# Influence of the Polarity of the Electric Field on Electrorheometry
## 3 Results and Discussion
### Corstarch/Oil Suspension
#### 3.2.2 Extensional Electrorheometry
According to the criteria of \(d_{f}<D_{y}\), the filament should stop breaking for intensities of electric field \(E_{0,cr}\geq 1.125\) kV/mm; however, results showed that an inverse polarity helped in the stabilization of the liquid bridge, and less intensity of the electric field was therefore required. Figure 8: Effect of the electric field (\(E=\Delta V/h_{f}\)) on the cornstarch suspension on direct polarity **(a)** and inverse polarity **(b)** in all cases; for the sake of clarity, these experimental curves only show one out of 10 points.. **(c)** Exponential relation of the break time (\(t_{b}\) (\(E_{0}\)) = \(A\cdot e^{b-E_{0}}\), with \(E_{0}\) in kV/mm), where the fitting parameters are provided in Table 6.  
However, the experimental results showed that in the case of the direct polarity, \(E_{0,cr}\) was somewhere between 0.75 and 1.125 kV/mm (Figure 8a), while in the case of the inverse polarity, the critical value was between 0.75 and 1 kV/mm (Figure 8b). This result is consistent with the one obtained for the Newtonian case, where we could see that in the inverse polarity, the Coulomb-type forces could counterbalance the effect of the gravitational force and provide a longer filament life. Now, in the case of the ERF, the inverse polarity helped to create stable liquid bridges at a lower electric field. Experimentally, it was not possible to extract the exact value of \(E_{0,cr}\), but a transition zone. This was due to the fact that the used fluid model was not monodisperse in particle size (see Figure 1a). Table 5 establishes some indicative limits for the transition zone based on the cases studied in this research. The imposed electric field allowed the cornstarch particles to form chains aligned in the direction of the field, producing a slow down in the thinning process. The greater the number of elements in the chains or the number of chains, due to an increase in the electric field, the greater the viscosity of the fluid and, therefore, the longer the filament break-time (\(t_{b}\)). In Figure 8c, it can be observed that the break-time increased exponentially with respect to the applied electric field (\(E_{0}\)). The polarity had almost no effect at low intensities of the electric field (\(E_{0}<0.5\) kV/mm); however, at higher electric field values, the break up time tended to be larger with the inverse polarity (Table 6). Figure 9 shows the time evolution of the minimum diameter for the working fluids under different electric fields. It could be observed that below a critical intensity of the electric field, the polarity had no effect on the thinning process of the filament, with the curves overlapping for both the Newtonian and the ERF fluids (Figure 9a). However, above a critical value of the intensity of the applied electric field (Figure 9b), the polarity had a clear effect on the time evolution of the minimum diameter for the ERF; for the Newtonian fluids, due to the absence of cornstarch particles, a much larger intensity of the electric field was required to see the influence of the polarity, i.e., Coulomb forces, as shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Polarity** & \(A\) & \(B\) & \(R^{2}\) \\ \hline Direct\% & 0.045 & 2.27 & 0.97 \\ Inverse\% & 0.040 & 2.46 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Dependence of the break time with the applied electric field and polarity (\(t_{b}\left(E_{0}\right)=A\cdot e^{b\cdot E_{0}}\), with \(E_{0}\) in kV/mm) for the cornstarch/olive suspension. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**wt.\%** & \(d_{f}\) & \(E_{0}=\frac{\Delta V}{h_{0}}\) & \(D_{y}=\frac{2\sigma}{\tau_{y\
u}\sqrt{3}}\) & **Direct** & **Inverse** \\ \hline \multirow{6}{*}{30} & & 0.5 & 9.284 & B & B \\  & & 0.75 & 5.86 & B & B \\  & & 0.9 & 2.96 & B and NB & B and NB \\  & & 1.125 & 2.08 & NB & NB \\  & & 1.25 & 1.76 & NB & NB \\  & & 1.5 & 1.17 & NB & NB \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(d_{f}\) vs. \(D_{y}\) for each extensional electric field value. NB, Not Break.