Thermo Scientific HAAKE RotoVisco 1 Instruction Manual page 96

L
a
R1
R 2
R 3
R 4
Sensor Systems
Geometry
The geometry of the sensor system is designed so that radii
relationship of the shear surfaces is almost equal so that
identical shearing conditions in both gaps can be expected.
R R
2 4
=
R R
1 3
R = Radius Beaker (Inside)
1
R = Radius Beaker (Outside)
4
R = Radius Rotor (Outside)
3
R = Radius Rotor (Inside)
2
L = Length of Shear Surface
a = Distance
Calculation Equations:
Shear Stress :
The shear stress  is proportional to the torque 'Md' and to
a stress factor i.e. stress factor 'A'.
 = A  Md
The factor 'A' can be calculated as described by the following
equation:
1
A =
2
2 ⋅ π ⋅ L ⋅ (R
2
.
Shear Rate :
γ
.
The shear rate is proportionally linked to the angular veloc-
γ
ity and thus speed and the shear factor 'M'.
.
= M ⋅ Ω
γ
The angular velocity  is calculated according to 2π
from the speed n. The factor M is calculated:
The factor 'M' is calculated as follows:
2
2 ⋅ R
a
M =
2 2
R -R
a
i
Deformation :
The deformation  is linearly linked to the angular deflection
and the geometry of a sensor system.
 = M   with  = Torsion angle rad
 is a dimensionless number
94
[A] = 1
2
+ R )
3
Ra = R4, R2
Ri = R3, R1
3
m
⋅ n
60