Dispersing of gases or immiscible liquids within another continuous liquid fluid phase
is a standard operation for the processing of multiphase systems in the industrial
areas like food, cosmetics pharmaceuticals and fine chemicals. The commonly used
dispersing tools are rotor-stator devices with tooth-/pin geometries arranged in
circular, concentric or axial, stacked disc configurations. Depending on the gap width
between the rotor-stator pins or tooth elements and the viscosity function of the twophase
system, laminar, turbulent or transitional flow conditions act in the dispersive
mixing procedure. – A new generation of dispersing devices are the static or dynamic
membrane devices in which the disperse drops or bubbles are formed once and
detached from the membrane surface by cross- or co-flowing fluid streams. This
procedure means significantly reduced mechanical treatment of the multiphase fluid
system and allows to tailor narrow disperse size distributions.
Rotor-Stator Dispersing Processes
Our recent work concerning Rotor-Stator (R/S) dispersing process developments
has mainly focused on laminar to transition domain flow conditions. We have
investigated bubble and drop break-up in some detail under steady and transient
shear or elongation as well as mixed flow conditions. Different types of R/S (model)
flow apparatus were applied comprising concentric  /eccentric  cylinder-, four
roller- , single-  and multi-toothed  geometries. From respective experiments
expanded maps of critical bubble-/drop break-up characteristics (critical Weber
(WeC) or critical Capillary (CaC) numbers as a function of viscosity ratio
λ, deformation rate G, total deformation D and flow type α have been derived.
Figure 1 exemplarily demonstrates CaC(α) for drop break-up under pure shear (α =
0), equibiaxial (α = -1), or planar (α = 1) elongation as well as for mixtures of these
flow types. Steady and transient drop break-up were investigated experimentally (a),
by numerical flow simulation using CFD (b) and by a non- equilibrium
thermodynamics modeling approach (c) /1-3/. Consistent results from these three
approaches (a-c) were received for surfactant free as well as for surfactant covered
drop interfaces.

Fig.1: Critical Ca- number for different flows

Fig.2: Surfactant distribution at drop
interface in shear flow

For surfactant covered drop interfaces a criterion to distinguish between diffusion
and convection driven interfacial coverage with surfactant molecules was defined as
the ratio of Peclet number (Pe) / Capillary number (Ca), denoted as α and
implemented into a convection diffusion equation which forms the bases for
respective CFD calculations. As a result of these calculations surfactant
concentration distributions along the interfacial contour of drops deformed in shear,
elongation and mixed flows were received and satisfying comparability with
experimental drop deformation data was found. Figure 2 shows such calculated
concentration distributions of surfactant at the deformed drop interface for different
Capillary numbers and a viscosity ratio λ of 4.
The impact of transient shear and elongation flows has been investigated within an
eccentric cylinder gap and transferred to a complex multi toothed rotor-stator
dispersing geometry. CFD based simulations applying a particle tracking procedure
along distinct particle flow tracks allowed us to quantify the transient drop
deformation history of selected drops along their paths through the dispersing
apparatus. Comparisons with respective experimental results demonstrated again
good agreement as demonstrated in Figure 3.

Fig. 3: left: Transient deformation and Ca-number; right: multi-toothed R/S geometry
Membrane / Micro-channel Dispersing Processes
In addition to rotor-stator flow devices we considered also channel / nozzle / pore
flows with respect to their dispersive mixing performance. New microfluidics devices
have been developed in our Laboratory at ETH Zürich in close collaboration with the
University of Queensland in Brisbane (Australia); Prof. J. Cooper-White. Within the
lasts two years we investigated drop formation in co-flow and cross-flow micro- and
macro channels. By means of micro particle imaging the velocimetry (Micro-PIV) we
accessed velocity fields around respective drops and used this information for
optimizing the dispersing channel flow geometries and to derive scale up criteria
(e.g. We = f (Re) characteristics) over several orders of magnitude like demonstrated
in figure 4 .
As a scaleable solution with application relevance, derived from micro channel cross
flow results, a Rotating Membrane Device (ROME) with Controlled Pore Distance
(CPD) was developed. The cross flow is generated by the rotational motion of a
membrane cylinder within a surrounding concentric housing through which the
continuous fluid phase is axially pumped. The disperse fluid or gas-phase enters

Fig 4: Micro-/macro channel co-flow dispersing; experimental data / M. Duxenneuner
through a hollow shaft into the rotating cylinder membrane body and forms disperse
liquid droplets or bubbles at the membrane surface, from which the cross flowing
continuous fluid phase flow detaches them as soon as a critical shear stress is
exceeded .

Mixing, or Segregation, can be defined using three dimensions. The instantaneous state of segregation has two dimensions:
the scale of segregation, and the intensity of segregation. The intensity of segregation is reported as the CoV in a blending
application, while the scale of segregation is reported as the striation thickness distribution, the drop size distribution, as
examples. Previous work has shown that the two dimensions contain different and independent information. The CoV tells
us nothing about the scale of segregation, and the scale of segregation contains no information about the range of
concentrations observed.
The exposure dimension conbines the intensity and scale of segregation with a third characteristic of the system to give a rate
of reduction in segregation. Many examples of exposure equations are given in the literature. The most familiar is the mass
transfer rate, where the scale of segregation can be related to the interfacial area, the intensity of segregation to the local
concentration gradients, and the tendency of the system to reduce segregation to the mass transfer coefficient, or the
molecular diffusivity. In this case, the exposure dimension is an integral combination of the local area and intensity of
segregation, so while it is correlated to both the scale and the intensity of segregation, it is not a linear combination of the
average measures.
In this talk, the exposure dimension will be reviewed in the context of existing literature and models. The goal is to
determine the underlying mixing variables which consistently drive a reduction in segregation, and the role that these
variables play in achieving a range of process objectives

Pulp fibre suspensions display non-Newtonian rheology,
including a yield stress. Under certain mixer operating
conditions this creates caverns (regions of active mixing)
around the impellers with the cavern size affecting the
extent and quality of mixing attained. Due to the opacity
of pulp suspensions it is not possible to measure cavern
size with direct optical techniques, like photography.
Consequently two non-invasive techniques suitable for use
in opaque media were evaluated for determining the
cavern dimensions: electrical resistance tomography
(ERT) and ultrasonic Doppler velocimetry (UDV). The
agitation of several pulp suspensions in a 38 cm diameter
cylindrical vessel was studied using these methods over a
range of operating conditions. ERT is a non-invasive
technique that images differences in conductivity between
regions in the mixer using voltage measurements made at
the vessel periphery. Cavern measurement by ERT is very
rapid (data are collected within a few seconds) but it
suffers from poor spatial resolution (approximately 5 to
10% of the vessel diameter – from 1.9 to 3.8 cm in our
case). Two methods were evaluated for creating the
conductive environment imaged by ERT – the injection of
saline solution or the addition of small metallic tracer
particles to the region surrounding the impeller. UDV was
used to determine the cavern boundary by measuring the
locations at which suspension velocity fell to zero for
multiple linear paths through the vessel. While UDV
provided better spatial resolution of the cavern than ERT
(about 2 mm), multiple measurements (and consequently
significant time) were needed to build up the profile of the
cavern boundary.
Cavern size as a function of impeller rotation speed is
reported for a range of pulp suspension mixing conditions
(hardwood and softwood pulps, suspension mass
concentrations from 2 to 4%, two impeller offsets from the
wall, and two suspension height-to-chest diameter ratios)
in the 38-cm diameter cylindrical chest. A scaled version
of a commercially available axial flow impeller designed
for use in pulp suspension agitation (the Maxflo,
Chemineer Inc.) was used in the standard side-entering
configuration used for pulp stock chests. Measured cavern
diameters were compared against the axial force model
developed by Ammaullah et al. (1998) for predicting
cavern diameters in non-Newtonian fluids. The
discrepancy between the experimental data and model
predictions were fairly large, although they decreased with
increasing yield stress Reynolds number. The discrepancy
was attributed to the proximity of the impeller to the
vessel walls in the side-entering configuration studied. An
alternative correlation is presented for predicting the
cavern volume in pulp suspensions in this mixing
configuration based on the suspension yield stress

increasing yield stress Reynolds number. The discrepancy
was attributed to the proximity of the impeller to the
vessel walls in the side-entering configuration studied. An
alternative correlation is presented for predicting the
cavern volume in pulp suspensions in this mixing
configuration based on the suspension yield stress