Abstract
Two optical methods, light absorption and LDA, are applied to measure the concentration and velocity profiles of droplet suspensions flowing through a tube. The droplet concentration is non-uniform and has two maxima, one near the tube wall and one on the tube axis. The measured velocity profiles are blunted, but a central plug-flow region is not observed. The concentration of droplets on the tube axis and the degree of velocity profile blunting depend on relative viscosity. These results can be qualitatively compared with the theory of Chan and Leal.
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Abbreviations
- a :
-
particle radius,m
- ā :
-
a/R, non-dimensional particle radius
- c :
-
volume concentration of droplets in suspension, m3/m3
- c 5 :
-
stream-average volume concentration of droplets in suspension,\({\text{m}}^{\text{3}} {\text{/m}}^{\text{3}} = {{\left( {2{\text{ }}\pi \int\limits_0^R {c{\text{ }}\upsilon {\text{ }}r{\text{ }}dr} } \right)} \mathord{\left/ {\vphantom {{\left( {2{\text{ }}\pi \int\limits_0^R {c{\text{ }}\upsilon {\text{ }}r{\text{ }}dr} } \right)} {\left( {2{\text{ }}\pi \int\limits_0^R {\upsilon {\text{ }}r{\text{ }}dr} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2{\text{ }}\pi \int\limits_0^R {\upsilon {\text{ }}r{\text{ }}dr} } \right)}}\)
- D :
-
2 R, tube diameter, m
- L :
-
optical path length, m
- L ij :
-
path length of laser beam through thej-th concentric layer when the beam crosses the tube diameter at the point on the inner circumference of thei-th layer, m
- N :
-
exponent in Eqs. (3) and (4)
- Q :
-
volumetric flowrate of suspension,\({\text{m}}^{\text{3}} {\text{/s,}} = 2{\text{ }}\pi \int\limits_0^R {\upsilon {\text{ }}r{\text{ }}dr} \)
- R :
-
tube radius, m
- Re :
-
ϱS νS D/µε, flow Reynolds number
- r :
-
radial position (r = 0 on a tube axis), m
- r :
-
r/R, non-dimensional radial position
- v :
-
velocity of suspension, m/s
- v :
-
v/v S , non-dimensional velocity
- v 0 :
-
centre-line velocity of suspension (r = 0), m/s
- v S :
-
Q/π R 2, stream-average velocity of suspension, m/s
- x :
-
streamwise position (x = 0 at tube inlet), m
- x :
-
x/D, non-dimensional streamwise position
- ϱc :
-
density of continuous phase, kg/m3
- ϱd :
-
density of dispersed phase, kg/m3
- ϱs :
-
stream-average density of suspension, kg/m3, equals density when homogenized
- Λϱ :
-
ϱd - ϱc, phase density difference, kg/m3
- µc :
-
viscosity of continuous phase, Pa · s
- µd :
-
viscosity of dispersed (droplet) phase, Pa · s
- λ:
-
µd/μc, viscosity ratio
- γ:
-
interfacial tension, N/m
References
Bossel, H. H.; Hiller, W. J.; Meier, G. E. A. 1972: Noise cancelling signal difference method for optical velocity measurements. J. Phys. E 5, 893–896
Chan, P. C.-H.; Leal, L. G. 1979: The motion of deformable drop in a second-order fluid. J. Fluid Mech. 92, 131–170
Goldsmith, H. L.; Marlow, J. C. 1979: Flow behaviour of erythrocytes. J. Colloid Interface Sci. 71, 383–407
Karnis, A.; Goldsmith, H. L.; Mason, S. G. 1966: The flow of suspensions through tubes. Can. J. Chem. Eng. 44, 181–193
Kowalewski, T. A. 1980: Velocity profiles of suspension flowing through a tube. Arch. Mech. 32, 857–865
Mason, G.; Clark, W. C. 1965: Liquid bridges between spheres. Chem. Eng. Sci. 20, 861–862
Segré, G.; Silberberg, A. 1962: Behaviour of macroscopic rigid spheres in Poisseuille flow. J. Fluid Mech. 14, 136–157
Vadas, E. B.; Goldsmith, H. L.; Mason, S. G. 1976: The microtheology of colloidal dispersions. Trans. Soc. Rheol. 20, 373–407
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This work was financially supported by the National Science Foundation (USA) through an agreement no. J-F7F019P, M. Sklodowska-Curie fund
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Kowalewski, T.A. Concentration and velocity measurements in the flow of droplet suspensions through a tube. Experiments in Fluids 2, 213–219 (1984). https://doi.org/10.1007/BF00571868
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DOI: https://doi.org/10.1007/BF00571868