Geodesic
Orientation instability of shear flow of a nematic liquid crystal
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 59-62 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of instability of shear flow of a nematic liquid crystal layer is considered. The case when the director and the velocity vector are parallel is studied. It is shown that the instability of this flow is possible in the case of the weak anchoring boundary condition and if the splay-bend constant in the Frank energy is taken into account. For this type of instability, periodical structures are possible to appear. Their wave vector is in plane of flow and is perpendicular to the velocity. An estimate for the medium constants is obtained from the existence condition for this instability. The wave number of periodical structures is evaluated. 
@article{VMUMM_2016_6_a10,
     author = {A. G. Kalugin},
     title = {Orientation instability of shear flow of a nematic liquid crystal},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {59--62},
     year = {2016},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a10/}
}
TY  - JOUR
AU  - A. G. Kalugin
TI  - Orientation instability of shear flow of a nematic liquid crystal
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 59
EP  - 62
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a10/
LA  - ru
ID  - VMUMM_2016_6_a10
ER  - 
%0 Journal Article
%A A. G. Kalugin
%T Orientation instability of shear flow of a nematic liquid crystal
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 59-62
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a10/
%G ru
%F VMUMM_2016_6_a10
A. G. Kalugin. Orientation instability of shear flow of a nematic liquid crystal. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2016), pp. 59-62. http://geodesic.mathdoc.fr/item/VMUMM_2016_6_a10/

[1] Leslie F.M., “Some constitutive equations for liquid crystals”, Arch. Ration. Mech. and Anal., 28 (1968), 265–283 | DOI | MR | Zbl

[2] Pieranski P., Guyon E., “Instability of certain shear flows in nematic liquids”, Phys. Rev. A, 9 (1974), 404–417 | DOI

[3] Cladis P.E., Torza S., “Stability of nematic liquid crystals in Couette flow”, Phys. Rev. Lett., 35 (1975), 1283–1286 | DOI

[4] Manneville P., Dubois-Violette E., “Shear flow instability in nematic liquids: theory steady simple shear flows”, J. Phys. France., 37 (1976), 285–296 | DOI

[5] Leslie F.M., “Magnetohydrodynamic instabilities in nematic liquid crystals”, Mol. Cryst. and Liquid Cryst., 37 (1976), 335–352 | DOI

[6] Pikin S.A., Chigrinov V.G., Indenbom V.L., “New types of instabilities in liquid crystals with tilted orientation”, Mol. Cryst. and Liquid Cryst., 37 (1976), 313–320 | DOI

[7] Pikin S., Ryschenkow G., Urbach W., “On new type of electrohydrodynamics instability in tilted nematic layers”, J. Phys. France, 37:3 (1976), 241–244 | DOI

[8] Golubyatnikov A.N., Kalugin A.G., “Ob ustoichivosti stekaniya plenki nematicheskogo zhidkogo kristalla”, Vestn. Mosk. un-ta. Matem. Mekhan., 2006, no. 4, 68–69

[9] Golubyatnikov A.N., Kalugin A.G., “O korotkikh poverkhnostnykh volnakh v anizotropnykh zhidkostyakh”, Vestn. Mosk. un-ta. Matem. Mekhan., 2001, no. 1, 42–43 | MR

[10] Kalugin A.G., “O roli divergentnykh chlenov v energii Franka nematicheskikh zhidkikh kristallov”, Vestn. Mosk. un-ta. Matem. Mekhan., 2013, no. 1, 69–71 | Zbl

[11] Kalugin A.G., “Ob orientatsionnoi neustoichivosti sloya nematicheskogo zhidkogo kristalla”, Izv. RAN. Mekhan. zhidkosti i gaza, 2016, no. 1, 67–70 | MR

[12] Kapustin A.P., Kapustina O.A., Akustika zhidkikh kristallov, Nauka, M., 1986

[13] Pasechnik S.V., Krekhov A.P., Shmeleva D.V., Nasibullaev I.Sh., Tsvetkov V.A., “Orientatsionnaya neustoichivost v nematicheskom zhidkom kristalle v zatukhayuschem puazeilevskom potoke”, Zhurn. eksperim. i teor. fiz., 127:4 (2005), 907–914

[14] Drovnikov E.M., Shmeleva D.V., “Vtorichnaya tsilindricheskaya neustoichivost, indutsirovannaya ostsilliruyuschim potokom Puazeilya”, Vestn. MGUPI. Ser. priborostr. i inform. tekhnol., 47 (2013), 9–14

[15] Sonin A.S., Vvedenie v fiziku zhidkikh kristallov, Nauka, M., 1983

[16] Kalugin A.G., Golubyatnikov A.N., “O ravnovesnoi forme kapli nematicheskogo zhidkogo kristalla”, Tr. Matem. in-ta RAN, 223, 1998, 171–177 | MR | Zbl

[17] Kalugin A.G., “O ravnovesii sloya nematicheskogo zhidkogo kristalla s neodnorodnoi granitsei”, Izv. RAN. Mekhan. zhidkosti i gaza, 2015, no. 2, 3–7 | MR | Zbl