# Influence of the Polarity of the Electric Field on Electrorheometry
## Materials and Methods
### Rheometry
#### 2.2.2 Capillary Breakup Extensional Electrorheometry  
Capillary breakup extensional electrorheometry experiments were carried out in a CaBER device (Thermo Fisher Scientific, Waltham, MA, USA) equipped with the Extensional Electrorheological Fixture (ExERF) [13]. The CaBER imposes a step strain extensional deformation (from \(h_{0}\) to \(h_{f}\)) to a stable liquid bridge, reaching a non-equilibrium state from which the capillary forces trigger the thinning process of the filament until it breaks. From the time evolution of the filament thinning process, it is possible to characterize the extensional behavior of the fluids [17; 18]. The ExERF generates a potential difference between the plates, limited to the maximum voltage generated by a high voltage sequencer (HVS448 3000V, LabSmith, Inc., Livermore, CA, USA). The desired electric field is given by \(\vec{E}=\Delta V/h_{0}\), \(\Delta V\) being the potential difference and \(h_{0}\) the initial gap, which was set at 2 mm for all the experiments. If the field goes from the upper to the lower plate, it is denoted as direct polarity; on the other hand, if the field goes from the lower to the top plate, it is denoted as inverse polarity (Figure 2b). The electric fields, which are aligned with the extensional flow, were set at: 0, 0.5, 0.75, 0.9, 1, 1.125, 1.25, and 1.5 kV/mm. The final height of the liquid bridge (\(h_{f}\)) was set to 6 mm for all cases studied. At least three independent runs were performed in order to ensure the reproducibility of the results presented below. These values provided a Hencky strain value \(\epsilon=ln\left(\frac{h_{f}}{h_{0}}\right)=1.10\). The optimal value of \(\Lambda_{0}=\frac{h_{0}}{d_{0}}\) is in the range of \(0.5\leq\Lambda_{0}\leq 1\), as indicated by the data from [PERSON] and [PERSON] [19]. In this study,  
Figure 2: (a) Sketch of the rotational rheometer equipped with an electrorheological cell and concentric cylinders (top view), where the electric and velocity fields are perpendicularly oriented. (b) Sketch of the CaBER device equipped with the electrorheological cell (front view), where the electric and velocity fields are parallel to each other, independent of the polarity. 4 mm diameter plates were used, and \(\Lambda_{0}\) was set at 0.5 due to the low value of the surface tension of the working fluids. Finally, the initial stretch profile was linear with a streak time \(t_{s}\) = 20 ms, and the temperature control was set to 20 \({}^{\circ}\)C (Thermo Haake DC10). The initial and final heights were checked regularly with thickness gauges, while the temperature of the fluid was measured before and after the experiments with a thermocouple sensor, which confirmed that the fluid temperature was not increased due to the Joule heating effect occurring during the lifetime of the experiments. As the fluid sample was based on olive oil, which had a conductivity close to 0 \(\mu\)S, the intensity of the current (\(I\)) through the liquid bridge was extremely low, resulting in a negligible power of heating (\(P\propto R^{2}\)) generated during the experiments. If the sample were conductive, the Joule heating effect would increase the temperature of the sample during the experiment, resulting in a decrease in the viscosity of the sample with time, which would make it impossible to decouple the effect of the polarity from the effect of the variation in the viscosity. The filament thinning process was recorded exclusively by means of a high-speed video camera (Photron FASTCAM Mini UX100) at 3200 fps (1024 \(\times\) 1280 square pixel) because for non-cylindrical filaments, the breaking is not fixed in the center of the filament and can be out of laser range [20; 21; 22]. The high speed camera was equipped with a set of optical lenses (Optem Zoom 70 XL) with 2\(\times\) magnification. A 52 mm Telecentric Backlight Illuminator connected to a metal halide light source (LeicaEL6000) by an optical fiber cable was used to illuminate the liquid bridge with truly collimated light and produce high contrast, silhouetted images.