Stay on Prof. Kelessidis approach; he is quite an expert in this issue (Yield Stress) involving suspensions of physical materials. In addition, the papers from Prof. J-M Piau research group are rather elucidating on this aspect.

{Check this one: Yield stress thixotropic clay suspension: Investigations of structure by light, neutron, and x-ray scattering, Phys. Rev. E 56, 3281 }.

Greeting Ernesto!

first we have to diferenciate from a yield stress measured and a yield stress calculated from H-B. H-B is a model with just a yield stress and a shear thining range. The behaviour of real meterials never shows a flow curve with only these two performances. at the same time than the yield stress there is a newtonian plateau that is mostly hidden by the cte yield stress at low shear rates. this means that 95 % of the samples will not show a cte shear stress at low torques. they will show a shear stress with a lower slope versus shear rate. so, I can happen that the extrapolation to 0 shear rate in a log log plot give us negative values.

regarding the experimental yield stress, wich are the main esperimental errors that arise also in negative yield stress values for the H-B model.

fitst, don´t let the sample to loose the memory after the loading. It is very common to see at low shear stresses, negative shear rates. the reason is that the sample is moving the cilinder becouse of the residual stresses in one direction while the rheometer moves the cilinder in the other direction qith a shear stress lower than the residual stress

second. to perform the experiment in a ramp instad of in a steady state experiment. It is almost mandatory that is you want to measure accurate yeild stress the sample must be in equilibrium at each point of shear stress. if not we will have a yield stress that depends on the shear stress rate versus time.

thirt and more important. If a sample has a yield stress, at stress below the yield stress, the sample itself is a solid. A solid can not be measured in flow becouse a solid does not flow. So the best way is to perform a stress sweep in oscillation. The yield stress is the stress to go out of the linear viscoelastic range.

there is another solution that can work. Do a steady state ramp (low curve) but from high shear rates to low shear rates. Advantages: the sample has forgotten the loading proccess and you really are pushing the sample to become a solid from the flow.

Dear Mr. Gracia,

Thanks a lot for your valuable comments.

Although the simplicity of HB model could be naive to address more complex phenomena, it can be helpful in a fast screening and it is widely reported when studying this clay suspensions.

Regarding the experimental conditions, by using creep measurements, I have set a pre-shear and equillibration time prior the viscometry essays in order to minimize memory effects. The time between measurements and the integration time were set to 5 and 7 s, respectively but I haven't tested if those conditions are enough to achieve the equilibrium. Until now I haven't perform any hysteresis experiments, but seems to be a logic step in my research, in addition to the oscillatory experiments.

If you want to do quick and dirty screening, then I suggest you use your HB model and switch to the Power law (Ostwald) when you obtain a negative yield stress.

Personally, I dislike the HB model for quick comparisons other than the yield stress as the viscosity is represented by two calculated values and similar fits can be obtained with large variations in the consistency and curvature values.

As Mr Garcia has suggested, a Cross or Carreau model might approximate your data more closely or you may try a modified Bingham model with a squared contribution for the curvature; you may compare first the yield stress and Bingham viscosity then the magnitude of the departure from the linear Bingham model.

These are the quick and dirty comparisons. Otherwise I do a full rheological study of each sample with a measured preshear to a basin viscosity, a measured recovery using low amplitude oscillatory measurement, then a shear sweep and a frequency sweep under oscillation using the values selected from the shear sweep. Finally, if there is a yield stress, I will complete with creep measurements as well as a stress ramp to confirm the yield stress values.

From my own tests with bentonite and similar suspensions. A negative yield stress usually results when the HB model is fitted to data with significant slip i.e., the low shear rate data is lower than it should be ...hence the much lower value of the yield stress, which results in the model tending to a negative yield value.

Dear Sir Carlos Alberto Gracia-Fernández ,

May I have your advice on following matter? I ran a flow test on my starch batter added with fatty acid, I intended to get parameters for the step 1 ramping (shear rate 0 to 100 s-1) but the data doesn't seem to fit any model. Not to mention the H-B parameters doesn't make any sense at all (to me at least)... Any idea why? Appreciate your input...

good morning Poh

clearly you have a slipage problem. Or maybe shear banding but I do think that it is a sliping problem

the sehar stress can not decrease when the shear rate increases. So I do recomend you to use cross hatched or sand blasted geometries. The TA aplication support in your country can help you better than me.

For everybody that wants to measure the yield stress, I do recomend a oscilatory stress sweep. It is the best and most reproducible method. It is not easy to explain here why a flow ramp it is abd method and why a steady state ramp is not usefull. regards

Why don´t you use other models to fit your data such as BMP?

Article On the yield stress of complex materials

Good luck!

Hello, very good contributions in this discussion. I just came across negative YS values and searched for a better regression model for H-B model using Origin software. I also found that the Winhab equation is reported to be a better choice than the H-B model in some dispersions. I concluded that I better place the YS = 0 for the cases where it gives me negative values and thus I calculate the other parameters of interest. I would like to know if anyone agrees with me.