Skip to main content
SpringerLink
Log in

Hydrodynamics of flow along the wall of a rotating cup

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

A study has been carried out of the influence of inertial and Coriolis forces on the hydrodynamics of flow along the inner wall of a rotating cup. It is shown that when these forces are pronounced, the liquid velocity components may be considerably less than those predicted from simple analyses based solely upon a balance of centrifugal and viscous forces, and the velocity at the lip may consequently be critically dependent upon the position of the feed.

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

Abbreviations

a :

half-angle of divergence of cup

B, C :

parameters in (21) and (22)

D :

diameter of spinning cup

e :

value of f subtended by liquid film

f :

a−θ

F :

body force per unit mass

h :

liquid film thickness

n :

kinematic viscosity

p :

pressure

Q :

volumetric flowrate

r :

radial distance in spherical coordinate system (see Fig. 1)

R :

radial distance of cup wall from axis of rotation

t :

time

V :

velocity

w :

angular velocity of cup

w′ :

mean angular velocity of liquid

θ :

angle in spherical coordinate system (see Fig. 1)

ρ :

liquid density

φ :

angle in spherical coordinate system (see Fig. 1)

H:

value ignoring inertial and Coriolis forces

i:

initial value

m:

mean value across liquid film

r:

component in r-direction

s:

value at air/liquid interface

θ :

component in θ-direction

φ :

component in φ-direction

References

  1. Bär, P., Doctoral dissertation, Technical College, Karlsruhe, 1935.

    Google Scholar 

  2. Emslie, A. G., F. T. Bonner, and L. G. Peck, J. of Appl. Phys. 29 (1958) 858.

    Article  MATH  MathSciNet  Google Scholar 

  3. Hinze, J. O., and H. Milborn, J. of Appl. Mech. 17 (1950) 145.

    Google Scholar 

  4. Lance, G. N., Numerical Methods for High Speed Computers (London: Iliffe and Sons), 1960.

    Google Scholar 

  5. Fraser, R. P., N. Dombrowski, and J. H. Routley, Chem. Eng. Sci. 18 (1963) 315.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leeds University, Leeds, England

    N. Dombrowski & T. L. Lloyd

Authors
  1. N. Dombrowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. L. Lloyd
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dombrowski, N., Lloyd, T.L. Hydrodynamics of flow along the wall of a rotating cup. Appl. Sci. Res. 28, 278–288 (1973). https://doi.org/10.1007/BF00413073

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00413073

Keywords

Search

Navigation