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Spreading fronts in sedimentation of dilute suspension of spheres
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10.1063/1.2883960
/content/aip/journal/pof2/20/2/10.1063/1.2883960
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/2/10.1063/1.2883960

Figures

Image of FIG. 1.
FIG. 1.

Dimensionless falling distance vs dimensionless time , for the median (◇), first (○), and third (◻) quartiles for batch B (a) and batch E (b). The different lines indicate the best linear fits. Experiments were held in a vessel. The suspension concentration was .

Image of FIG. 2.
FIG. 2.

Normalized cumulative sum of the square of the radius () vs dimensionless radius () for the five batches of particles: A (○), B (◻), C (▵), D (◇), and E (▿).

Image of FIG. 3.
FIG. 3.

Dimensionless interface thickness vs dimensionless falling distance , for batch C at . The line indicates the best linear fit. The different cross sections presented are (▵), (○), and (◻).

Image of FIG. 4.
FIG. 4.

Dimensionless interface thickness vs dimensionless falling distance . The lines indicate the best linear fits. Three different experiments were realized for each different batch of particles; A (○), B (◻), C (▵), D (◇), and E (▿).

Image of FIG. 5.
FIG. 5.

(a) Dimensionless interface thickness vs dimensionless predicted quartile interface . The symbols correspond to the batches A (○), B (◻), C (▵), D (◇), and E (▿). (b) Dimensionless half-widths (open symbols) and (filled symbols) vs dimensionless predicted half-widths and , respectively.

Image of FIG. 6.
FIG. 6.

Relative quartile interface thickness vs the concentration . The solid curve represents a quadratic fit to the first five concentration values. The dotted curve is explained in the conclusion.

Image of FIG. 7.
FIG. 7.

Concentration profile of the sedimentation front vs the normalized height . The results correspond to experiments in the cross-section vessel with particles of batch B at . The symbols correspond to the different times (○), 669.1 (×), 961.8 (▵), and 1087.2 (◻).

Image of FIG. 8.
FIG. 8.

Concentration profiles at , , , , and for a box with 4000 point-particles, Fourier modes, sedimentation velocity , and monodisperse particles . For this figure, an average was made over 80 realizations instead on the normal 20 for this number of particles.

Image of FIG. 9.
FIG. 9.

Height of concentration quartiles, i.e., , , and , as functions of time for the same simulation as Fig. 8.

Image of FIG. 10.
FIG. 10.

Growth of thickness of the front in time for the same monodisperse simulation as Fig. 8. Also plotted are the best linear fit (solid line) and the best fit (dotted curve).

Image of FIG. 11.
FIG. 11.

Scaled rate of growth of the front as a function of the numerical resolution for monodisperse simulations with sedimentation velocity and (+), 1372 (×), 4000 (▵), and 6912 (◻).

Image of FIG. 12.
FIG. 12.

(a) Scaled growth rate of the front as a function of the scaled polydispersity , with various and , and with (+), 1372 (×), 4000 (▵), and 10976 (◻). The line is the contribution of the polydispersity without hydrodynamic interactions. The dotted curve is explained in the conclusion. (b) Scaled rates of growth of the (lower data) and the (upper data) quartiles for the same simulations. The line is the contribution of the polydispersity without hydrodynamic interactions.

Image of FIG. 13.
FIG. 13.

Concentration profiles of Fig. 8 replotted in a frame moving with the mean sedimentation speed and rescaled by the growing thickness of the front .

Tables

Generic image for table
Table I.

Particle characteristics.

Generic image for table
Table II.

Dimensionless isoconcentration velocities and relative interface thicknesses deduced from the experiments and from predictions accounting solely for polydispersity for the different particle batches at . The experimental data correspond to averages over three experimental runs.

Generic image for table
Table III.

Dimensionless isoconcentration velocities and quartile interface thickness deduced from the experiments for particles of batch B at different concentrations. The experimental data correspond to averages over three experimental runs.

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/content/aip/journal/pof2/20/2/10.1063/1.2883960
2008-02-29
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spreading fronts in sedimentation of dilute suspension of spheres
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/2/10.1063/1.2883960
10.1063/1.2883960
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