Drop race: How electrostatic forces influence drop motion

Abstract

Water drops sliding down inclined planes are an everyday phenomenon and are important in many technical applications. Previous understanding is that the motion is mainly dictated by viscous and capillary forces. Here we demonstrate that, in addition to these forces, drops on hydrophobic surfaces are affected by self-generated electrostatic forces. In a novel approach to determine forces on moving drops we imaged their trajectory when sliding down a tilted surface and apply the equation of motion. We found that drop motion on low-permittivity substrates is significantly influenced by electrostatic forces. Sliding drops deposit a negative charge on the surface, which interact with the positively charged drops. We derive an analytical model to describe the force and validate it by numerical computations. The results indicate how to describe and facilitate drop motion in applications, such as in microfluidics, water management on car surfaces, and the creation of sliding drop electrical generators.

Tuning the Charge of Sliding Water Drops

“…The high permittivity of silicon substrates reduces electrostatic forces, thus eliminating the influence of charging. 26 The surface preparation was identical to that on glass. One thousand drops (33 μL) were then deposited (Δ t = 2 s) on the functionalized silicon substrates at a tilt angle of 50° (i.e., charge measurement conditions).…”

“…To this end, a silicon substrate was employed (Figures d and S3). The high permittivity of silicon substrates reduces electrostatic forces, thus eliminating the influence of charging . The surface preparation was identical to that on glass.…”

Adaptive two capacitor model to describe slide electrification in moving water drops

“…Using this contact time, we fit eq (9) to the saturated drop voltage as a function of ∆t, and obtained the A2C model parameters as follows: U d = 6.6 ± 0.3 V and U w ≈ 0.9 ± 0.2 V; t w = 0.11 ± 0.01 s and t d = 152 ± 13 s. Using these parameters and equation above 9, we calculated U cl (n) and simulated the drop charge versus drop number and slide length. Deviations from the model could be explained by variations in the drop contact time coming from slight changes in drop path or variations in velocity, either caused because the drop not yet reaching terminal velocity, or by electrostatic forces between the drop and surface charges [40]. Furthermore, the observed behavior might be caused by more complex adaptation processes involving several time scales or an additional adaptation in one of the other parameters.…”

Polarity-Induced Reactive Wetting: Spreading and Retracting Sessile Water Drops

“…However, careful observation into the initial dynamics of drop contact provides further information. On macroscopically flat nonpolar hydrophobic bilayer surfaces (Figure a,c, purple data, PFOTS–PDMS), we see a rapid alignment between the initial and final contact angle, measured at t contact = 0.02 or 60 s at 115°, respectively, well within the hysteresis range , of typical PFOTS-functionalized surfaces (Figure S9). Fluctuations in measured contact angles (Figure c, purple data, PFOTS–PDMS) exist due to the drop vibration after detachment.…”