I am working on drilling fluids. When we perform rheological experiments with a viscometer, usually it gives us shear stress values corresponding to particular revolution per minute (rpm). Then we convert rpm into a shear rate by multiplying a factor 1.7. After that we have a set of values shear stress and shear rate. Then, we plot this data and calculate plastic viscosity, yield stress etc. The question is how a shear rate is measured by multiplying just a factor 1.7. I mean what is this factor?
Shear rate, gamma dot, is defined as v/h, where v is the velocity of the moving geometry of your viscometer and h is the separation of the plates or the thickness of your sample.
Given the dimensions of your plate, you could convert RPM into a speed and use this to calculate shear rate. Your 1.7 should therefore be a combination of dimensions of your system.
Based on this definition, it is therefore clear that a parallel plate viscometer/rheometer geometry will apply different shear rates at different points within the sample as a function of radius. For this reason, cone-plate geometries are preferred compared to parallel plates as homogeneous shear is applied.
Assuming that the rheometer spindle is a cylindrical one, what you are measuring is the shear force extreted by the fluid on the rotating spindle.
F= mu x ( surface area of spindle x linear velocity of spindle surface/ fluid film thickness).
The factor 1.7 is a combination of the bracketed terms .
I have attached the exact equation for what you are looking for. If you want to know what different terms in this equation are, please read the following thesis section 2.4.2.
https://www.researchgate.net/publication/311283113_DYNAMIC_AND_MAGNETO-OPTIC_PROPERTIES_OF_BENT_CORE_LIQUID_CRYSTALS
Thesis DYNAMIC AND MAGNETO-OPTIC PROPERTIES OF BENT CORE LIQUID CRYSTALS
Sayyid Muhammad Salili : I browsed through your thesis. And while i appreciate your work, at the same time, i do have a question about this formula. Isn't this formula valid only for the given geometry of the Rheometer used in your thesis. Can it be extended to a rotor in bucket type of configuration?
Yes, that's true. Most likely, this formula is only true for cone and plate geometry but you can still look at the reference I took the formula from to find it for your desired geometry.
Dear Hafez,
As you know for two co-axial concentric cylinders Rheometr with the inner is stationary and has a radius (r1) while the outer has radius (r2) and is rotating with rpm (N) the shear rate may be given by:-
[{(Pi* r22) /15 (r22 - r12)}*N]
For Fann rheometr Model 35 with standard configuration B1C1F1 the dimensions are:
Bob, r1 is 1.7245 cm
Rotor, r2 is 1.8415 cm
so by direct plugging of the values you can see that
3.14159*1.8415^2/15*(1.8415^2-1.7245^2)=1.7023
which is the constant k3 necessary for converting the rheometr RPM to sec-1/rpm for Model35 with its previous dimensions as listed by Fann company.
you may like to see this video for further details
https://www.youtube.com/watch?v=A6bMypTqL7g
My best wishes.
Alexander Malm , if you have different shear rates in different part of the plates how would you calculate the shear rate?
A great guide from the people of Brookfield.
https://www.che.utah.edu/~tony/chen4903/equipment/A_Viscometers/MIS_Brookfield_Viscometry_Guide.pdf
Here you can find the shear rate calculations for many spindle geometries.
Dear all,
Please can I ask you here how he did converted the rpm to shear rate in the highlighted area in the attached? As far as I know to convert from rpm to sec-1 we should use this equation 2*pi(3.14)/60 , is that correct?
Thanks
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