Geodesic
Studying of the relations on the flat strong discontinuity for the polymeric liquid
Matematičeskoe modelirovanie, Tome 33 (2021) no. 1, pp. 89-104.

Voir la notice de l'article provenant de la source Math-Net.Ru

We are studying the flat strong discontinuity within the rheological modified Vinogradov–Pokrovskii model. The relation on the discontinuity are introduced. We justify the existence of steady-state solutions with discontinuity both with constant direction of the flow across the discontinuity and with changing direction (rotating discontinuity). The examples of numerical solutions are introduced in the paper.
Keywords: polymeric liquid, strong discontinuity, rotating discontinuity. 
@article{MM_2021_33_1_a6,
     author = {A. M. Blokhin and R. E. Semenko},
     title = {Studying of the relations on the flat strong discontinuity for the polymeric liquid},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {89--104},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_1_a6/}
}
TY  - JOUR
AU  - A. M. Blokhin
AU  - R. E. Semenko
TI  - Studying of the relations on the flat strong discontinuity for the polymeric liquid
JO  - Matematičeskoe modelirovanie
PY  - 2021
SP  - 89
EP  - 104
VL  - 33
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2021_33_1_a6/
LA  - ru
ID  - MM_2021_33_1_a6
ER  - 
%0 Journal Article
%A A. M. Blokhin
%A R. E. Semenko
%T Studying of the relations on the flat strong discontinuity for the polymeric liquid
%J Matematičeskoe modelirovanie
%D 2021
%P 89-104
%V 33
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2021_33_1_a6/
%G ru
%F MM_2021_33_1_a6
A. M. Blokhin; R. E. Semenko. Studying of the relations on the flat strong discontinuity for the polymeric liquid. Matematičeskoe modelirovanie, Tome 33 (2021) no. 1, pp. 89-104. http://geodesic.mathdoc.fr/item/MM_2021_33_1_a6/

[1] P. G. De Gennes, Scaling concept in polymer physics, Cornell University Press, London, 1979, 324 pp.

[2] L. D. Landau, E. M. Lifshitz, Fluid mechanics, Pergamon Press, Oxford, 1987, 539 pp. | MR | MR | Zbl

[3] J. G. Oldroyd, “On the formulation of rheological equations of state”, Proc. R. Soc., 200:1063 (1950), 523–541 | MR | Zbl

[4] A. I. Leonov, A. N. Prokunin, Nonlinear phenomena in flows of viscoelastic polymer fluids, Chapman and Hall, New York, 1994, 475 pp.

[5] P. J. Flory, Statistical mechanics of chained molecules, Interscience, Geneva, 1969, 432 pp.

[6] P. E. Rouse, “A theory of the linear viscoelastic properties of dilute solutions of coiling polymers”, J. Chem. Phys., 21:7 (1953), 1271–1280 | DOI

[7] M. Doi, S. Edwards, The theory of polymer dynamics, Clarendon press, Oxford, 1986, 391 pp.

[8] R. Bird, R. Armstrong, O. Hassager, Dynamics of polymeric liquids, Wiley, York, 1987, 649 pp. | MR

[9] H. Giesekus, “A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility”, J. Non-Newt. Fluid Mech., 11 (1982), 69–109 | DOI | Zbl

[10] V. N. Pokrovskii, The mesoscopic theory of polymer dynamics, 2nd Ed., Springer, New York–London–Dordrecht-Heidelberg, 2010, 256 pp.

[11] Iu. A. Altukhov, A. S. Gusev, G. V. Pyshnograi, Vvedenie v mezoskopicheskuiu teoriiu tekuchikh polimernykh sistem, AltGPA, Barnaul, 2012, 122 pp.

[12] L. I. Sedov, A course in continuum mechanics, v. 1, Wolters Noordhoff Publ., Groningen, 1972, 309 pp.

[13] P. A. Yampol'skii, I. M. Barkalov, V. I. Gol'danskii et. al., “Chemical reactions in polymers caused by shock waves”, Polymer Sci. USSR, 10:4 (1967), 929–939 | DOI

[14] S. W. J. Brown, P. R. Williams, “An experimental study of liquid jets formed by bubble-shock wave interaction in dilute polymer solutions”, Exper. in Fluids, 29:1 (2000), 56–65 | DOI

[15] V. Yu. Liapidevskii, V. V. Pukhnachev, A. Tani, “Nonlinear waves in incompressible viscoelastic Maxwell medium”, Wave Mot., 48:8 (2011), 727–737 | DOI | MR | Zbl

[16] Iu. L. Kuznethova, O. I. Skulskii, “Rassloenie potoka zhidkosti s nemonotonnoi zavisimostiu napriazheniia techeniia ot skorosti deformatsii”, Vych. mekh. splosh. sred, 11:1 (2018), 68–78

[17] N. V. Bambaeva, A. M. Blokhin, “Stationary solutions of equations of incompressible viscoelastic polymer liquid”, Comp. Math. and Math. Phys., 54:5 (2014), 874–899 | DOI | MR | Zbl

[18] N. V. Bambaeva, A. M. Blokhin, “The t-Hyperbolicity of a nonstationary system governing flows of polymeric media”, Journ. of Math. Sci., 188:4 (2013), 333–343 | DOI | MR | Zbl

[19] N. V. Bambaeva, A. M. Blokhin, “Symmetrization of the system of equations governing an incompressible viscoelastic polymeric fluid”, Journ. of Math. Sci., 203:4 (2014), 436–443 | DOI | MR | Zbl

[20] L. V. Ovsiannikov, Lektsii po osnovam gazovoi dinamiki, Nauka, M., 1981, 368 pp. | MR

[21] L. G. Loitsianskii, Mekhanika zhidkosti i gaza, Nauka, M., 1978, 677 pp.

[22] J. M. Delhaye, “Jump conditions and entropy sources in two-phase systems. Local instant formulation”, Int. J. Multiphase Flow, 1:3 (1974), 395–409 | DOI | Zbl

[23] Y. Shibata, “On the r-boundedness for the two phase problem with phase transition: Compressible-incompressible model problem”, Funkcialaj Ekvacioj, 59:2 (2016), 243–287 | DOI | MR | Zbl

[24] A. M. Blokhin, Yu. L. Thakhinin, Stability of strong discontinuities in magnetohydrodynamics and electrohydrodynamics, Nova Science Publishers, Inc., New York, 2003, 307 pp. | MR