International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.1, No.2, Apr. 2015, Pub. Date: Apr. 8, 2015
Study of Multilayer Flow of Viscous Incompressible Fluid and Application of Its Results for Capillary Blood Flow Simulation
Pages: 76-86 Views: 4695 Downloads: 1078
Authors
[01] N. Khomasuridze, I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili Tbilisi State University, 2 University St., Tbilisi, Georgia.
[02] N. Zirakashvili, I. Vekua Institute of Applied Mathematics of Iv. Javakhishvili Tbilisi State University, 2 University St., Tbilisi, Georgia.
Abstract
Linear stationary multilayer flows of a viscous incompressible fluid in tubes bounded by coordinate surfaces of generalized cylindrical coordinates and circular flows of multilayer liquids in a circular cylindrical system of coordinates are investigated. In other words, multilayer flows are studied in rectilinear tubes of rectangular, circular, elliptic and parabolic cross-sections and in circular tubes of rectangular cross-section. Layers of flowing fluids of different viscosity are arranged along one of the coordinates. Related boundary-value contact problems of hydromechanics are stated and their effective solutions are found. The obtained results are used in studies of blood microcirculation.
Keywords
Viscous Incompressible Fluid, Boundary-Value Contact Problem, Fourier Trigonometric Series
References
[01] Happel J., Brenner G.: Hydrodynamics for small Reynolds numbers. Mir, Moscow (in Russian) (1976)
[02] Bermant A.F.: Mapping Linear Coordinates. Transformation. Green's Formulas. Fizmatgiz, Moscow (in Russian) (1958)
[03] Aleksander S. Popel and Paul C. Johnson: Microcirculation and Hemorheology. Ann..Rev. Fluid Mech. 37: 43-69 (2005)
[04] Mchedlishvili G.: Dynamic Structure of Blood in Microvessels. Microcirculation Endothelium and Lymphatic, vol. 7, Butterworth-Heinemann, 3-49 (1991)
[05] Robert M. Berne, Matthew N. Levy.: Cardiovascular Physiology. The C.V. Mosby Company. Saint Louis (1972)
[06] Caro C.C., Pedley T.J., Schoter R.C., Seed W.A.: The Mechanics of the Circulation. Oxford University Press. Oxford-New York- Toronto (1978)
[07] Mchedlishvili G. and Nobuji Maeda: Blood Flow Structure Related to Red Cell Flow. A Determinant of Blood Fluidity in Narrow Microvessels. Japanese Journal of Physiology 51: 19-30 (2001)
[08] Skalak R., Chen P.H. and Chien S.: Effect of Hematocrit and Rouleaux on Apparent Viscosity in Capillaries. Biorheology 9: 67-82 (1972)
[09] Masako Sugihara-Seki and Richard Skalak: Numerical Study of Asymmetric Flows of Red Calls in Capillaries. Microvascular Research 36: 64-74 (1988)
[10] Sharan M. and Popel A.S.: A two phase model for flow of blood in narrow tubes with increased effective viscosity near the wall. Biorheology 38: 415-428 (2001)
[11] David S. Long, Michael L. Smith, Axel R. Pries, Klaus Ley and Edward R. Damiano: Microviscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemodilution, PNAS, July 6, vol. 101, no. 27, 10060-10065 (2004)
[12] Krasnoperov K.A., Stoyan D.: Second-order stereology of spatial fibre systems. Journal of Microscopy 216(2): 156-164 (2004)
[13] El-Kareh A.W., Secomb T.W.: A Model for red blood cell motion in bifurcating microvessels. International Journal of Mult. Phase Flow 26: 1545-1564 (2000)
[14] Slezkin N.A.: Dynamics of a viscous incompressible fluid. Gos. Izdat. Tekh. Teor. Literaturi, Moscow (in Russian) (1955)
[15] Brown, J. W. and Churchill, R. V.: Fourier Series and Boundary value problems, 5th ed. New York: McGraw-Hill (1993)
[16] Bitsadze A.V. :Equations of mathematical physics, Mir Publishers (Translated from Ruusian) (1980)
[17] Khomasuridze N.G.: On some stationary multi-layer flows of viscous incompressible liquids. Proceedings of the International Scientific and Technical Conference “Architecture and Construction – Contemporary Problems”, 15-18 October, Yerevan-Jermuk, 285-290 (in Russian) (2008)
[18] Khomasuridze N., Ninidze K. and Siradze Z.: A steady flow of a viscous multi-layer fluid in a toroidal tube with small radius. Mem. Differential Equations. Math. Phys. 44: 151-154 (2008).
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