### Abstract

Axisymmetric Stokes flow impinging upon a spherical cap on a solid plane wall is analysed. An analytical integral expression for the streamfunction is obtained from separation of variables in toroidal coordinates; Mehler-Fock transforms are used in applying the boundary conditions. Streamlines are shown for spherical caps ranging from very flat to very round. Regions of recirculation are found near the edges of caps fuller than a hemisphere. The pressure distribution on the cap, and the net force in the axial direction, are also determined for a range of shapes. The axial force is proportional to the volume of caps of fixed shape, but relatively insenstiive to the degree of flattening for caps of fixed volume. Implications of the results for the deformation of red blood cells and other deformable particles are examined.

Original language | English (US) |
---|---|

Pages (from-to) | 179-193 |

Number of pages | 15 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 49 |

Issue number | 2 |

State | Published - May 1996 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Safety, Risk, Reliability and Quality
- Applied Mathematics

### Cite this

**Stokes flow impinging on a spherical cap on a plane wall.** / Fox, Ardith El-Kareh; Secomb, Timothy W.

Research output: Contribution to journal › Article

*Quarterly Journal of Mechanics and Applied Mathematics*, vol. 49, no. 2, pp. 179-193.

}

TY - JOUR

T1 - Stokes flow impinging on a spherical cap on a plane wall

AU - Fox, Ardith El-Kareh

AU - Secomb, Timothy W

PY - 1996/5

Y1 - 1996/5

N2 - Axisymmetric Stokes flow impinging upon a spherical cap on a solid plane wall is analysed. An analytical integral expression for the streamfunction is obtained from separation of variables in toroidal coordinates; Mehler-Fock transforms are used in applying the boundary conditions. Streamlines are shown for spherical caps ranging from very flat to very round. Regions of recirculation are found near the edges of caps fuller than a hemisphere. The pressure distribution on the cap, and the net force in the axial direction, are also determined for a range of shapes. The axial force is proportional to the volume of caps of fixed shape, but relatively insenstiive to the degree of flattening for caps of fixed volume. Implications of the results for the deformation of red blood cells and other deformable particles are examined.

AB - Axisymmetric Stokes flow impinging upon a spherical cap on a solid plane wall is analysed. An analytical integral expression for the streamfunction is obtained from separation of variables in toroidal coordinates; Mehler-Fock transforms are used in applying the boundary conditions. Streamlines are shown for spherical caps ranging from very flat to very round. Regions of recirculation are found near the edges of caps fuller than a hemisphere. The pressure distribution on the cap, and the net force in the axial direction, are also determined for a range of shapes. The axial force is proportional to the volume of caps of fixed shape, but relatively insenstiive to the degree of flattening for caps of fixed volume. Implications of the results for the deformation of red blood cells and other deformable particles are examined.

UR - http://www.scopus.com/inward/record.url?scp=0030141970&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030141970&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030141970

VL - 49

SP - 179

EP - 193

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

SN - 0033-5614

IS - 2

ER -