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Applied Scientific Research

, Volume 28, Issue 1, pp 278–288 | Cite as

Hydrodynamics of flow along the wall of a rotating cup

  • N. Dombrowski
  • T. L. Lloyd
Article

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.

Keywords

Radial Velocity Coriolis Force Viscous Force Velocity Ratio Viscosity Liquid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

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)

Subscripts

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

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References

  1. [1]
    Bär, P., Doctoral dissertation, Technical College, Karlsruhe, 1935.Google Scholar
  2. [2]
    Emslie, A. G., F. T. Bonner, and L. G. Peck, J. of Appl. Phys. 29 (1958) 858.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Hinze, J. O., and H. Milborn, J. of Appl. Mech. 17 (1950) 145.Google Scholar
  4. [4]
    Lance, G. N., Numerical Methods for High Speed Computers (London: Iliffe and Sons), 1960.Google Scholar
  5. [5]
    Fraser, R. P., N. Dombrowski, and J. H. Routley, Chem. Eng. Sci. 18 (1963) 315.CrossRefGoogle Scholar

Copyright information

© Martinus Nijhoff, The Hague 1973

Authors and Affiliations

  • N. Dombrowski
    • 1
  • T. L. Lloyd
    • 1
  1. 1.Leeds UniversityLeedsEngland

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