# Influence of the Polarity of the Electric Field on Electrorheometry
## 3 Results and Discussion
### Corstarch/Oil Suspension
#### 3.2.2 Extensional Electrorheometry  
Shear electrorheometry measurements allowed confirming that the ERF exhibited a Newtonian-like behavior when no electrical field was applied, but a yield stress behavior under the presence of an electrical field. The ERF showed a potential dependence of the yield stress value with the applied electric field. Once the shear sample was studied, we knew that our fluid had a yield stress behavior under the action of the electric field. The characterization of yield stress fluids under uniaxial extensional flow had been previously reported by [18; 21; 29; 30]. It is well accepted in the literature that the filament will begin the thinning process once the capillary pressure (\(2\sigma/D_{min}\)) is greater than the dynamic yield stress (\(\tau_{yd}\)). Although [PERSON]'s model is not accurate for predicting the temporal variation of the minimum filament diameter [21], it is able to predict the yielding diameter (Equation (3)) very accurately: [13]:  
\[D_{y}=\frac{2\sigma}{\tau_{yd}\sqrt{3}}, \tag{3}\]  
where \(\sigma\) is the surface tension and \(\tau_{yd}\) the dynamic yield stress. The yielding diameter is defined as the threshold diameter necessary to cross in order to start the thinning process; thus:  
* if \(D_{y}>d_{f}\), being \(d_{f}\approx d_{0}\sqrt{h_{0}/h_{f}}\), the capillary pressure exceeds the dynamic yield stress, and the filament thinning will be triggered;
* if \(D_{y}<d_{f}\), the capillary pressure does not exceed the dynamic yield stress, and the thinning process will not begin, so the filament will not break;  
where \(d_{f}\) is the filament diameter at the end of the step strain deformation. The results from the extensional electrorheometry of the cornstarch suspension are shown in Figure 8, where the effect of the intensity of the electric field and its polarity becomes evident. In the absence of the electric field, the minimum diameter of the filament corresponding to the ERF followed a similar evolution to the one of the carrier fluid, as both showed Newtonian behavior. As the intensity \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fitting Parameters** & \(A\) & \(B\) & \(R^{2}\) \\ \hline
30 wt.\% & 14.7 & 1.54 & 0.983 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dependence of the dynamic yield stress with the applied electric field (\(\tau_{yd}\left(E_{0}\right)=A\cdot E_{0}^{B}\), with \(E_{0}\) in kV/mm) for the cornstarch/olive suspension. Figure 7: **(a)** Steady-state viscosity curves for the suspending fluid and the ERF under an imposed electrical field of 0, 0.5, 0.75, 1, 1.5, 2.25, and 3 kV/mm. **(b)** Dependence of the dynamic yield stress with the intensity of the electric field imposed at \(h_{0}\). of the electric field increased, the internal structure developed by the cornstarch particles helped the filament to counterbalance the capillary pressure, and consequently, the filament lived longer. There was a critical intensity of the electric field (\(E_{0,cr}\)) beyond which the filament became stable, and it did Not Break (NB), which can be observed by the fact that the diameter of the filament reached a constant value (Figure 8). The dynamic yield stress increased with the imposed electric field; therefore, if the capillary force after step strain did not exceed that value of dynamic yield stress, the filament thinning process did not begin, and the liquid bridge remained stable, bridging the \(h_{f}\) distance between the two plates. As stated above, if the diameter of the filament at the end of the streak time (\(d_{f}\)) was greater than the yielding diameter (\(D_{y}\)), then the capillary pressure did not exceed the dynamic yield stress, and the thinning process could not start. Table 4 presents the comparison between the diameter at the end of the streak time and the yielding diameter for all cases studied.