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 Dˆv
(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,
Dˆv 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.