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 .

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High shear rotor-stator mixers are widely used in process industries including the
manufacture of many food, cosmetic, health care products, fine chemicals and
pharmaceuticals. Rotor-stator devices provide a focussed delivery of energy, power & shear
to accelerate physical processes such as mixing, dissolution, emulsification and deagglomeration.
To reliably scale-up these devices we need to understand the relationship
between rotor speed and flow rate and the energy dissipated by these devices. In-line rotor
stator mixers differ from in-tank versions because the flow is usually controlled
independently of the rotor speed. For in-tank devices the turbulent power can usually be
adequately described by single impeller type power number1. For an in-line rotor-stator
mixer it is found that the power transmitted by the rotor drops in proportion to decreased
flow rate and a single power number is not adequate. Kowalski2 and Baldyga et al.3
proposed that the power draw of a rotor-stator mixer can be described by the expression;
P= POZ ρ N3 D5 + k1 M N2 D2 (1)
This expression consists of two main elements. Firstly a term reflecting the power required
to rotate the shaft in response to the resistance of the liquid in the process chamber where ρ
is density (kg/m3), N is rotor speed (rps) and D is rotor diameter (m). Secondly a term for the
centrifugal energy given to the fluid which is then convected away by the mass flow rate, M
(kg/s). The two constants POZ and k1 are normally obtained from a multi-linear regression a
large matrix of experiments covering a wide range of flow rates and rotor speeds 4.
In the experiments described herein, it has been found that good estimates of the constants
can be obtained using a simplified set of trials. In Method 1 we note that there are two sets
of conditions under which constant turbulent power numbers are obtained as follows.
• When the outlet valve is closed, so we have zero flow, then the power is a minimum
given by P = POZ ρ N3 D5 with the characteristic power number POZ
• When the valve is fully open and the rotor-stator device acts as the sole pumping agent
then the flow rate is proportional to the rotor speed (figure 1) with M = ρ k2ND3. Power
draw is a maximum given by Pmax = POU ρ N3 D5 which can also be expressed as:
POZ ρ N3 D5 + (POU – POZ)ρN3 D5 with the characteristic power number POU
Substituting for M in eq 1 & rearranging gives Pmax = (POZ + k1 k2) ρ N3 D5 = POU ρ N3 D5 (2)
which in turn yields k1 = (POU – POZ) / k2 (3)
Figure 2 presents an example of the values of PO determined for these two extreme cases
and illustrates that the values are constant for all rotor speed and figure 3 presents the
comparison of measured and predicted power draw for a range of conditions.
In Method 2 we consider the example of a fixed speed device where flow rate can be varied
by means of a backpressure valve. In this case the power is a linear function of the flow rate
(fig 4) where the intercept is given by POZ ρ N3 D5 and the gradient by k1 N2 D2 and thus POZ
and k1 can be determined. This method also has the advantage of being suitable with power

determined from a heat balance because it does not explicitly require measurement at zero
flow rate (this is possible with the torque measurement used above). However at low rotor
speeds and high flow rates the temperature rise is small the heat balance is subject to
significant errors although the accuracy was improved by lagging the equipment and careful
calibration of the temperature probes. Table 1 presents the values of the constants
determined by the two approaches for an example arrangement of rotor and stator. In the
presentation we will present results for other arrangements complete with statistical analysis. easy pay through payday loan