First a strain sweep needs to be run covering a range from 0 – 100 % strain at a chosen temperature of interest T (oC or oF) and at a low enough frequency between 0.01 – 0.1 radians/s, say 0.05 radians/s.  The complex modulus |G*| versus strain or complex viscosity (= |G*|/w) versus strain needs to be plotted and the highest value of strain (critical strain gCR) until the complex modulus or the complex viscosity maintains a constant value before it begins to deviate from linearity needs to be identified.

Next, at that value of critical strain gCR and the same chosen temperature of interest T (oC or oF), a frequency sweep needs to be run covering a range from 0.01 – 10 radians/s.  The complex viscosity (= |G*|/w) versus frequency needs to be plotted and the highest value of frequency (critical frequency wCR) until the complex viscosity maintains a constant value before it begins to deviate from linearity needs to be identified.  In case, the complex viscosity deviates from linearity at the very first point of frequency of 0.01 radians/s, then a lower range of frequency like 0.001 – 0.01 radians/s needs to be chosen and the above mentioned tests need to be run. This is the method to check how small the value should be.

Now, if both values of strain and frequency which are less than gCR and wCR are selected to run future rheological experiments on the same sample at the temperature of interest T (oC or oF), then the measurements would be in the linear viscoelastic range.  For most non-Newtonian fluids, it should be possible to find this linear viscoelastic range.  However, it can be a little tricky for non-Newtonian fluids with a yield stress though such a region would exist in most cases except highly filled systems.  More about non-Newtonian fluids and their rheological behavior can be understood by looking into the following references in case they are available in the library.

Aroon V. Shenoy, Rheology of Filled Polymer Systems, Kluwer Academic Publishers, Netherlands (1999).

A. V. Shenoy and D. R. Saini, Thermoplastic Melt Rheology and Processing, Marcel Dekker Inc., New York (1996).

Dear Anthony,

It is depending on the equipment you use.

To my mind you can do the following things:

1. You can measure simple flow curves in a wide region of shear rate ( for example from 0.01 1/s to 1 or 10 1/s) to determine how your system behaves, then repeat measurements after different rest of time, and when you get the initial flow curve back, you have found the adequate relaxation time.

2. You can try to measure a creep test, to check your systems recovery. (For this you also need to know the maximum shear stress from the flow curve, as you have to adjust a value below that.)

3.The other opportunity is to perform an amplitude sweep and a frequency sweep oscillation measurement to find the linear viscoelastic regime.

To my best knowledge non-Newtonian  systems seem to be Newtonian by applying high stress, so to my mind it can not happen, that you find Newtonian behavior under small strains for this type of system. So it is easy to find out, what is high strain, because, in that case you simple get a straight line, but small enough is if you can see the typical shape of pseudoplastic flow curve.

I hope I could help you.

Best regards.

Zsuzsanna

Your fluid is shear thinning and thixotropic.

If it is thixotropic, it probably has a yield stress.

For  non-Newtonian fluid a linear viscoelastic domain is generally observed . This domain may be slightly extended.

Since your fluid is thixotropic, you can not apply the  Cox Merx law  that allows to calculate viscosity in function of shear rate  from the viscosity measured in  dynamic tests under  small strain.

Such  non-Newtonian fluid can not be approximated as Newtonian under small strains.

The first thing would be measure the viscoelastic linear region.

While measuring this region it is likely that the strain limit of the viscoelastic region will be crossed. If this is the case, equilibrate the sample for reasonable time and do the viscoelastic measurement in the linear region.

In general, the pseudoplastic materials cannot be approximated as Newtonian fluids

First a strain sweep needs to be run covering a range from 0 – 100 % strain at a chosen temperature of interest T (oC or oF) and at a low enough frequency between 0.01 – 0.1 radians/s, say 0.05 radians/s.  The complex modulus |G*| versus strain or complex viscosity (= |G*|/w) versus strain needs to be plotted and the highest value of strain (critical strain gCR) until the complex modulus or the complex viscosity maintains a constant value before it begins to deviate from linearity needs to be identified.

Next, at that value of critical strain gCR and the same chosen temperature of interest T (oC or oF), a frequency sweep needs to be run covering a range from 0.01 – 10 radians/s.  The complex viscosity (= |G*|/w) versus frequency needs to be plotted and the highest value of frequency (critical frequency wCR) until the complex viscosity maintains a constant value before it begins to deviate from linearity needs to be identified.  In case, the complex viscosity deviates from linearity at the very first point of frequency of 0.01 radians/s, then a lower range of frequency like 0.001 – 0.01 radians/s needs to be chosen and the above mentioned tests need to be run. This is the method to check how small the value should be.

Now, if both values of strain and frequency which are less than gCR and wCR are selected to run future rheological experiments on the same sample at the temperature of interest T (oC or oF), then the measurements would be in the linear viscoelastic range.  For most non-Newtonian fluids, it should be possible to find this linear viscoelastic range.  However, it can be a little tricky for non-Newtonian fluids with a yield stress though such a region would exist in most cases except highly filled systems.  More about non-Newtonian fluids and their rheological behavior can be understood by looking into the following references in case they are available in the library.

Aroon V. Shenoy, Rheology of Filled Polymer Systems, Kluwer Academic Publishers, Netherlands (1999).

A. V. Shenoy and D. R. Saini, Thermoplastic Melt Rheology and Processing, Marcel Dekker Inc., New York (1996).

Dear Anthony,

just run a strain sweep at a fixed frequency (usually I do it at the lowest and at the highest frequency of the frequency sweep you want to perform) in a very wide range of strain values. If the viscoelastic moduli are constant in a range of strain, then you are in the linear regime in this range and you can use a value of strain in this range to perform your small amplitude frequency sweep.

Best

Rossana

Dear Anthony,

There are two key time dependent responses of viscoelastic materials those that occur within the linear viscoelastic region at small strains and stresses due to rearrangement or relaxation of the microstructure – an example being play putty or an entangled polymer system.

The other is when you break down this microstructure by applying a sufficient stress or strain to take the material in to its non-linear regime, where shear thinning or strain softening (or sometimes strain hardening or shear thickening) would occur. For this to happen significant re-arrangement of the microstructure must take place and this occurs when sufficient energy is inputted to move away from the low energy equilibrium rest state – overcoming Brownian motion and any associative interactions in the microstructure. This re-arrangement can take time to reach a new equilibrium state, which is what thixotropy refers to, and on removing (or reducing) the shear may take some time to get back to its initial equilibrium state.

To quantify thixotropy then we need to be able to measure the sample in two different states, this can be in the linear region and then in the non-linear region or both measurements could be in the non-linear region so low shear rate and high shear rate.

The best way to achieve this is to use a use a step strain or step shear rate test, or even a combination of the two. With a step strain test you make a measurement in the linear region for a given time say 60s and then increase the strain to a larger value for another 60s say and then step back to the initial strain and see how long the microstructure take to recover, best done through G’. What you want is a time of how long it takes to recover say 90% of its initial structure. To find the appropriate linear and non-linear strain you run an amplitude sweep first. Ideally you want to use the smallest strain that you get acceptable data for (minimize signal to noise ratio) and/or a measuring system that allows you to work at higher angular displacements or torques for a given strain.

Another method is to perform a step shear rate test so low shear – high shear –  low shear, and measure the time to recover a % of the original structure. Here you are looking at the transition between two non-linear states. It is also possible to combine oscillation and steady shear by applying a linear strain- shear rate –linear strain. If your sample is prone to fracture under steady shear then sometimes a step strain test is best.

There are some excellent reviews on thixotropy by Jan Mewis and Howard Barnes in Journal of Non-Newtonian fluid mechanics which are worth checking out. Howard will also be giving a Malvern Instruments webinar later this year if you want to check that out.

Cheers

John

As a rule at small mechanical stresses the response of  Rheological fluid in non-linear.

Response becomes linear at large stresses.