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Rotary Flow

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Abstract

Axially symmetric creeping flow generated by rotary motion of solid boundaries is treated. If the Reynolds number is not zero, there will be a secondary flow, due to centrifugal force, in the meridional planes. For the case of flow between concentric spheres, this is calculated to first order using the Reynolds number as a perturbation parameter. Rotlets are introduced.

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References

  • Abramowitz M, Stegun IA (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables, 10th edn. Wiley, New York

    MATH  Google Scholar 

  • Adam NK (1968) The physics and chemistry of surfaces. Dover, New York

    Google Scholar 

  • Anagnostou G, Maday Y, Mavriplis C, Patera A (1990) On the mortar element method: generalizations and implementation. In: Chan T, Glowinski R, Périaux J, Widlund O (eds) Third international symposium on domain decomposition methods for partial differential equations, Philadelphia. SIAM, pp 157–173

    Google Scholar 

  • Aris R (1962) Vectors, tensors, and the basic equations of fluid mechanics. Dover, New York

    MATH  Google Scholar 

  • Azaïez M, Deville M, Mund E (2011) Éléments finis pour les fluides incompressibles. Presses Polytechniques et Universitaires Romandes, Lausanne

    MATH  Google Scholar 

  • Babuška I (1973) The finite element method with Lagrangian multipliers. Numer Math 20:179–192

    MATH  Google Scholar 

  • Bairstow L, Cave BM, Lang ED (1922) The two-dimensional slow motion of viscous fluids. Proc R Soc Lond A 100:394–413

    Google Scholar 

  • Barenblatt GI (2003) Scaling. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Barlow EJ, Langlois WE (1962) Diffusion of gas from a liquid into an expanding bubble. IBM J Res Dev 6:329–337

    MATH  Google Scholar 

  • Barthès-Biesel D (2012) Microhydrodynamics and complex fluids. CRC/Taylor and Francis, Boca Raton

    MATH  Google Scholar 

  • Basdevant C, Deville M, Haldenwang P, Lacroix JM, Ouazzani J, Peyret R, Orlandi P, Patera AT (1986) Spectral and finite difference solutions of the Burgers equation. Comput Fluids 14:23–41

    MATH  Google Scholar 

  • Batchelor GK (1953) The theory of homogeneous turbulence. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Batchelor GK (1992) An introduction to fluid dynamics. Cambridge University Press, Cambridge

    Google Scholar 

  • Batcho P, Karniadakis G (1994) Generalized Stokes eigenfunctions: a new trial basis for the solution of incompressible Navier-Stokes equations. J Comput Phys 115:121–146

    MATH  MathSciNet  Google Scholar 

  • Benton ER, Platzmann GN (1972) A table of solutions of one-dimensional Burgers equation. Q Appl Math 29:195–212

    Google Scholar 

  • Berker R (1963) Intégration des équations du mouvement d’un fluide visqueux incompressible. In: Flügge S (ed) Encyclopedia of physics, vol VIII/2. Springer, Berlin, pp 1–384

    Google Scholar 

  • Bernardi C, Maday Y, Patera A (1994) A new nonconforming approach to domain decomposition: the mortar element method. In: Brezis H, Lions JL (eds) Collège de France Seminar, vol XI. Pitman, Boston, pp 13–51

    Google Scholar 

  • Bikerman JJ (1958) Surface chemistry. Academic, New York

    Google Scholar 

  • Boger DV, Walters K (1993) Rheological phenomena in focus. Elsevier, Amsterdam

    MATH  Google Scholar 

  • Bosshard C, Bouffanais R, Deville M, Gruber R, Latt J (2011) Computational performance of a parallelized three-dimensional high-order spectral element toolbox. Comput Fluids 44:1–8

    MATH  MathSciNet  Google Scholar 

  • Botsis J, Deville M (2006) Mécanique des milieux continus: une Introduction. Presses Polytechniques et Universitaires Romandes, Lausanne

    Google Scholar 

  • Brenner H (1962) Effect of finite boundaries on the Stokes resistance of an arbitrary particle. J Fluid Mech 12:35–48

    MATH  MathSciNet  Google Scholar 

  • Brenner H, Graham AL, Abbott JR, Mondy LA (1990) Theoretical basis for falling-body rheometry in suspensions of neutrally buoyant spheres. Int J Multiph Flow 16:579–596

    MATH  Google Scholar 

  • Brezzi F (1974) On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers. RAIRO Anal Numer 8:129–151

    MATH  MathSciNet  Google Scholar 

  • Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer, Berlin

    MATH  Google Scholar 

  • Carey FG, Oden JT (1983) Finite elements: a second course. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Carrier GF (1953) On slow viscous flow. Final report, Office of Naval Research Contract nonr-653(00), Brown University

    Google Scholar 

  • Chang ID (1961) Navier-Stokes solutions at large distances from a finite body. Indiana Univ Math J 10:811–876

    MATH  Google Scholar 

  • Chester W (1962) On Oseen’s approximation. J Fluid Mech 13:557–569

    MATH  MathSciNet  Google Scholar 

  • Chester W, Breach DR, Proudman I (1969) On the flow past a sphere at low Reynolds number. J Fluid Mech 37:751–760

    MATH  Google Scholar 

  • Chorin AJ (1968) Numerical solution of the Navier-Stokes equations. Math Comput 22:745–762

    MATH  MathSciNet  Google Scholar 

  • Ciarlet PG (1978) The finite element method for elliptic problems. North-Holland, Amsterdam

    MATH  Google Scholar 

  • Cochran WG (1934) The flow due to a rotating disc. Math Proc Camb Philos Soc 30:365–375

    MATH  Google Scholar 

  • Constantin P, Foias C (1988) Navier-Stokes equations. Chicago lectures in mathematics. University of Chicago Press, Chicago

    MATH  Google Scholar 

  • Dean WR (1958) An application in hydrodynamics of the Green’s function of an elastic plate. Mathematika 5:85–92

    MATH  MathSciNet  Google Scholar 

  • Deville MO, Gatski TB (2012) Mathematical modeling for complex fluids and flows. Springer, Berlin

    MATH  Google Scholar 

  • Deville MO, Fischer PF, Mund EH (2002) High-order methods for incompressible fluid flow. Cambridge monographs on applied and computational mathematics. Cambridge University Press, Cambridge

    Google Scholar 

  • Dowty EL (1963) A solution to the oscillating plate problem with discontinuous initial conditions. J Basic Eng 85D:477–478

    Google Scholar 

  • Drazin PG, Reid WH (2004) Hydrodynamic stability, 2nd edn. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Dussan V EB (1976) On the difference between a bounding surface and a material surface. J Fluid Mech 75:609–623

    MATH  Google Scholar 

  • Elrod HG (1960) A derivation of the basic equations for hydrodynamic lubrication with a fluid having constant properties. Q Appl Math 27:349–385

    MathSciNet  Google Scholar 

  • Ericksen JL (1960) Tensor fields. In: Flügge S (ed) Encyclopedia of physics, vol lll/l. Springer, Berlin, pp 794–858

    Google Scholar 

  • Eringen AC (1962) Nonlinear theory of continuous media. McGraw-Hill, New York

    Google Scholar 

  • Eymard R, Herbin R, Gallouet T (2000) Finite volume methods. In: Ciarlet P, Lions J (eds) Handbook of numerical analysis, vol VII. North Holland, Amsterdam, pp 713–1020

    Google Scholar 

  • Finn R, Noll W (1957) On the uniqueness and nonexistence of Stokes flows. Arch Ration Mech Anal 1:97–106

    MathSciNet  Google Scholar 

  • Frey PJ, George PL (2000) Mesh generation: application to finite elements. Hermes Science, Paris

    Google Scholar 

  • Fung YC (1984) Biodynamics: circulation. Springer, New York

    Google Scholar 

  • Girault V, Raviart PA (1986) Finite element methods for Navier-Stokes equations. Springer, Berlin

    MATH  Google Scholar 

  • Goldstein S (1929) The steady flow of a viscous fluid past a fixed spherical obstacle at small Reynolds numbers. Proc R Soc Lond A 123:225–235

    MATH  Google Scholar 

  • Goldstein S (1938) Modern development in fluid dynamics. Clarendon Press, Philadelphia

    Google Scholar 

  • Goldstein S (1960) Lectures on fluid mechanics. Lectures in applied mathematics, vol 2. Interscience, London

    Google Scholar 

  • Goodier JN (1934) An analogy between the slow motions of a viscous fluid in two dimensions, and systems of plane stress. Philos Mag 17:554–576

    MATH  Google Scholar 

  • Gray J, Hancock GJ (1955) The propagation of sea-urchin spermatozoa. J Exp Biol 32:802–804

    Google Scholar 

  • Gresho PM, Sani RL (2000) Incompressible flow and the finite element method: Part I and II. Wiley, Chichester

    Google Scholar 

  • Gresho PM, Lee RL, Sani RL (1980) On the time-dependent solution of the incompressible Navier-Stokes equations in two and three dimensions. In: Taylor C, Morgan K (eds) Recent advances in numerical methods in fluids, vol 1. Pineridge Press, Swansea, pp 27–79

    Google Scholar 

  • Gross WA (1962) Gas film lubrication. Wiley, Chichester

    MATH  Google Scholar 

  • Guazzelli E, Morris JF (2011) A physical introduction to suspension dynamics. Cambridge University Press, Cambridge

    Google Scholar 

  • Guyon E, Hulin JP, Petit L (2012) Hydrodynamique physique, 3rd edn. CNRS Éditions & EDP Sciences, Paris

    Google Scholar 

  • Haberman WL (1962) Secondary flow about a sphere rotating in a viscous liquid inside a coaxially rotating spherical container. Phys Fluids 5:625–626

    MathSciNet  Google Scholar 

  • Hamel G (1916) Spiralförmige Bewegungen zäher Flussigkeiten. Jahresber d Deutschen Mathematiker-Vereinigung 25:34–60

    MATH  Google Scholar 

  • Hancock GJ (1953) The self-propulsion of microscopic organisms through liquids. Proc R Soc Lond A 217:96–121

    MATH  MathSciNet  Google Scholar 

  • Happel JR, Brenner H (2013) Low Reynolds number hydrodynamics: with special applications to particulate media. Springer, Berlin

    Google Scholar 

  • Harlow FH, Welch JE (1965) Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids 8:2181–2189

    Google Scholar 

  • Hasimoto H (1956) A sphere theorem on the Stokes equation for axisymmetric viscous flow. J Phys Soc Jpn 11:793–797

    MathSciNet  Google Scholar 

  • Hayes WD, Probstein RF (2004) Hypersonic inviscid flow. Dover, Mineola

    Google Scholar 

  • Hill R, Power G (1956) Extremum principles for slow viscous flow and the approximate calculation of drag. Q J Mech Appl Math 9:313–319

    MATH  MathSciNet  Google Scholar 

  • Hirsch C (1991) Numerical computation of internal and external flows: fundamentals of numerical discretization. Wiley, Chichester

    Google Scholar 

  • Hori Y (2006) Hydrodynamic lubrication. Springer, Berlin

    MATH  Google Scholar 

  • Jeffrey DJ, Sherwood JD (1980) Streamline patterns and eddies in low-Reynolds-number flow. J Fluid Mech 96:315–334

    MATH  MathSciNet  Google Scholar 

  • Jeffreys H (1931) Cartesian tensors. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Johnson C (1990) Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Cambridge

    Google Scholar 

  • Kantorovich LV, Krylov VI (1964) Approximate methods of higher analysis. Interscience, New York

    Google Scholar 

  • Kanwal RP (1961) Slow steady rotation of axially symmetric bodies in a viscous fluid. J Fluid Mech 10:17–24

    MATH  MathSciNet  Google Scholar 

  • Kaplun S (1957) Low Reynolds number flow past a circular cylinder. J Math Mech 6:595–603

    MATH  MathSciNet  Google Scholar 

  • Kestin J, Persen LN (1955) The lnfluence of edges on shearing stresses in viscous laminar flow. Technical report no. 3, Brown University

    Google Scholar 

  • Knopp K (1945) Theory of functions. Dover, New York

    Google Scholar 

  • Koschmieder EL (1993) Bénard cells and Taylor vortices. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Kovasznay LIG (1948) Laminar flow behind a two-dimensional grid. Math Proc Camb Philos Soc 44:58–62

    MATH  MathSciNet  Google Scholar 

  • Krakowski M, Charnes A (1951) Stokes’ paradox and biharmonic flows. Technical report no. 37, Carnegie Institute of Technology

    Google Scholar 

  • Labrosse G, Leriche E, Lallemand P (2014) Stokes eigenmodes in cubic domain: their symmetry properties. Theor Comput Fluid Dyn. DOI: 10.1007/s00162-014-0318-5

    Google Scholar 

  • Ladyzhenskaya OA (1969) The mathematical theory of viscous incompressible flow. Mathematics and its applications, vol 2, 2nd edn. Gordon and Breach, New York

    Google Scholar 

  • Lamb SH (1995) Hydrodynamics. Cambridge University Press, Cambridge

    Google Scholar 

  • Landau L, Lifshitz EM (1997) Fluid mechanics. Butterworth Heinemann, Oxford

    Google Scholar 

  • Langlois WE (1958) Creeping viscous flow through a two-dimensional channel of varying gap. In: Proceedings of the third U.S. National Congress of applied mechanics, Rhode Island, p 777

    Google Scholar 

  • Langlois WE (1962) Isothermal squeeze films. Q Appl Math 20:131–150

    MATH  Google Scholar 

  • Langlois WE (1963) Similarity rules for isothermal bubble growth. J Fluid Mech 15:111–118

    MATH  MathSciNet  Google Scholar 

  • Langlois WE (1971) An elementary proof that the undetermined stress in an incompressible fluid is of the form − p I. Am J Phys 39:641–642

    Google Scholar 

  • Langlois WE (1981) Conservative differencing procedures for rotationally symmetric flows with swirl. Comput Methods Appl Mech Eng 25:315–333

    MATH  Google Scholar 

  • Langlois WE (1985) Buoyancy-driven flows in crystal growth melts. Annu Rev Fluid Mech 17:191–215

    Google Scholar 

  • Leal LG (2007) Advanced transport phenomena, fluid mechanics and convective transport processes. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Leriche E, Labrosse G (2004) Stokes eigenmodes in square domain and the stream function–vorticity correlation. J Comput Phys 200:489–511

    MATH  MathSciNet  Google Scholar 

  • Leriche E, Labrosse G (2005) Fundamental Stokes eigenmodes in the square: which expansion is more accurate, Chebyshev or Reid-Harris? Numer Algorithms 38:111–131

    MATH  MathSciNet  Google Scholar 

  • Leriche E, Labrosse G (2011) Are there localized eddies in the trihedral corners of the Stokes eigenmodes in cubical cavity? Comput Fluids 43:98–101

    MATH  Google Scholar 

  • Lighthill J (1976) Flagellar hydrodynamics. SIAM Rev 18:161–230

    MATH  MathSciNet  Google Scholar 

  • Lighthill J (1996) Helical distributions of stokeslets. J Eng Math 30:35–78

    MATH  MathSciNet  Google Scholar 

  • McConnell AJ (1957) Applications of tensor analysis. Dover, New York

    Google Scholar 

  • Milne-Thomson LM (1996) Theoretical hydrodynamics. Dover, New York

    Google Scholar 

  • Moffatt HK (1964) Viscous and resistive eddies near a sharp corner. J Fluid Mech 18:1–18

    MATH  Google Scholar 

  • Moisil GC (1955) Metoda funcţiilor analitice in hidrodinamica lichidelor viscoase. Comunicǎrile Academiei R P Romîne 5:1411

    MATH  MathSciNet  Google Scholar 

  • Muskhelishvili NI (1963) Some basic problems of the mathematical theory of elasticity. Noordhoff, Groningen

    MATH  Google Scholar 

  • Ockendon H, Ockendon JR (1995) Viscous flow. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Orszag S, Israeli M, Deville M (1986) Boundary conditions for incompressible flows. J Sci Comput 1:75–111

    MATH  Google Scholar 

  • Panton RL (1984) Incompressible flow. Wiley, New York

    MATH  Google Scholar 

  • Payne LE, Pell WH (1960) The Stokes problem for a class of axially symmetric bodies. J Fluid Mech 7:529–549

    MATH  MathSciNet  Google Scholar 

  • Pell WH, Payne LE (1960) On Stokes flow about a torus. Mathematika 7:78–92

    MATH  MathSciNet  Google Scholar 

  • Peyret R, Taylor TD (1983) Computational methods for fluid flow. Springer, Berlin

    MATH  Google Scholar 

  • Pinkus O, Sternlicht B (1961) Theory of hydrodynamic lubrication. McGraw-Hill, New York

    MATH  Google Scholar 

  • Plesset MS, Zwick SA (1954) The growth of vapor bubbles in superheated liquids. J Appl Phys 25:493–500

    MATH  MathSciNet  Google Scholar 

  • Pólya G (1948) Torsional rigidity, electrostatic capacity, and symmetrization. Q Appl Math 6:267–277

    MATH  Google Scholar 

  • Pozrikidis C (2009) Fluid dynamics: theory, computation, and numerical simulation. Springer, New York

    Google Scholar 

  • Proudman I, Pearson JRA (1957) Expansions at small Reynolds number for the flow past a sphere and a circular cylinder. J Fluid Mech 2:237–262

    MATH  MathSciNet  Google Scholar 

  • Purcell EM (1997) The efficiency of propulsion by a rotating flagellum. Proc Natl Acad Sci USA 94:11307–11311

    Google Scholar 

  • Quarteroni A, Valli A (1997) Numerical approximation of partial differential equations. Springer, Berlin

    Google Scholar 

  • Rappaz M, Bellet M, Deville M (2003) Numerical modeling in materials science and engineering. Springer, Berlin

    MATH  Google Scholar 

  • Rieutord M (1997) Une introduction à la dynamique des fluides. Masson, Paris

    Google Scholar 

  • Rivlin RS (1957) Preliminary notes to a course of lectures on solid mechanics. Technical report, summer seminar in applied mathematics, Boulder

    Google Scholar 

  • Rivlin RS, Ericksen JL (1955) Stress-deformation relations for isotropic materials. Arch Ration Mech Anal 4:323–425

    MATH  MathSciNet  Google Scholar 

  • Rivlin RS, Smith GF (1957) The anisotropic tensors. Q Appl Math 15:308–314

    MATH  MathSciNet  Google Scholar 

  • Rønquist E (1991) Spectral element methods for the unsteady Navier-Stokes equations. In: Von Karman Institute for Fluid Dynamics (eds) Computational fluid dynamics. Lecture series 1991-01. von Karman Institute for Fluid Dynamics, Rhode St-Genèse, Belgium

    Google Scholar 

  • Rubinow SI, Keller JB (1961) The transverse force on a spinning sphere moving in a viscous fluid. J Fluid Mech 11:447–459

    MATH  MathSciNet  Google Scholar 

  • Saad Y (2003) Iterative methods for sparse linear systems. SIAM, Philadelphia

    MATH  Google Scholar 

  • Salbu EOJ (1964) Compressible squeeze films and squeeze bearings. J Basic Eng 86:355–366

    Google Scholar 

  • Sani R, Gresho P, Lee R, Griffiths D, Engleman M (1981) The cause and cure (?) of the spurious pressures generated by certain FEM solutions of the incompressible Navier-Stokes equations. Int J Numer Meth Fluids 1:17–43; 171–204

    MATH  Google Scholar 

  • Schlichting H (1960) Boundary layer theory. McGraw Hill, New York

    MATH  Google Scholar 

  • Schmid PJ, Henningson DS (2001) Stability and transition in shear flows. Springer, New York

    MATH  Google Scholar 

  • Scott JF (2013) Moffatt-type flows in a trihedral cone. J Fluid Mech 725:446–461

    MathSciNet  Google Scholar 

  • Sengupta TK (2013) High accuracy computing methods: fluid flows and wave phenomena. Cambridge University Press, Cambridge

    Google Scholar 

  • Serrin J (1959) Mathematical principles of classical fluid mechanics. In: Flügge S (ed) Encyclopedia of physics, vol Vlll/l. Springer, Berlin, pp 125–263

    Google Scholar 

  • Shankar PN (2007) Slow viscous flows: qualitative features and quantitative analysis using complex eigenfunction expansions. Imperial College Press, London

    Google Scholar 

  • Snoeijer JH, Andreotti B (2013) Moving contact lines: scales, regimes, and dynamical transitions. Annu Rev Fluid Mech 45:269–292

    MathSciNet  Google Scholar 

  • Sokolnikoff IS (1951) Tensor analysis. Wiley, New York

    MATH  Google Scholar 

  • Sokolnikoff IS (1983) Mathematical theory of elasticity. Krieger, Malabar

    MATH  Google Scholar 

  • Spencer AJM (2004) Continuum mechanics. Dover, Mineola

    MATH  Google Scholar 

  • Strang G (1986) Introduction to applied mathematics. Wellesley-Cambridge Press, Wellesley

    MATH  Google Scholar 

  • Strang G, Fix G (1973) An analysis of the finite element method. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Taneda S (1979) Visualization of separating Stokes flows. J Phys Soc Jpn 46:1935–1942

    Google Scholar 

  • Taylor GI (1922) Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc A 73:289–343

    Google Scholar 

  • Taylor GI (1962) On scraping viscous fluid from a plane surface. In: Batchelor GK (ed) The scientific papers of Sir Geoffrey Ingram Taylor, vol IV. Cambridge University Press, Cambridge, pp 410–413

    Google Scholar 

  • Taylor C, Hood P (1973) A numerical solution of the Navier-Stokes equations using the finite element technique. Comput Fluids 1:73–100

    MATH  MathSciNet  Google Scholar 

  • Témam R (1969) Sur l’approximation des équations de Navier-Stokes par la méthode des pas fractionnaires ii. Arch Ration Mech Anal 33:377–385

    MATH  Google Scholar 

  • Tipei N (1962) Theory of lubrication. Stanford University Press, Stanford

    MATH  Google Scholar 

  • Tran-Cong T, Blake JR (1982) General solutions of the Stokes’ flow equations. J Math Anal Appl 90:72–84

    MATH  MathSciNet  Google Scholar 

  • Tritton DJ (1980) Physical fluid dynamics. Van Nostrand Reinhold, New York

    Google Scholar 

  • Truesdell C (1952) The mechanical foundations of elasticity and fluid dynamics. J Ration Mech Anal 1:125–300

    MATH  MathSciNet  Google Scholar 

  • Truesdell C (1966) The elements of continuum mechanics. Springer, New York

    MATH  Google Scholar 

  • Truesdell C, Toupin RA (1960) The classical field theories. In: Flügge S (ed) Encyclopedia of physics, vol lll/l. Springer, Berlin, pp 226–793

    Google Scholar 

  • Tu C, Deville M, Dheur L, Vanderschuren L (1992) Finite element simulation of pulsatile flow through arterial stenosis. J Biomech 25:1141–1152

    Google Scholar 

  • Van Dyke M (1983) An album of fluid motion. Parabolic Press, Stanford

    Google Scholar 

  • Versteeg HK, Malalasekera W (2007) An introduction to computational fluid dynamics: the finite volume method. Pearson, Harlow

    Google Scholar 

  • von Kármán T (1921) Über laminare und turbulente Reibung. Zeit Ang Math Mech 1:233–252

    MATH  Google Scholar 

  • von Mises R (2004) Mathematical theory of compressible flow. Dover, Mineola

    Google Scholar 

  • Walsh O (1992) Eddy solutions of the Navier-Stokes equations. In: Heywood J, Masuda K, Rautmann R, Solonnikov S (eds) The Navier-Stokes equations II – theory and numerical methods. Lecture notes in mathematics, vol 1530. Springer, Berlin, pp 306–309

    Google Scholar 

  • Wannier GH (1950) A contribution to the hydrodynamics of lubrication. Q Appl Math 8:1–32

    MATH  MathSciNet  Google Scholar 

  • Weinstein SJ, Ruschak KJ (2004) Coating flows. Annu Rev Fluid Mech 36:29–53

    Google Scholar 

  • Widder DV (1989) Advanced calculus, 2nd edn. Dover, New York

    MATH  Google Scholar 

  • Williamson CHK (1996) Vortex dynamics in cylinder wake. Annu Rev Fluid Mech 28:477–539

    Google Scholar 

  • Zamir M (2000) The physics of pulsatile flow. Springer, New York

    MATH  Google Scholar 

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Authors and Affiliations

  1. Division of Science and Mathematics, San Jose City College, San Jose, CA, USA

    William E. Langlois

  2. Ecole Polytechnique Fédérale de Lausanne STI DO MXD 130, Station 12, Lausanne, Switzerland

    Michel O. Deville

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Langlois, W.E., Deville, M.O. (2014). Rotary Flow. In: Slow Viscous Flow. Springer, Cham. https://doi.org/10.1007/978-3-319-03835-3_8

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