In:
Journal of Fluid Mechanics, Cambridge University Press (CUP), Vol. 361 ( 1998-04-25), p. 309-331
Abstract:
Individual falling balls were allowed to settle through otherwise
quiescent well-mixed suspensions of non-colloidal neutrally buoyant spheres dispersed in a Newtonian liquid. Balls were tracked in three dimensions to determine the variances
in their positions about a mean uniform vertical settling path. The primary experimental parameters investigated were the size of the falling ball and the volume
fraction and size of the suspended particles. Unlike the horizontal variances, the
vertical variances were found to be affected by short-time deterministic behaviour
relating to the instantaneous local configurational arrangement of the suspended
particles. For sufficiently long intervals between successive observations, the trajectories
of the balls were observed to disperse about their mean settling paths in
a random manner. This points to the existence of a Gaussian hydrodynamic dispersivity
that characterizes the linear temporal growth of the variance in the position
of a falling ball. The functional dependence of these horizontal and vertical dispersivities
upon the parameters investigated was established. The dispersivity dyadic was observed to be transversely isotropic with
respect to the direction of gravity, with the vertical component at least 25 times
larger than the horizontal component. The vertical dispersivity Dˆ v (made dimensionless with the
diameter of the suspended spheres and the mean settling velocity) was observed to decrease with increasing falling ball diameter, but to decrease less rapidly with
concentration than theoretically predicted for very dilute suspensions; moreover,
for falling balls equal in size to the suspended spheres, Dˆ v increased linearly with
increasing volume fraction ϕ of suspended solids. In addition to the above experiments performed on suspensions of spheres,
previously published settling-velocity data on the fall of balls through neutrally
buoyant suspensions of rods possessing an aspect ratio of 20 were re-analysed,
and vertical dispersivities calculated therefrom. (These data, taken by several of the
present investigators in conjunction with other researchers, had only been grossly
analysed in prior publications to extract the mean settling velocity of the ball, no attempt
having been made at the time to extract dispersivity data too.) The resulting vertical
dispersivities, when rendered dimensionless with the rod length and mean settling velocity,
showed no statistically significant dependence upon the falling-ball diameter;
moreover, all other things being equal, these dispersivities were observed to increase
with increasing rod concentration.
Type of Medium:
Online Resource
ISSN:
0022-1120
,
1469-7645
DOI:
10.1017/S0022112098008763
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1998
detail.hit.zdb_id:
1472346-3
detail.hit.zdb_id:
218334-1
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