Hello Shravan,

Regarding your question, generally we consider that the vane geometry is equivalent to Couette bob of radius Rband heighth, if the fluid is assumed to be incompressible and inelastic and there is no-slip boundary layer condition achieved between the vane and the mortar. According to these hypotheses, the shear stress τ and the shear rate can be estimated from the shearing average torque M and the rotation speed Ω by using formulas which were developed by Estellé et al, you can find more details in those articles enclosed, i hope i did answer your question.

Good luck.

Dear Shravan

Our colleage Ilhame is correct if you assume that the vane is equivalent to a Couette geometry, which is not actually true. Recent findings [Medina-Bañuelos EF, Marín-Santibáñez BM, Pérez-González J, Kalyon DM (2019) Rheo-PIV analysis of the vane in cup flow of a viscoplastic microgel. J Rheol (NYNY) 63:905–915. https ://doi. org/10.1122/1.5118900] suggest that the vane drags only part of the sample as a rigid body and therefore the determination of an equivalent radius for this geometry would be inaccurate. In fact, the manual of the rheometers warns of this fact, as you can see in the attached file (page 118):

"Due to the fact that there is no defined flow field for the flow of the sample around the vane, the shear-rate in the sample can not be calculated. As consequence the geometry factor M for the shear-rate is not defined and set to 1.0".

Therefore, I suggest to present the results as torque vs rpm.

Hope its useful. Regards, Paulo.

Dear Shravan,

for Viskomat XL, the company has given a conversion for torque to shear stress which is available on the manual of the Viskomat XL. Please check it. It is valid for the 4 and 6 vane probe geometries. However, for fishbone probe, it shall not be applicable. For that case the best solution will be to use torque and rpm for now.

Thank you @Ilhame Harbouz and @Paulo Ricardo de Matos . Assuming vane as a coutte geometry is a bit tricky, as you both mentioned. I did publish my results in Torque and RPM, but few reviewers wanted me to represent the values in Shear stress and shear rate respectively.

Nevertheless, thank you very much for your time and comments again.

@Mirza Abdul Basit Beigh. Thank you for your comment but those conversion factors were derived after taking elementary assumptions. I personally feel shear stress derived from that constant does not represent reality.

Thank you very much for your time and comment. Really appreciate

Hi Shravan,

Please follow the attached link. It will be useful

https://www.tandfonline.com/doi/full/10.1080/1023697X.2017.1375433?src=recsys&

Most rheometer assume vane to act as a wide gap couette geometry and use this conversion equation. If you can see the book "Rheology: Principles, Measurements, and Applications" by Macosko, you can find the derivation for the conversion equation for the wide gap couette geometry.

However, as mentioned in one of the previous comments, the assumption of couette geometry is valid only if the entire material within the vane blades has rigid body without being sheared. However, this may not be always true and there may be errors in making vane measurements as compared to using an actual couette geometry.

Shravan Muthukrishnan The fact that those derivations may have flaws is undeniable but it depends on the type of concrete. Since your mixture looks to be stiff than conventional concrete and as you haven't mentioned the time of your measurement after addition of water, it really is a special case and the answer cannot be generalised based on the feeling alone.

At the same time, it also depends on the techniques used to determine the rheological properties. For example, if you apply a hysteresis loop test to this material, you won't get anything coherent because the material will have clear differential shearing and the centre vane portion will be broken off from the rest of the material.

Now, for example, if you use a constant shear test, then you have to use multiple batch approach so that you really measure what you are aiming at. In this case, this formula is perfectly applicable just because you are testing the specimen for one time to determine your torque at the maximum strain. If you aim to repeat the same test on this same specimen again, you may end up measuring friction. So prepare a new sample and test again at the required age.

Or for example, you are using oscillation technique wherein you apply, for example, a time sweep or strain sweep, you have to be sure about the critical strain so that you may not have the critical strain passed well before you actually aim to determine the torque and then your measurement will be quite ambiguous.

Additionally, you should also know that if your mixture is a fine-grained mortar of max aggregate size of 2 mm, then please do not use the vane probe. The manual suggests using a fish-bone probe. But the fishbone probe is quite new and there aren't any conversion formulae. You will have to use the mathematics to derive the conversion formulae in this case.

Bottom line is that you have a problem specific question and there are no general answers to it. You will have to work out a solution based on the specifics from different inputs here. Good luck.

@Mirza Abdul Basit Beigh

I can't agree more. One should take different approaches while converting torque observed from hysterical loop test or static yield stress measurement (SYS).Within SYS measurements, methods with shearing history (single batch) and without (multiple batch) would also require different conversion factors. It come backs to my original question, why do we still represent rheological parameters in stress and shear rate (unreliable ones) instead of torque and RPM ?

In the case of oscillatory mode, we actually use different transformation techniques, (i.e lissajous plot, Fourier transformation etc.) for material at linear (< critical strain) and non-linear viscoelastic range (> critical strain). The reason why, I believe this method to be more accurate one to characterise fresh properties of printable concrete.

Nevertheless, thank you very much for your comment. If represeting rheological properties in independent variables is important. Personally I feel, adapting wide gap coutte geometry is the closest you can get. Factors given in the manual requires serious correction.

Dear Shravan,

I am not sure if the question is still of interest to you, but I would like to say a few things. I hope they will be relevant.

In the case of the dynamic properties, I would suggest you consider your geometry as coaxial cylinders and apply the Reiner-Riwlin equation. Please check out this paper by Dimitri Feys et al.: Extension of the Reiner–Riwlin equation to determine modified Bingham parameters measured in coaxial cylinders rheometers.

In the case of the static properties, you can use the following simple equation to calculate the SYS: τ = T/(2*r2*π*h), where r and h are the radius and the height of the probe. Here we consider that only a small region in the vicinity of the probe is sheared, which will be the actual case if you are testing stiff 3DP concretes. The equation will not change depending on using single-batch or multi-batch approach. What can change is the determined value of Athix, especially if you test a highly thixotropic mixture with a high volume fraction of aggregates. Then the single-batch approach will give you underestimated results. However, this approach is basically the only one you can apply to control Athix of your 3DP concrete by means of rotational rheometry, unless you have multiple identical rheometers in the lab, of course :)

Regarding your comment on giving torque and rot.velocity instead of SS and SR, I would like to say that they can be very different for different tools, therefore, other researchers who are using another rheometer will not be able to get what your values are representing. That is why we all try to present SS and SR. It gives us a feeling of the mixture's properties.

Dear Shravan,

I do support @Irina Ivanova submission. You can also check out

https://doi.org/10.1016/j.conbuildmat.2019.07.240

for the practical application of modified Reiner-Riwlin and SYS equations to a vane-in-cylinder ICAR rheometer.

The modified Reiner-Riwlin equation takes care of the dead zone highlighted by @Paulo Ricardo de Matos

Irina Ivanova actually there is no "static" and "dynamic" properties, but higher or lower shear rates. I believe that by "static" properties you mean static yield stress determined by stress growth test. You may refer to this very traditional paper [Barnes, H.A., Walters, K. The yield stress myth?. Rheol Acta 24, 323–326 (1985). https://doi.org/10.1007/BF01333960]. To have yield stress, you need an "infinite viscosity", which actually doesn't exist. Viscosity increases several orders of magnitude as the shear rate decreases but always converges to a finite value.

Anyway, this equation that you are proposing basically relates the torque and the area of the assumed Couette geometry. If your test is either "static" or "dynamic", the actual flow around a vane spindle is not a perfect cylinder.

The following discussion seemingly can be found of some interest, concerning to your query: https://www.researchgate.net/post/Does_anybody_know_how_to_measure_viscosity_on-line_in_a_bioreactor