Skip to main content
SpringerLink
Log in

Stagnation-point flow against a liquid film on a plane wall

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

Stagnation-point flow of a semi-infinite viscous fluid against a liquid film resting on a plane wall is considered under conditions of Stokes flow and for arbitrary Reynolds numbers. Assuming that the interface remains flat and parallel to the wall at all times, the lateral spatial coordinate is scaled out to yield a simplified system of governing equations in the transverse coordinate normal to the wall, describing the evolution of the flow and displacement of the interface. In this inherently unsteady flow the film keeps thinning in time, while the rate of thinning decreases as the interface approaches the wall. Orthogonal two-dimensional, axisymmetric, three-dimensional, and oblique two-dimensional flow are individually considered. In each case, exact solutions of a similarity form are constructed, and an evolution equation describing the film thickness is formulated and solved by numerical methods. Quasi-steady solutions compare favourably with full calculations of the unsteady flow, suggesting that the unsteady terms have only a minor effect on the rate of film thinning. Dual solutions are uncovered in the case of three-dimensional flow.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • G. K. Batchelor (1967) An introduction to fluid dynamics Cambridge University Press Cambridge Occurrence Handle0152.44402

    MATH  Google Scholar 

  • M. G. Blyth P. Hall (2003) ArticleTitleOscillatory flow near a stagnation point Siam J. Appl. Math. 63 1604–1614 Occurrence Handle10.1137/S0036139902408175 Occurrence Handle2001210 Occurrence Handle1039.76013

    Article  MathSciNet  MATH  Google Scholar 

  • K. Brattkus S. H. Davis (1991) ArticleTitleThe linear stability of plane stagnation-point flow against general disturbances Q. J. Mech. Appl. Math. 44 135–146 Occurrence Handle0736.76024

    MATH  Google Scholar 

  • A. V. Coward P. Hall (1996) ArticleTitleThe stability of two-phase flow over a swept wing J. Fluid Mech. 329 247–273 Occurrence Handle0905.76024

    MATH  Google Scholar 

  • A. Davey (1961) ArticleTitleBoundary-layer flow at a saddle point of attachment J. Fluid Mech. 10 593–610 Occurrence Handle0100.22501 Occurrence Handle134089

    MATH  MathSciNet  Google Scholar 

  • A. Davey D. Schofield (1967) ArticleTitleThree-dimensional flow near a two-dimensional stagnation-point J. Fluid Mech. 28 149–151 Occurrence Handle0163.20204

    MATH  Google Scholar 

  • J. M. Dorrepaal (1986) ArticleTitleAn exact solution of the Navier-Stokes equation which describes non-orthogonal stagnation-point flow in two dimensions J. Fluid Mech. 161 141–147 Occurrence Handle834711

    MathSciNet  Google Scholar 

  • M. B. Glauert (1956) ArticleTitleThe laminar boundary layer on oscillating plates and cylinders J. Fluid Mech. 1 97–110 Occurrence Handle0071.19903 Occurrence Handle81110

    MATH  MathSciNet  Google Scholar 

  • R. E. Hewitt P. W. Duck S. R. Stow (2002) ArticleTitleContinua states in boundary-layer flows J. Fluid Mech. 468 121–152 Occurrence Handle10.1017/S0022112002001507 Occurrence Handle1930635 Occurrence Handle1064.76033

    Article  MathSciNet  MATH  Google Scholar 

  • K. Hiemenz (1911) ArticleTitleDie Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder Dilglers Polytech. J. 326 321–410

    Google Scholar 

  • F. Homann (1936) ArticleTitleDer Einfluß großer Zähigkeit bei der Strömung um den Zylinder und um die Kugel Z. Angew. Math. Mech. 16 153–164 Occurrence HandleJFM 62.0984.02

    MATH  Google Scholar 

  • L. Howarth (1951) ArticleTitleThe boundary layer in three-dimensional flow. Part II: The flow near a stagnation point Phil. Mag. 42 1433–1440 Occurrence Handle0043.39901 Occurrence Handle44974

    MATH  MathSciNet  Google Scholar 

  • D. G. Lasseigne T. L. Jackson (1992) ArticleTitleStability of a nonorthogonal stagnation flow to three-dimensional disturbances Theor. Comput. Fluid Dyn. 3 107–218 Occurrence Handle10.1007/BF00417913

    Article  Google Scholar 

  • P. A. Libby (1967) ArticleTitleHeat and mass transfer at a general three-dimensional stagnation point AIAA J. 5 507–517 Occurrence Handle0158.23303

    MATH  Google Scholar 

  • C. Pozrikidis (1997) Introduction to theoretical and computational fluid dynamics Oxford University Press Oxford Occurrence Handle0886.76002

    MATH  Google Scholar 

  • C. Pozrikidis M. G. Blyth (2004) ArticleTitleEffect of stretching on interfacial stability Acta Mech. 170 149–162 Occurrence Handle10.1007/s00707-004-0116-z Occurrence Handle1064.76045

    Article  MATH  Google Scholar 

  • N. Riley (1993) ArticleTitleUnsteady flow at a stagnation point J. Fluid Mech. 256 487–498 Occurrence Handle0783.76034 Occurrence Handle1251411

    MATH  MathSciNet  Google Scholar 

  • N. Riley R. Vasantha (1988) ArticleTitleAn unsteady stagnation point flow Q. J. Mech. Appl. Math. 42 511–521 Occurrence Handle1033699

    MathSciNet  Google Scholar 

  • D. Schofield A. Davey (1967) ArticleTitleDual solutions of the boundary-layer equations at a point of attachment J. Fluid Mech. 30 809–811 Occurrence Handle0168.46602

    MATH  Google Scholar 

  • J. T. Stuart (1959) ArticleTitleThe viscous flow near a stagnation point when the external flow has uniform vorticity J. Aero/Space Sci. 26 124–125

    Google Scholar 

  • K. Tamada (1979) ArticleTitleTwo-dimensional stagnation-point flow impinging obliquely on a plane wall J. Phys. Soc. Japan 46 310–311

    Google Scholar 

  • C. Y. Wang (2003) ArticleTitleStagnation flows with slip: Exact solutions of the Navier-Stokes equations ZAMP 54 184–189 Occurrence Handle1036.76005 Occurrence Handle10.1007/PL00012632

    Article  MATH  Google Scholar 

  • A. Yeckel S. Middleman (1987) ArticleTitleRemoval of a viscous film from a rigid plane surface by an impinging liquid jet Chem. Eng. Comm. 50 165–175

    Google Scholar 

  • A. Yeckel L. Strong S. Middleman (1994) ArticleTitleViscous film flow in the stagnation region of the jet impinging on planar surface AIChE J. 40 1611–1617 Occurrence Handle10.1002/aic.690401003

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, England, UK

    M. G. Blyth

  2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California, 92093-0411, U.S.A

    C. Pozrikidis

Authors
  1. M. G. Blyth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Pozrikidis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Pozrikidis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blyth, M.G., Pozrikidis, C. Stagnation-point flow against a liquid film on a plane wall. Acta Mechanica 180, 203–219 (2005). https://doi.org/10.1007/s00707-005-0240-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-005-0240-4

Keywords

Search

Navigation