Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Stokes flow in a two-dimensional spatially periodic boundary driven by a combination of line singularities

Authors: K. Ma and D. W. Pravica
Journal: Quart. Appl. Math. 50 (1992), 743-757
MSC: Primary 76D07
DOI: https://doi.org/10.1090/qam/1193664
MathSciNet review: MR1193664
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Abstract: The analytical solution is obtained for two-dimensional creeping flow generated by a source-sink combination located on a spatially periodic boundary. Separation is found to occur when the source and sink are located on concave regions of the boundary. The velocity profile of the two-dimensional Poiseuille flow for a channel is compared to that of the circle problem and the rough channel obtained from the analytical solution. It is found that the mid-channel velocity (or pressure gradient) of the rough case is greater (less) than that of the circle problem.

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  • [1] A. C. Payatakes, Chi Tien, and R. M. Turian, A new model for granular porous media, A. I. Ch. E. J. 11, 58-76 (1973)
  • [2] N. Phan-Thien, C. J. Goh, and M. B. Bush, Viscous flow through a corrugated tube by boundary element method, Z. Angew. Math. Phys. 36, 475-480 (1985)
  • [3] H. Tennekes and J. L. Lumley, A First Course in Turbulence, M.I.T. Press, Cambridge, MA, 1972
  • [4] N. Phan-Thien, On the Stokes flow of viscous fluids through corrugated pipes, Trans. ASME Ser. E J. Appl. Mech. 47 (1980), no. 4, 961–963. MR 597891
  • [5] M. Lessen and P. S. Huang, Poiseuille flow in a pipe with axially symmetric wavey walls, Physics Fluids 19, 945-950 (1976)
  • [6] A. M. J. Davis and K. B. Ranger, A model for Stokes flow through a stenotic channel, Phys. Fluids A 1 (1989), no. 2, 193–198. MR 1021628, https://doi.org/10.1063/1.857489
  • [7] D. E. R. Godfrey, Theoretical elasticity and plasticity for engineers, Thames and Hudson, London, 1959. MR 0105861
  • [8] E. G. Philips, Functions of a Complex Variable with Applications, Oliver and Boyd, Interscience Publishers Inc., 1958, p. 31
  • [9] Lord Rayleigh, Scientific Papers, Vol. IV, Cambridge, 1900
  • [10] K. B. Ranger and H. Brenner, A model for Stokes flow in a two-dimensional bifurcating channel, J. Fluid Mech. 152 (1985), 1–13. MR 791526, https://doi.org/10.1017/S0022112085000532

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DOI: https://doi.org/10.1090/qam/1193664
Article copyright: © Copyright 1992 American Mathematical Society

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