Optimal conditions for pre-shearing thixotropic or aging soft materials

Abstract

Pre-shearing is widely recognized as a necessary step to guarantee repeatability in rheological studies of thixotropic or aging soft materials. When one-directional pre-shear protocols are used, unrecovered elastic strain which leads to biased material states that are not always relaxed because of the build-up of structure during the relaxation process. We propose a way of guaranteeing unbiased material states by incorporating recovery steps, consisting of steps of strain opposing the initial direction of shearing, into any pre-shear protocol. Using such a multi-step pre-shear protocol, we show that it is possible to produce identical results from shearing in the positive and negative directions for the same magnitude of rate after pre-shearing. We further show how this idea of unbiased material states can be used to obtain unbiased results for other fundamental rheological experiments such as flow curves and frequency sweeps. By performing the new pre-shear protocol for every single measurement point of a flow curve or frequency sweep, it is possible to obtain data which is not affected by previous data collection, which leads to material responses with simple and clear shear histories.

Appendices

Appendix 1. Stress response during recovery step and rebuilding step

We propose the third criterion for optimal pre-shear as a way of checking the second criterion. If there exists a residual stress or residual strain in the system, we can recognize them by comparing stress responses to positive and negative shear start-up tests. Checking the stress response during the recovery and rebuilding steps is another way of ensuring the pre-shear satisfies the second criterion. We show in Fig. 9 that the step-strain recovery protocol we propose does indeed reduce the stress to essentially noise during the step process, as well as in the rebuilding phase.

Fig. 9

Stress response (absolute values) during a recovery step and b rebuilding step

Appendix 2. Shear rate input in ARES-G2 rheometer

On ARES-G2 rheometer, when constant shear rate is applied to the rheometer, it takes 0.04 seconds to apply desired shear rate. For example, when we apply 10 s⁻¹ of shear rate to the rheometer, the measured shear rate is visualized in Fig. 10. Regardless of shear rate magnitude, the rheometer has 0.04 seconds of delay.

Fig. 10

Measured shear rate with respect to time on ARES-G2 rheometer, when 10 s⁻¹ of constant shear rate is applied to the rheometer

Appendix 3. Determination of minimum rate amplitude for breakdown step

We can divide up the steady flow curve into three sections as shown in Fig. 11: plateau (P), high shear region (H), and transition (T). In high shear rate regime, the steady flow curve is a straight line. An intermediate section between the plateau and the high shear rate section exists, which is called the transition.

Fig. 11

Steady flow curve of fumed silica suspension. P, plateau; T, transition; H, high rate regimes, respectively

Any rate value in high rate regime can be used as shear rate value in breakdown step.

Appendix 4. Traditional frequency sweep with and without recovery step

We have focused our attention on the effects of pre-shearing with and without a strain recovery step on steady-shear start-up experiments in “Comparison between pre-shears with and without strain recovery.” In this section, we expand this to frequency sweep which is traditional linear rheological experiments to show the importance in a general rheological investigation of time-varying materials. We have performed frequency sweeps with four different pre-shear protocols: a traditional one-directional pre-shear at 300 s⁻¹ without a strain recovery step; a traditional one-directional pre-shear at − 300 s⁻¹ without a strain recovery step; positive one-directional pre-shear at 300 s⁻¹ with recovery step with negative direction; and negative one-directional pre-shear at − 300 s⁻¹ with recovery step with positive direction. Moreover, frequency sweep can be measured in upward or downward manner. So, we visualized upward frequency sweep without recovery step from positive and negative traditional pre-shear in Fig. 12a, upward frequency sweep with recovery step from positive initial shear and negative initial shear in Fig. 12b, downward frequency sweep without recovery step from positive and negative traditional shear in Fig. 12c, and downward frequency sweep with recovery step from positive initial shear and negative shear in Fig. 12d.

Fig. 12

a Frequency sweep measured from low shear rate to high shear rate without recovery step, b frequency sweep measured from low shear rate to high shear rate with recovery step, c frequency sweep measure from high shear rate to low shear rate without recovery step, and d frequency sweep from high shear rate to low shear rate with recovery step

The overall shapes are similar regardless of pre-shear protocols but have a strong dependence on whether high or low frequencies are probed first. Even though the shapes are similar, the values of moduli differ significantly according to the different pre-shear protocols. These results are, in some ways, not surprising. The application of any shearing to a structured thixotropic suspension is going to affect the rheology, and the rate at which the shearing is applied dictates the magnitude of those effects. The choice of high or low frequencies to begin the frequency sweep will therefore impart different shear histories, which one must expect will lead to different rheology, as observed here.

Appendix 5. Determination of linear regime based on amplitude sweeps

We performed strain amplitude sweeps for 0.1 rad s⁻¹ and 100 rad s⁻¹ to determine linear regime, because we compare frequency sweeps with consecutive and separated ways from 0.1 to 100 rad s⁻¹ in “Comparison between consecutive and separated frequency sweep.”

Fig. 13

Strain amplitude sweeps of fumed silica suspension for a 0.1 rad/s and b 100 rad/s