Document 4207Q258 V3.00 January 2018
Page 11 of 30
Chirascan Couette Cell LD Accessory User Manual
Due to the curvature of the cylindrical surfaces, the shear rate,
γ̇
, varies slightly across the gap [1]. If the
sample viscosity,
, is independent of the shear rate, as it is likely to be for the dilute materials normally used
with the Couette cell, then the shear rate at the inner cylinder is given by:
γ̇
i
= 2
R
o
2
/ (R
o
2
– R
i
2
)
and at the outer cylinder is given by:
γ̇
o
= 2
R
i
2
/ (R
o
2
– R
i
2
)
where
is the angular velocity in radians per second (rad s
-1
), R is the radius, and the subscripts i and o refer
to the inner and outer cylinders respectively [1]. Thus there is a difference in shear rate between the outer and
inner cylinders of a factor of (R
o
/R
i
)
2
or about 11%. This difference is small enough to allow the approximation:
γ̇ =
R
o
/ (R
o
– R
i
)
This expression is used in the accessory software to calculate the shear rate. It is central to the design of the
accessory that the shear rate is as homogenous as possible, so that all parts of the sample are experiencing
almost the same shear rate, and the error introduced by using a single value shear rate is minimized.
A coincidence! The factor R
o
/ (R
o
– R
i
) is equal to 19.1 for a 9.55 mm diameter rotor and a 0.25 mm gap.
Since the conversion from revolutions per second (rps) to radians per second (rad s
-1
) is to multiply by 2
, the
conversion factor from rps to shear rate is 19.1 x 2
which equals almost exactly 120. The apparent neatness
of this number is entirely coincidental on the dimensions used for the Couette cell (to put it another way, 30/9.55
is a very good approximation to
).
Note that the absorbance can be measured simultaneously with the linear dichroism, but that the circular
dichroism (CD) cannot be measured on a system with a significant linear dichroism component, as the
calculation of the CD requires that there is no LD or birefringence component to the response.
1,
R.W. Whorlow,
“Rheological Techniques”
,
2
nd
edition, Ellis Horwood, 1992, p103.
For more information on linear dichroism and its measurement, see B. Norden, A. Rodger and T. Dafforn
“Linear Dichroism and Circular Dichroism”
, 2
nd
edition, RSC Publishing, 2010
