High Voltages in Sliding Water Drops

Water drops on insulating hydrophobic substrates can generate electric potentials of kilovolts upon sliding for a few centimeters. We show that the drop saturation voltage corresponds to an amplified value of the solid–liquid surface potential at the substrate. The amplification is given by the substrate geometry, the drop and substrate dielectric properties, and the Debye length within the liquid. Next to enabling an easy and low-cost way to measure surface- and zeta- potentials, the high drop voltages have implications for energy harvesting, droplet microfluidics, and electrostatic discharge protection.

which vaporized the PFOTS.Then the chamber was left on a stir plate for 30 minutes to complete the silanization process.The motion of the magnetic stir bar provided airflow within the desiccator for more homogeneous deposition.The PFOTS surface had advancing and receding contact angles of (107 ± 2)°and (89 ± 3)°, respectively.Our experimental setup is shown in figure S1(a).The experiments were done under ambient conditions (temperature: 21 ± 1°C, humidity: 30-50%), where minimal influence of humidity and temperature has been reported. 1We placed the PFOTS-coated substrates on an inclined grounded plate with a tilt angle of 50 • (unless otherwise noted).We neutralized any surface charge using an ionizing air blower (IAB, Simco-Ion Aerostat PC Ionizing air blower) for 2 minutes (air ion concentration to 300000 ions/cm 3 , measured with an Ionometer, IM806v3, 66687 Wadern, Germany), and waited some minutes until ions in the air dissipated and an equilibrium air ion concentration (200-400 ions/cm 3 ) was reached.Next, a peristaltic pump (Gilson Minipuls 3, Wisconson, USA) was used to pump deionized water (Sartorius Arium Pro VF, 18.2 MΩ resistivity, Germany, pH= 6.4 ± 0.3) into the grounded metallic syringe (diameter 2 mm), that produced water drops of volume 45 µL.As we showed in our previous work (Supplemental information in 2 ), the falling drops were neutral.It is well-known that DI water quickly dissolves CO 2 from the atmosphere, 3,4 leading to a pH of around 6. Dissolved CO 2 can introduce HCO - 3 ions in the drop in addition to OH -and

S1.2 Drop charge measurement
We chose a drop interval time of ∆t = 1.8 ± 0.2 s between drops for all experiments (unless otherwise noted).The drops fell from the height of (0.5 ± 0.2) cm and slid for (1.0 ± 0.2) cm to a grounding metal electrode, where they were neutralized to begin the slide electrification experiment.We choose a thin metal grounding wire so that the drop motion was not influenced.We have to follow this procedure because drops can already accumulate charges through the spreading and retraction of the drop on the surface during impact. 2The grounding electrode marked the starting point of the slide experiment (L = 0).Drop widths (w) and lengths (l) were measured using a calibrated telecentric high-speed camera.From previous studies of our group, it was found: for 45 µL drops: w = 5 mm, and l = 6.7 mm. 5 After getting neutralized at the grounding electrode, the drop then slid a known distance (accuracy of L ± 0.2 cm) to a gold plated metal probe electrode.A laser trigger system consisting of a 657 nm laser diode (CPS186, Thorlabs, United States) and a laser detector were placed 1 cm before the probe electrode and served as a trigger for data acquisition.

S1.3 Current and voltage measurement
When the charged droplet touched the probe electrode, the drops were either discharged via a a sub-femtoampere current amplifier (current measurement, FEMTO DLPCA-200 , Berlin, Germany; rise time: 0.7-1.8µs) or directly on a capacitor (voltage measurement).
We used a national instrument data acquisition board (NI USB-6366 x-Series) to record the current or voltage signal.The current measurement yielded signals as shown in figure S1b.
To calculate the accumulated drop charge over a chosen slide length, we integrated the initial peak of the measured current signal, which was within the first 0.5 ms (S1 b) of drop probe contact.
To measure the voltage of sliding drops, we connected a 1 nF capacitor in parallel with the input of the NI card.The input has a high input resistance of 100 GΩ and an input capacitance of 100 pF.Together with the cable, we measured a total capacitance of the system of 1.35 nF using an LCR meter and also using the discharge time and resistor (Fig. S2   d).An additional resistor with 400 MΩ ensures that the capacitors can discharge in between drops, while keeping the voltage stable during the drop contact.The schematic of the voltage probe is shown in figure S2

S1.4 Capacitance measurements
To measure the capacitance of the drop-surface system, we conducted an experiment where we charged up the capacitor externally using a potential, V , and measured the charge, Q, in the capacitor system.Using Q and V for 45 µL drop , we estimated an average C D =1.22 ± 0.02 pF and C D =0.47 ± 0.09 pF for 1 and 3 mm glass substrate respectively.Another way to estimate the capacitance is by using a plate capacitor approximation.We used the substrate dielectric ϵ r ≈ 7.0 for soda lime glass, drop base area (A = π•l•w 4 ), and the glass thickness d in the following equation which yields the approximated capacitance of our system ≈ 1.38 pF and 0.48 pF for 1 and 3 mm substrate, respectively.The slight deviation from the measurement should be caused by the difference between sessile and moving drops.We further want to state that the measurement of such a small capacitance is highly susceptible to error.Thus the good agreement of mesaurement and theoretical prediction confirms the parameter value.
As discussed in the main text, we use the same value for the static and the dynamic dropsubstrate capacitance.While effects of contact angle hysteresis can substantially change the shape of sliding drops, the wetted area stays approximately constant. 6Additionally, electrowetting effects might influence the drop capacitance at high drop potentials.For a similar setup of a sliding drop on a 1 mm substrate, Li and Ratschow et al. 7 reported a contact angle decrease due to electrowetting of around 10°.With an initial contact angle of 98°, this would increase the drop capacitance by by a maximum of 17%.
This analysis assumes no interaction between the effects of electrowetting and contact angle hysteresis.Such interactions could potentially deform the wetted area in a way that is not easily described theoretically.Due to this complexity and the low influence suggested by the good agreement of our measurements with reported values, we neglect changes in the drop capacitance.Both previous slide electrification models 5 and our new model fundamentally consist of a set of coupled differential equations for drop and surface charge.Based on these models, a set of analytical solutions for the first and steady-state drops can be derived. 5Due to the recursive nature of the equations

Figure
Figure S1: (a) Illustration of experimental setup, (b) current signal measured as the probe electrode discharges the sliding drop , (c) drop-surface contact time t c , and (d) drop charge estimated by integrating the initial peak of around 0.5 ms.
(a).The voltage in capacitor C D before the contact with the probe capacitor, with capacitance C in , is denoted as U D .The charge in C D is represented as Q.After the contact, the total charge equilibrates between the two parallel capacitors, and both attain the same voltage.The total charge in this situation is given by Q = C total U in = (C D + C in )U in .Solving this equation yields the voltage ratio: U D = C in +C D C D U in .From the measured voltage, we calculated the initial drop voltage using the ratio of two capacitance U D = C in +C D C D U in .Figure S2(b) shows the measured voltage curves.The high voltage measured with this technique is consistent with the voltage we estimated using the capacitance method.For the simple estimation of the capacitance (C D ) of subsequent drops, we used the the total charge (Q) measured using the transimpedance amplifier and drop voltage (U D ). Figure S2(c) shows that the capacitance for each drop is in accordance with the value we measured with capacitance method.

Figure
Figure S2: (a) Setup to measure the high drop voltage using capacitors in parallel.(b) Drop voltage measured for successive drops.(c) Capacitance estimated using the drop charge and drop voltage (C D = Q U D ).(d) Discharge time of the input capacitor via 400 MΩ resistor.

Figure S3 :
Figure S3: (a) Setup to measure the capacitance using the plate capacitor system.(b) Capacitive current caused by the 0-100V square potential.) Figure S5: Steady-state drop charge (Q) vs. drop interval (∆t), and fit an exponential fit to obtain decay time.