Abstract
In applications of chemical engineering often the sedimentation is used to separate disperse particles from liquid phases. Some real liquids, e.g., polymer fluids, paints, and skin creams show viscoplastic flow behavior, i.e., they have a yield stress. In such fluids it is possible that suspended particles do not move under action of gravity although the density of the particles is greater than the fluid density. A possibility to sediment stuck spherical particles is shown. The fluid is set in sinusoidal vibration so that the particles undergo forced oscillations. This effect is investigated for single spheres. A model is given and several theoretical results are discussed. A criterion is presented that allows one to predict the combinations of the vibration parameters (amplitude and frequency) which are needed to sediment the spheres. The theoretical investigations are confirmed by experiments. The motion of several glass and steel spheres in an oscillating tube filled with aqueous carbopol solutions are detected. The comparison between theory and experiment shows good agreement.
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Abbreviations
- C :
-
Stokes drag coefficient
- D :
-
strain rate tensor
- E :
-
unit tensor
- F, F w :
-
external resp. drag force
- f :
-
body force vector
- G :
-
Green deformation tensor
- G :
-
dimensionless (shear) modulus
- g :
-
acceleration of gravity
- K :
-
abbreviation (Eq. (15))
- p :
-
pressure
- R, ϑ:
-
spherical coordinates
- R 0, R a :
-
sphere resp. body radius
- T :
-
extra stress tensor
- t :
-
time
- S :
-
stress tensor
- U 0, W 0 :
-
displacement amplitude
- u :
-
displacement vector
- ν:
-
velocity vector
- V :
-
viscoelastic number
- V k :
-
sphere volume
- V ∞ :
-
steady sink velocity
- Y :
-
yield stress parameter
- Y g :
-
limiting value
- Z:
-
Stokes number
- Λ:
-
density ratio
- ή:
-
second invariant of D
- δ:
-
radii ratio
- y:
-
differential viscosity
- λ, μ:
-
Lamé constants
- μ* =μ′ + iμ″:
-
complex (shear) modulus
- ϱf, ϱ k :
-
fluid resp. sphere density
- τ:
-
second invariant of T
- τ f :
-
yield stress
- ϕ:
-
phase angle
- Ω:
-
frequency
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Wünsch, O. Oscillating sedimentation of spheres in viscoplastic fluids. Rheola Acta 33, 292–302 (1994). https://doi.org/10.1007/BF00366955
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DOI: https://doi.org/10.1007/BF00366955