Direct Measurement of Wall Shear Stress in an
Arde Barinco Rotor-Stator High-Shear Laboratory Mixer
I N N O VATI O N BY ANY M EAS U R E
Vadim Stepaniuk, C. Mark Denning, Valery Sheverev - Lenterra, Inc. 105 Lock St., Newark, NJ 07103 www.lenterra.com
Roy Scott, Richard Barbini - Arde Barinco, 875 Washington Ave., Carlstadt, NJ 07072 www.arde-barinco.com
RealShear Sensors:
Principle of Operation
Abstract
Real-time measurements of wall shear stress at the stator wall in an Arde Barinco highshear mixer were obtained for the first time using a Lenterra RealShear sensor. Glycerol
(Newtonian) and shampoo (non-Newtonian) were tested. A model F-8K sensor was used
with a +/-8 kPa range. The shear stress as a function of motor RPM was measured for
both clockwise and counter-clockwise rotation of the impeller. A measurement rate of 10
kHz enabled resolution of individual passes of each impeller blade which manifested
themselves as peaks in the shear stress signal. The sensor was rotated to determine the
longitudinal and azimuthal components of the wall shear stress at various RPMs. Data of
the type presented here is envisioned to provide a means to verify the shear rate of new
and existing mixer designs and also as a means to monitor the viscosity or flow rate of
process fluids in real-time.
Shear Stress
Shear stress is a force that acts on an
object in a direction that is parallel to its
surface. The amount of shear stress is
determined by the viscosity of the fluid
flowing across it and how much the fluid
velocity varies with varying distance from
the wall (known as the “velocity gradient” or
“shear rate”). If the shear rate is known, the
wall shear stress measured by a RealShear
sensor can be used to measure viscosity. In
high-shear mixers the shear rate can be
calculated using the known geometry of the
rotor-stator and the rotation rate of the rotor.
A floating element that is in direct
contact with the fluid under test, is
attached to a cantilever beam which
deflects in response to shear stress
applied to the floating element
surface, and transmits a force to a
micro-optical resonator. This
resonator has an optical spectrum
with peaks centered at particular light
wavelengths. When the cantilever
deflects, the micro-optical resonator
attached to the cantilever
experiences strain, causing a shift in
its resonant optical wavelength
measured with an optical controller.
This shift is proportional to the shear
stress and viscosity of the fluid.
Photograph of the mixing head of an Arde Barinco CJ-4E
Reversible Homogenizing Laboratory Mixer with the
Lenterra RealShear shear stress sensor attached to the
cylindrical stator element. The inset shows the mixing head
with the stator removed, revealing the position of the
impeller blades. The sensor is mounted into a finely
threaded ¼”-80 custom mounting hole, so that the face of
the sensor is flush with the inner wall of the cylindrical stator.
Applications
Figure: High-shear mixer dynamics.
Fluid and rotor velocities are shown as
well as the wall shear stress induced on
the mixer components by the fluid
•Scale up of mixing processes from the laboratory to the
factory floor
•Continuous monitoring of mixing operations to prevent
under/overprocessing
•Flow rate and viscosity monitoring of flowing or mixing
fluids
•Characterization of multiphase flows
Left: Lenterra RealShear sensor and 2-channel controller.
Right: Arde Barinco mixer and control box
Wall Shear Stress vs. Time
Below are figures showing the wall shear stress signal vs. time for glycerol with the
sensor directed horizontally and in the same direction as the impeller motion. The mixer
is turned on, allowed to reach steady state operation at 1020 RPM, and then turned off.
Wall Shear Stress vs. RPM
Time-averaged steady-state wall shear stress as a function of mixer RPM for glycerol and shampoo. Positive values of
RPM indicate upward flow (clockwise rotation) while negative values indicate downward flow (counter-clockwise rotation).
The apparent viscosity of shampoo was calculated using the known viscosity of Glycerol (1000 mPa-s for room
temperature) to determine the coefficient A relating wall shear stress and RPM to viscosity for this particular sensor position
and mixer geometry, and applying it to shampoo under the assumption that shear rate and flow conditions are similar. The
relation is:
μ = A τ / RPM
where μ is the viscosity and τ is the measured shear stress.
Full view of wall shear stress signal as mixer
is turned on and off.
Zoom in of the shear stress signal for
steady state operation. The peaks in the
signal represent moments when an
impeller blade passes by the sensor face.
Glycerol
Shampoo
Wall Shear Stress vs. Sensor Angle
Close-up of the shear stress as the mixer
is turned on. The increasing frequency of
the impeller rotation can be seen.
Close-up of the shear stress as the
mixer is turned off.
The wall shear stress was measured for various angles of the sensor’s
axis of sensitivity with the horizontal. The sensor was rotated from 0
degrees (pointing in the direction of impeller motion) to 180 degrees
(pointing against the impeller motion) . Measurements were made for
both upward flow (clockwise rotation) and downward flow (counterclockwise rotation). Counter-intuitively, when the sensor is oriented
vertically (90 degrees), the wall shear stress vector points downward
for the upward flow configuration of the mixer and vice versa. This
unexpected result illustrates that variation of local conditions within the
mixing head can be complex.