. Lanos, and Z. Toutou, ”Identification of Bingham fluid flow parameters using a simple squeeze test,” J. Non-Newton. Fluid Mech., 135, No. 1, 1–7 (2006). · Zbl 1195.76049 · doi:10.1016/j.jnnfm.2005.12.001
[273] L. I. Rubinshtein, Stefan Problem [in Russian], Zvaigzne, Riga (1967).
[274] A. Ya. Sagomonyan, ”Motion of landslips arising at slopes of heights under the action of rain,” Vestn. MGU, Ser. 1. Mat. Mekh., 4, 30–36 (1999).
[275] A. Ya. Sagomonyan, ”Rain erosion of soils at slopes of heights,” Vestn. MGU, Ser. 1. Mat. Mekh., 4, 28–34 (2000).
[276] R. Salvi, ”On the existence of two phase problem for Bingham fluids,” Nonlinear Anal., 47, No. 6, 4205–4216 (2001). · Zbl 1042.76505 · doi:10.1016/S0362-546X(01)00537-5
[277] H. Schmitt, ”Numerical simulation of Bingham fluid flow using prox-regularization,” J. Optim. Theory Appl., 106, No. 3, 603–626 (2000). · Zbl 1028.90064 · doi:10.1023/A:1004661513837
[278] G. A. Seregin, ”Continuity for the strain velocity tensor in two-dimensional variational problems from the theory of the Bingham fluid,” Ital. J. Pure Appl. Math., 2, 141–150 (1997). · Zbl 0953.49002
[279] V. V. Shelukhin, ”Bingham viscoplastic as a limit of non-Newtonian fluid,” J. Math. Fluid Mech., 4, No. 2, 109–127 (2002). · Zbl 1002.35097 · doi:10.1007/s00021-002-8538-7
[280] J. D. Sherwood and D. Durban, ”Squeeze flow of a power-law viscoplastic solid,” J. Non-Newton. Fluid Mech., 62, No. 1, 35–54 (1996). · doi:10.1016/0377-0257(95)01395-4
[281] S. V. Serikov, ”On the stability of flows of a planar plastic ring with free boundaries,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 94–101 (1975).
[282] G. S. Shapiro and V. A. Shachnev, ”On the dynamical behavior of a viscous-plastic body possessing irreversible viscosity,” In: Waves in Inelastic Media [in Russian], Izd. Akad. Nauk MSSR, Kishinev (1970), pp. 215–220.
[283] V. V. Shelukhin, ”A model of Binhgam fluids in variables stress–velocity,” Dokl. Ross. Akad. Nauk, 377, No. 4, 455–458 (2001). · Zbl 1090.76506
[284] A. M. Slobodkin, ”On the stability of equilibria of conservative systems with infinite number of degrees of freedom,” Zh. Prikl. Mat. Mekh., 26, No. 2, 356–358 (1962). · Zbl 0104.31003
[285] A. M. Slobodkin, ”On features of the concept of the equilibrium stability in the Lyapunov sense for systems with infinite number of degrees of freedom,” Izv. Akad. Nauk SSSR. Mekh., 26, No. 5, 38–46 (1965).
[286] A. M. Slobodkin, ”On justification of the energy criterion of equilibrium stability,” In: Elasticity and Nonelasticity [in Russian], MGU, Moscow (1971). · Zbl 0255.73056
[287] B. Storakers, ”Plastic and visco-plastic instability of a thin tube under internal pressure, torsion and axial tension,” Int. J. Mech. Sci., 10, No. 6, 519–529 (1968). · doi:10.1016/0020-7403(68)90032-5
[288] M. B. Sugak, ”Motion of a viscous-plastic mass between two coaxial cones,” Inzh. Fiz. Zh., 11, No. 6, 802–808 (1966).
[289] P. S. Symonds and T. C. T. Ting, ”Longitudinal impact on viscoplastic rods: Approximate methods and comparisons,” Trans. ASME. Ser. E. J. Appl. Mech., 31, No. 4, 611–620 (1964). · Zbl 0128.19506 · doi:10.1115/1.3629722
[290] D. A. Tarzia and C. V. Turner, ”The asymptotic behavior for the two-phase Stefan problem with a convective boundary condition,” Commun. Appl. Anal., 7, No. 2–3, 313–334 (2003). · Zbl 1085.35128
[291] V. P. Tikhonov, S. A. Gulyaev, and S. S. Semenyuta, ”On the break of a layer of a viscous-plastic fluid between two surfaces,” Kolloid. Zh., 55, No. 4, 104–109 (1993).
[292] T. C. T. Ting and P. S. Symonds, ”Impact on rods of nonlinear viscoplastic material–numerical and approximate solutions,” Int. J. Solids Struct., 3, No. 4, 587–605 (1967). · doi:10.1016/0020-7683(67)90010-8
[293] D. B. Tokbergenov, ”Dynamical deformation of a viscous-plastic thread,” Izv. Akad. Nauk KazSSR. Ser. Fiz. Mat., No. 1, 72–76 (1973).
[294] D. L. Tokpavi, P. Jay, A. Magnin, and L. Jossic, ”Experimental study of the very slow flow of a yield stress fluid around a circular cylinder,” J. Non-Newton. Fluid Mech., 164, No. 1–3, 35–44 (2009). · doi:10.1016/j.jnnfm.2009.08.002
[295] G. Torres and C. Turner, ”Method of straight lines for a Bingham problem in cylindrical pipe,” Appl. Numer. Math., 47, No. 3–4, 543–558 (2003). · Zbl 1137.76316 · doi:10.1016/S0168-9274(03)00088-6
[296] J. A. Tsamopoulos, M. E. Chen, and A. V. Borkar, ”On the spin coating of viscoplastic fluids,” Rheol. Acta, 35, No. 4, 597–615 (1996). · doi:10.1007/BF00396510
[297] S. Tsangaris, C. Nikas, G. Tsangaris, and P. Neofytou, ”Couette flow of a Bingham plastic in a channel with equally porous parallel walls,” J. Non-Newton. Fluid Mech., 144, No. 1, 42–48 (2007). · Zbl 1195.76062 · doi:10.1016/j.jnnfm.2007.03.004
[298] P. Tugcu and K. W. Neale, ”Analysis of neck propagation in polymeric fibres including the effects of viscoplasticity,” Trans. ASME. J. Eng. Mater. Technol., 110, No. 4, 395–400 (1988). · doi:10.1115/1.3226068
[299] N. V. Tyabin, ”Flow of a viscous-plastic fluid disperse system in a diffuser and immersion of a wedge in a disperse system,” Dokl. Akad. Nauk SSSR, 84, No. 5, 943–946 (1952).
[300] N. V. Tyabin, ”Rheodynamical theory of viscous-plastic lubricants,” Tr. Kazan. Sel’khoz. Inst., 39, 132–150 (1958).
[301] N. V. Tyabin andM. A. Pudovkin, ”Flows of a viscous-plastic disperse system in a conic diffuser,” Dokl. Akad. Nauk SSSR, 92, No. 1, 53–56 (1953).
[302] I. G. Vardoulakis, ”Stability and bifurcation in geomechanics,” In: Proc. 6th Intern. Conf. on Numerical Methods in Geomechanics. Innsbruck, 1988, 1, Baekema, Rotterdam; Brookfield (1988), pp. 155–168.
[303] A. Vikhansky, ”Lattice-Boltzmann method for yield-stress liquids,” J. Non-Newton. Fluid Mech., 155, No. 3, 95–100 (2008). · Zbl 1274.76285 · doi:10.1016/j.jnnfm.2007.09.001
[304] G. Vinay, A. Wachs, and J.-F. Agassant, ”Numerical simulation of non-isothermal viscoplastic waxy crude oil flows,” J. Non-Newton. Fluid Mech., 128, No. 2–3, 144–162 (2005). · Zbl 1195.76065 · doi:10.1016/j.jnnfm.2005.04.005
[305] G. Vinay, A.Wachs, and J.-F. Agassant, ”Numerical simulation of weakly compressible Bingham flows: The restart of pipeline flows of waxy crude oils,” J. Non-Newton. Fluid Mech., 136, No. 1, 93–105 (2006). · Zbl 1195.76066 · doi:10.1016/j.jnnfm.2006.03.003
[306] G. V. Vinogradov and A. A. Mamakov, ”Flow of greases under the action of complex shear,” Trans. ASME. Ser. F. J. Lubr. Technol., 90, No. 3, 604–607 (1968). · doi:10.1115/1.3601633
[307] G. V. Vinogradov, A. A. Mamakov, and V. P. Pavlov, ”Flows of anomalous viscous systems under the action of two pure shears in mutually perpendicular directions,” Dokl. Akad. Nauk SSSR, 127, No. 2, 362–365 (1959).
[308] V. I. Vishnyakov, K. B. Pavlov, and A. S. Romanov, ”Peristaltic flows of a non-Newtonian viscous-plastic fluid in a gap channel,” Eng. Phys. J., 31, No. 3, 499–505 (1976).
[309] D. Vola, L. Boscardin, and J. C. Latché, ”Laminar unsteady flows of Bingham fluids: A numerical strategy and some benchmark results,” J. Comput. Phys., 187, No. 2, 441–456 (2003). · Zbl 1061.76035 · doi:10.1016/S0021-9991(03)00118-9
[310] M. P. Volarovich, ”Investigation of rheological properties of disperse systems,” Colloid J., 16, No. 3, 227–240 (1954).
[311] M. P. Volarovich and N. V. Lasovskaya, ”Investigation of peat flows in conic nozzles,” Dokl. Akad. Nauk SSSR, 76, No. 2, 211–213 (1951).
[312] A. Wachs, ”Numerical simulation of steady Bingham flow through an eccentric annular crosssection by distributed Lagrange multiplier/fictitious domain and augmented Lagrangian methods,” J. Non-Newton. Fluid Mech., 142, No. 2, 183–198 (2007). · Zbl 1143.76350 · doi:10.1016/j.jnnfm.2006.08.009
[313] E. Walicki and A. Walicka, ”An approximate analysis for conical flow of viscoplastic fluids,” Zecz. Nauk. Bud. WSI Zielonej Gorze, 106, 97–217 (1994).
[314] L. L. Wang, ”A criterion of thermo-viscoplastic instability for adiabatic shearing,” Proc. Intern. Symp. on Intense Dynam. Loading and Effects, Beijing, 1986, Oxford (1988), pp. 787–792.
[315] P. G.Wang and Z. D. Wang, ”The analysis of stability of Bingham fluid flowing down an inclined plane,” Appl. Math. Mech., 16, No. 10, 1013–1018 (1995). · Zbl 0837.76024 · doi:10.1007/BF02538843
[316] R. A. Williams and L. E. Malvern, ”Harmonic dispersion analysis of incremental waves in uniaxially prestressed plastic and viscoplastic bars, plates, and unbounded media,” Trans. ASME. Ser. E. J. Appl. Mech., 36, No. 1, 59–64 (1969). · Zbl 0181.53303 · doi:10.1115/1.3564586
[317] G. Wittum, V. Schulz, B. Maar, and D. Logashenko, ”Numerical mrthods for parameter estimation in Bingham-fluids,” In: Mathematics – key technology for the future, Springer-Verlag, Berlin (2003), pp. 204–215. · Zbl 1076.76573
[318] W. Wojewòdzki, ”Buckling of short viscoplastic cylindrical shells subjected to radial impulse,” Int. J. Non-Linear Mech., 8, No. 4, 325–343 (1973). · Zbl 0286.73072 · doi:10.1016/0020-7462(73)90022-X
[319] W.Wojewòdzki and P. Lewinski, ”Viscoplastic axisymmetrical buckling of spherical shell impulse subjected to radial pressure,” Eng. Struct., 3, No. 3, 168–174 (1981). · doi:10.1016/0141-0296(81)90025-0
[320] C. W. Wu and H. X. Sun, ”A new hydrodynamic lubrication theory for bilinear rheological fluids,” J. Non-Newton. Fluid Mech., 56, No. 3, 253–256 (1995). · doi:10.1016/0377-0257(94)01277-O
[321] V. O. Yablonskii, N. V. Tyabin, and V. M. Yashchuk, ”Application of viscous-plastic lubricants in hydrostatic supports for improvement of their exploitation characteristics,” Vestn. Mashinostr., 3, 11–14 (1995).
[322] E. I. Zababakhin, ”Filling of bubbles in a viscous fluid,” Zh. Prikl. Mat. Mekh., 24, No. 6, 1129–1131 (1998).
[323] V. S. Zarubin and M. M. Lukashin, ”Solution of the Stefan problem by method of continuous counting,” In: Problems of Gas Dynamics and Heat Mass Exchanging in Energy Engines [in Russian], MEI, Moscow (2003), 2, pp. 372–375.
[324] Yu. V. Zhernoviy and M. T. Saichuk, ”On the application of the method of Green functions for the numerical simulation of multi-dimensional Stefan problems,” Inzh.-Fiz. Zh., 71, No. 5, 910–916 (1998).
[325] H. Zhu, Y. D. Kim, and D. De Kee, ”Non-Newtonian fluids with a yield stress,” J. Non-Newton. Fluid Mech., 129, No. 3, 177–181 (2005). · Zbl 1195.76078 · doi:10.1016/j.jnnfm.2005.06.001
[326] K. J. Zwick, P. S. Ayyaswamy, and I. M. Cohen, ”Variational analysis of the squeezing flow of a yield stress fluid,” J. Non-Newton. Fluid Mech., 63, No. 2–3, 179–199 (1996). · doi:10.1016/0377-0257(95)01423-3
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.