GENERAL RESEARCH
Solids Settling Velocity and Distribution in Slurry Reactors with
Dilute Pseudoplastic Suspensions
Davide Pinelli and Franco Magelli*
DICMA-Department of Chemical, Mining and Environmental Engineering, University of Bologna,
viale Risorgimento 2, 40136 Bologna, Italy
The solids distribution was investigated in a tank stirred with multiple Rushton turbines. The
analysis of the behavior of suspensions made of solid particles and non-Newtonian liquids allowed
us to better single out the role of the most significant parameters that define the solids profiles:
particle settling velocity is confirmed to be a key parameter for this process. It is shown that
the same concept of terminal velocity in these systems is to be considered with care. The settling
velocity in the stirred liquid is usually intermediate between the terminal settling velocity in
the still liquid and the terminal settling velocity calculated with an effective liquid viscosity
based on Metzner and Otto’s concept. A correlation between the first and last settling velocities
with the ratio of Kolmogoroff length scale and particle diameter is in very good agreement with
that determined previously for Newtonian liquids.
1. Introduction
Mixing in stirred tanks is a common practice in many
areas of the chemical and process industry. An under-
standing of the complex fluid dynamic behavior prevail-
ing in slurry agitated reactors and other equipment for
solid-liquid treatment is crucial for rational design and
reliable process operation. Three different topics are
usually considered in the fluid dynamic context of solid-
liquid systems, namely, off-bottom particle suspension,
spatial solids distribution inside the equipment, and
solids separation at the withdrawal tube.
1
This paper addresses the second of the above-
mentioned items. The main results obtained in the
analysis of particle-liquid interaction, which is a key
phenomenon for solids distribution, are reviewed in the
following section. Suffice it to mention here that most
of these studies arrived at the conclusion that the
particle settling velocity in a stirred medium, considered
either as a real suspension property or as a model
parameter, is usually less than the settling velocity in
a still liquid (the so-called terminal velocity).
The aim of this paper is to discuss this last aspect
further. The investigation was conducted with dilute
suspensions of spherical particles in pseudoplastic
liquids in order that the liquid environment “seen” by
the single particles and the nature of particle-liquid
interaction are affected by nonlinear rheological behav-
ior, while particle-particle interactions are minimized.
The analysis was performed in a tank of high aspect
ratio stirred with multiple impellers, which allows for
the solids concentration gradients along the vertical axis
to be maximized while those in the radial direction are
neglected, thus making the study more straightforward.
The experimental results are discussed in terms of
the simple one-dimensional sedimentation-dispersion
model with the particle velocity as a parameter. A
limited number of ancillary experiments aimed at
determining the terminal particle settling velocity and
characterizing liquid macromixing in pseudoplastic
fluids were also conducted and were instrumental in the
above-mentioned analysis.
2. Background on Particle Settling Velocity in
Stirred Media
The first experimental analyses of particle-liquid
interactions in stirred tanks date back to about 30 years
ago. Different research groups
2-5
have concluded that
the average particle settling velocity in a stirred liquid
is 30-60% of the settling velocity in the quiescent liquid
at rest, U
t
, thus implying a relevant drag coefficient
increase. Although the techniques on which these
results were based exhibit some limitations and the data
themselves were relatively limited, the essence of these
findings is consistent with turbulent statistical theory
and with turbulence-related phenomena such as par-
ticulate mass transfer. More recently, detailed LDV
measurements have revealed that the particles actually
lag or lead the liquid in the zones characterized by
upward or downward flow, respectively.
6
On average,
however, these last results do not seem to contradict
the previous ones.
Similarly, the drag coefficients of spheres falling in
liquids have been reported to be affected by “external”
turbulence (sometimes referred to as “free stream”
turbulence), that is, turbulence other than that pro-
duced by particle motion itself.
7
Although the form of
this influence has been questioned recently,
8
the general
effect remains undisputed.
* Corresponding author: Dr. Franco Magelli, DICMA-
Department of Chemical, Mining and Environmental Engi-
neering, University of Bologna, viale Risorgimento 2, 40136
Bologna, Italy. Fax: +39-051-581200. Telephone: +39-051-
2093147. E-mail: franco.magelli@mail.ing.unibo.it.
4456 Ind. Eng. Chem. Res. 2001, 40, 4456-4462
10.1021/ie0010518 CCC: $20.00 © 2001 American Chemical Society
Published on Web 09/05/2001