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 .