Two-dimensional and One-dimensional Quations and Their Applications

Povstenko, J.

Artykuł - szczegóły

Tytuł artykułu

Two-dimensional and One-dimensional Quations and Their Applications

Autorzy

Povstenko J.

Wybrane pełne teksty z tego czasopisma

http://www.scientificissues.wnspt.ujd.edu.pl

Identyfikatory

Warianty tytułu

Języki publikacji

Abstrakty

An interfacial region and a three-phase line region are considered as two dimensional and one-dimensional continua. Equations of the linear momentum balance and moment-of-momentum balance generalize the Laplace equation for surfaces and the Young equation for lines. Balance equations for surface dislocations and disc1inations are also considered. The motor analysis is used for a description of continua with couple stresses.

Słowa kluczowe

two-dimensional equations of equilibrium one-dimensional equilibrum equations Young's equation

równanie równowagi dwuwymiarowe jednowymiarowe równania równowagi równanie Younga

Wydawca

Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie

Czasopismo

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

Rocznik

2006

Tom

Vol. 11

Strony

79--102

Opis fizyczny

Bibliogr. 90 poz.

Twórcy

autor

Povstenko J.

j.povstenko@ajd.czest.pl

Institute of Mathematics and Computer Science Jan Długosz University of Częstochowa al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland

Bibliografia

[1] E. Ruckenstein. An explanation for the unusual phase behavior of microemulsions. Chem. Phys. Lett., 98, 573-576, 1983.
[2] C.A. Miller, P. Neogi. Thermodynamics of microemulsions: Combined effects of dispersion entropy of drops and bending energy of surfactant films. AIChE J., 26, 212-220, 1980.
[3] C.A. Miller. Interfacial bending effects and interfacial tensions in microemulsions. J. Dispersum Sci. Techn., 6,159-173,1985.
[4] P.G. De Gennes, C. Taupin. Microemulsions and the flexibility of oil /water interfaces. J. Phys. Chem., 86, 2294-2304, 1982.
[5] C. Hu. Equilibrium of an microemulsion that coexists with oil or brine. Soc. Petrol. Eng. I, 23, 829-847, 1983. Two-dimensional and one-dimensional balance equations 95
[6] A. Pouchelon, D. Chatenay, J. Meunier, D. Langevin. Origin of low interface tensions in systems involving microemulsion phases. J. Colloid Interface Sci., 82, 418-422, 1981.
[7] W. Helfrich. Elastic properties of lipid bilayers: Theory and possible experiments. Z. Naturforschung. C: Bioscience, 28, 693-703, 1973.
[8] W. Helfrich. Blocked lipid exchange in bilayers and its possible influence on the shape of vesicles. Z. Naturforschung. C: Bioscience, 29, 510-515, 1974.
[9] I.R. Kramer. Influence of the surface layer on the plastic flow. Deformation of aluminium single crystals. Trans Met. Soc.AIME, 233, 1462-1467,1965.
[10] V.P. Alekhin. Physics of Strength and Plasticiry of the Sutface Layers of Materials. Nauka, Moscow, 1983. (In Russian).
[11] L.S. Milevskiy, 1.L. Smolskiy. Change of dislocation mobility under coming at the surface of a crystal wit h high Peierls barrier. Phys. Solid (Fizika Tverdogo Tela) , 16, 1028-1031, 1974. (In Russian).
[12] L.S. Milevskiy, 1.L. Smolskiy. Mobility of dislocations generated by internal sources in crystals with high Peierls barrier. Dynamics of Dislocations, Naukova Dumka, Kiev, pp. 30-36, 1975. (In Russian).
[13] V.I. Betekhtin, VJ. Vladimirov, AJ. Petrov, A.G. Kadomtsev. Microcracks in near-surface layers of strained crystals. Surface. Phys., Chem., Mech., No. 7, 144-151, 1984. (In Russian).
[14] R. Bullough, B.A. Bilby. Continuous distributions of dislocations: surface dislocations and the crystallography of martensitic transformations. Proc. Phys. Soc. Sec. B, 69, 1276-1286, 1956.
[15] M.J. Marcinkowski. The differential geometry of grain boundaries: tilt boundaries, Acta Cryst., A33, 865-872, 1977.
[16] K.N. Knowles. The dislocation geometry of interface boundaries. Phil. Mag., A46, 951-969, 1982.
[17] A.E. Volkov, V.A. Likhachev, L.S. Shykhobalov. Theory of grain boundaries as independent crystal imperfections. Phys. Metals Metal Sci., 47, 1127-1140, 1979. (In Russian).
[18] A.E. Volkov, V.A. Likhachev, L.S. Shykhobalov. Continuos theory of boundaries in heterogeneous crystals. Phys. Metals Metal Sci., 51, 935-944, 1981.
[19] G.E. Braynin, A.E. Volkov, V.A. Likhschev. Continuum description of the dislocation inheritance and the formation of difference dislocations due to internal boundaries movement. Surface. Phys., Chem., Mech., No. 7, 34-38, 1983.
[20] W.F. Harris. The geometry of disclinations in crystals. Surface and Defect Properties of Solids, vol. 3, pp. 57-92, 1974.
[21] P.A. Bereznyak, V.S. Boiko, LM. Mukhailovskiy. A new type of structural defects of large-angle grain boundaries and radiadionstimulated grain-boundary creeping. Probl. Atomic Sci. Engng, Phys. Radiation Damage and Radiation Sci. Mater., No. 1, 19-23, 1988. (In Russian).
[22] A.M. Kosevich, Yu.A. Kosevich. A step on the surface of a crystal formed by the emergence of an edge dislocation. Fizika Nizkikh Temperatur (Low Temperature Phys.) , 7, 1347-1349, 1981.
[23] A.M. Kosevich, Yu.A. Kosevich. Interaction of a dislocation with a crystal surface and emergence of dislocations onto a surface. The Structure and Properties od Crystal Dejects, Elsevier, Amsterdam, pp. 397-405, 1984.
[24] Y.Z. Povstenko. Continuous theory of dislocations and disclinations in a two-dimensional medium. 1. Appl. Math. Mech., 49, 782-786, 1985.
[25] Y.Z. Povstenko. Connection between non-metric differential geometry and mathematical theory of imperfections. Jnt. J. Engng Sci., 29, 37-46, 1991. Two-dimensional and one-dimensional balance equations
[26] R. Ghez. A generalized Gibbsian surface. Surface Sci., 4, 125- 140, 1966.
[27] Ya.S. Podstrigach, Y.Z. Povstenko. Jntroduction to the Mechanics of Surface Phenomena in Defermoble Solids. Kiev: Naukova Dumka, 1985. (In Russian).
[28] Y.Z. Povstenko. Conditions on the line of contact of three media. J. Appl. Math. Mech., 45, 690-693, 1981.
[29] Y.Z. Povstenko. The momentum balance equation at the line of contact of three media. Dokl. Akad. Nauk Ukrainian SSR, Ser. A, No. 10, 45-47, 1980. (In Russian).
[30] Y.Z. Povstenko. Generalizated Laplace and Young conditions of mechanical contact. Math. Meth. Phys.-Meeh. Fields, No. 16, 30-32, 1982. (In Russian).
[31] Y.Z. Povstenko. Generalizations of Laplace and Young equations involving couples. J. Colloid Tnierajce Sci., 144, 497-506, 1991.
[32] Y.Z. Povstenko. Influence of surface energy inhomogeneity on the stress state of an elastic half-space. Math. Meth. -Phys.- Mech. Fields, No. 9, 84-87, 1979. (In Russian).
[33] Y.Z. Povstenko. Distribution of stresses and concentration of impurities in the subsurface layer at the boundary of a solid due to a jumpwise change in the surface energy. Jnt. Appl. Mech., 17, 376-380, 1981.
[34] A.A. Borgardt, M.A. Krishtal, Y.Z. Povstenko, A.V. Katsman. About the mechanism of dislocation origin under spreading of low-melting-point melts on a metal surface. Dokl. Akad. Nauk Ukrainian SSR, Ser. A, No. 2, 22-25, 1989. (In Russian).
[35] Y.Z .. Povstenko. About contact angle of wetting of heterogeneous surfaces. Dokl. Akad. Nauk Ukrainian SSR, Ser. A, No. 11, 46-48, 1989. (In Russian).
[36] Y.Z. Povstenko. Theoretical investigation of phenomena caused by heterogeneous surface tension. J. Mech. Phys. Solids, 41, 1499-1514, 1993.
[37] J Y.Z. Povstenko. Stresses due to heterogeneous surface tension in solids. Proc. Appl. Math. Mech., 1, 193-194, 2002.
[38] H. Elwing, S. Welin, A. Askendal, U. Nilsson, L Lundstrom, A wettability gradient method for studies of macromolecular interaction at the liquid/surface interface. J. Colloid Interface Sci., 119, 203-210, 1987.
[39] C. Casagrande, M. Veyssie. Janus beads - realization and 1st observation of interfacial properties. C. R. Acad. Sci. Paris, 306, 1423-1425, 1988.
[40] C. Casagrande, P. Fabre, E. Raphael, M. Veyssie. Janus beadsrealization and behavior at water oil interfaces. Europhys. Lett., 9, 251-255, 1989.
[41] T. Ondarcuhu, P. Fabre, E. Raphael, M. Veyssie. Specific properties of amphiphilic particles at fluid interfaces. J. Phys. (Paris), 51, 1527-1536, 1990.
[42] E. Raphaël, Étalement de gouttes sur une surface bigarree. C. R. Acad. Sci. Paris, 306, 751-754, 1988.
[43] E. Raphaël. Équilibre d’un “Grain Janus” à. une interface eau/huile. C. R. Acad. Sci. Paris, 307, 9-12, 1988.
[44] A.B.D. Cassie. Contact angles. Disc. Faraday Soc., No. 3, 11-16, 1948.
[45] RE. Johnson, Jr., RH. Dettre. Contact angle hysteresis. III. Study of an idealized heterogeneous surface. J. Phys. Chem., 68, 1744-1750, 1964.
[46] RE. Johnson, Jr., RH. Dettre. Contact angle hysteresis. IV. Contact angle measurements on heterogeneous surface. J. Phys. Chem., 69, 1507-1515, 1965.
[47] RE. Johnson, Jr., RH. Dettre. Wettability and contact angles. Surface and Colloid Science, New York, pp. 85-153, 1969.
[48] A.W. Newmann, R.J. Good. Thermodynamics of contact angles. Part l: Heterogeneous solid surfaces. J. Colloid Jnterface Sci., 38, 341-349, 1972.
[49] A. Horsthemke, J.J Schroder. Ein thermodynamisches Modell zur Beschriebung der Benetzungseigenschaften heterogener Oberflachen. Chemie-Ingenier-Technik, 53, 62-63, 1981.
[50] L.W. Schwartz, S. Garoff. Contact angle hysteresis on heterogeneous surfaces. Langmuir, 1, 219-230, 1985.
[51] Y. Pomeau, J. Vannimenus. Contact angles on heterogeneous surfaces: weak heterogeneities. J. Colloid Jnterface Sci., 104, 477-488, 1985.
[52] S. Prussin. Generation and distribution of dislocations by soluted diffusion. J. Appl. Phys., 32, 1876-1881, 1961.
[53] M.A. Krishtal. Formation of dislocations in metals under diffusion of low-soluble surface-active substances. Phys.-Chem. Mech. Mater., No. 6, 643-649, 1969. (In Russian).
[54] M.A. KrishtaI, A.A. Borgardt, P.V. Loshkarev. Acustical emission under interaction of iron and ferro-alloys with surface-active melts. Dokl. Acad. Sci. SSSR, 267, 626-629, 1982. (In Rus- sian).
[55] M.A. Krishtal, A.A. Borgardt, P.V. Loshkarev. Formation of dislocations and acustical emission under interaction of ferroalloys with surface-active melts. Phys. Metals Metal Sci., 56, 587-592, 1983. (In Russian).
[56] M.A. Krishtal, A.A. Borgardt,A.V. Katsman, P.V. Loshkarev. On the origin and development of the dislocation structure under diffusion interaction. Phys.-Chem. Mech. Mater., No. 5, 15-20, 1988. (In Russian).
[57] M.A. Krishtal, P.V. Loshkarev, A.A. Borgardt. On conditions of appearance of nucleating crack under liquid-metal brittleness. Mechanisms of Dynamic Deformation of Metals, Kuibyshev Polytechnical Institute Press, pp. 131-134, 1986.
[58] H.J. Tress. Some distinctive contours worn on alumina-silica refractory faces by different mol ten glasses: surface tension and the mechanism of refractory attack. J. Soc. Glass Techn., 38, 89T-100T, 1954.
[59] M.L. Mironova, O.K. Botvinkin. The role of of surface tension in arising of stresses under skeletonization of two-phase natroborosilicate glasses. Physical Chemistry of Surface Phenomena under High Temperatures. Naukova Dumka, Kiev, pp. 226-230, 1971. (In Russion).
[60] AJ. Rusanov. On the theory of wetting of solids. 5. Reduction of deformation effects to linear tension. Colloid J., 39, 704-710, 1977. (In Russian).
[61] V.S. Veselovskiy, V.N. Pertsov. Attachment of bubbles to solid surfaces. Zhurnal Fizicheskoy Khimii (J. Phys. Chem.), 8, 245- 259, 1936. (In Russian).
[62] L.M. Shcherbakov, P.P. Ryazantsev. About influence of energy of wetting perimeter on edge conditions. Investigations in the Field of Surface Forces. Nauka, Moscow, pp. 26-28, 1964. (In Russian).
[63] T. Young. An essay on the cohesion of fluids. Phil. Trans. Roy. Soc., 94, 65-87, 1805.
[64] A.Yu. Davidov. The Theory of Capillar Phenomena. Moscow University Press, Moscow, 1851.
[65] F.E. Neumann. Vorlesungen über die Theorie der Kapillarität. Teubner, Leipzig, 1894.
[66] V. Bugakov, N. Brezhneva. Dependence of the rate of diffusion of metals on the crystallographic direction (anisotropy of diffusion). Zhurn. Tekhn. Fiz. (J. Techn. Phys.), 5, 1632-1637, 1935.
[67] VV. Gerlach. Über die Diffusion von Quecksilber in Zinnfolien. S.-B. math.-natur. Abteilung Bauer. Akad. Wiss., No. 3, 223- 224, 1930.
[68] F.W. Spiers. The diffusion of mercury on rolled tin foils. Phil. Mag., 15, 1048-1061, 1933. Two-dimensional and one-dimensional balance equations 101
[69] K. Prügel. Diffusion von Quecksilber in Zinnfolien. Z. Mettalk, 30, 25-27, 1938.
[70] W. Seit. Diffusion in Metals, Izd. Inostr. Lit., Moscow, 1958. (Russian translation).
[71] AJ. Bykhovskii. Spreading, Naukova Dumka, Kiev, 1983. (In Russian).
[72] Th. Heumann, K. Forch. Die Ausbreitung von Quecksilber auf Edelmetallen. Metall, 14, 691-694, 1960.
[73] Th. Heumann, K. Forch. Die Ausbreitung flüssiger Metalle auf der Oberfiache fest er Metalle. Z. Metallk., 53, 122-130, 1962.
[74] G.M. Bartenev, L.A. Akopyan. On the anisotropy of surface tension of a deformed rubberlike polymer. Vysokomolekulyarnye Soedineniya (High-molecular Substances), Ser. B, 12, 395-397, 1970. (In Russian).
[75] G.M. Bartenew, L.A. Akopjan. Die freie Oberflächenenergie der polymeren und die Methoden zu ihrer Bestimmung. Plaste und Kautschuk, 16, 655-657, 1969. "
[76] L.A. Akopyan, N.A. Ovrutskaya, G.M. Bartenev. Anisotropy of wetting and molecular orientability under deformation of elastomers. Vysokomolekulyarnye Soedineniya (High-molecular Substances), Ser. A, 24, 1705-1710, 1982. (In Russian).
[77] AJ. Rusanov, N.A. Ovrutskaya, L.A. Akopyan. Investigation of anisotropy in the wetting of deformed elastomers. Kolloid. Zhurn. (Colloid J.), 43, 685-697, 1981. (In Russian).
[78] AJ. Rusanov, L.A. Akopyan, N.A. Ovrutskaya. Effective linear tension and anisotropy of wetting of deformable elastomere Kolloid. Zhurn. (Colloid J.), 49, 61-65, 1987. (In Russian).
[79] A.P. Vyatkin, U.M. Kulish. Wetting of silieon by alloys under contact melting with metals. Surface Phenomena in Melts and Solid Phases Arising from Them, Nalchik, pp. 620-627, 1965. (In Russian).
[80] P.A. Savintsev, U.M. Kulish. On the anisotropy of surface tension in metal-semiconductor systems. Proceedings oj the Second Workshop on Problems of Chemical Bonding in Semiconductors, Minsk, p. 42, 1963. (In Russian).
[81] Yu.V. Naidich, G.A. Kolesnichenko, RP. Voitovich, B.D. Kostyuk, G.l. Gavrilyuk. Wetting of inhomogeneous solid surfaces by metal melts. Capillar and Adhesive Properties of Melts, Naukova Dumka, Kiev, pp. 18-25, p. 65, 1987. (In Russian).
[82] Yu.V. Naidich, RP. Voitovich, G.A. Kolesnichenko, B.D. Kostyuk. Wetting of inhomogeneous solid surfaces by metal melts for the system with ordered location of heterogeneous regions. SurJace. Phys., Chem., Mech., No. 2, 126-132, 1988: (In Russian).
[83] R. DeWitt. Linear theory of static disclinations. Fundamental Aspects of Dislocation Theory, Vol. 1, U.S. Government Printing Office, Washington, pp. 651-673, 1970.
[84] E. Kossecka, R DeWitt. Disclination kinematics. Arch. Mech., 29, 633-651, 1977.
[85] R. Mises. Mororrechnung, ein neues Hilfsmittel der Mechanik. Z. angew. Math. Mech., 4, 155-181, 1924.
[86] P.M. Osipov. Ostrogradsky theorem in motor calculus. Dokl. Acad. Sci. Ukrainian SSR, No. 8, 1019-1023, 1960. (In Ukrainian).
[87] P.M. Osipov. Stokes theorem and Green formulae in motor calculus. Dokl. Acad. Sci. Ukrainian SSR, No. 10, 1334-1339, 1960. (In Ukrainian).
[88] H. Schaefer. Analysis der Motorfelder im Cosserat-Kontinuum. Z. angew. Math. Mech., 47, 319-328, 1967.
[89] S. Kessel. Die Spannungfunktionen des Cosserat-Kontinuum. Z. angew. Math. Mech., 47, 329-336, 1967.
[90] Y.Z. Povstenko. Analysis of motor fields in Cosserat continua of two and one dimensions and its applications. Z. angew. Math. Mech., 66, 505-507, 1986

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-665068f9-316b-438d-844f-a2314c861820