Slide electrification of drops at low velocities

Slide electrification of drops is mostly investigated on tilted plate setups. Hence, the drop charging at low sliding velocity remains unclear. We overcome the limitations by developing an electro drop friction force instrument (eDoFFI). Using eDoFFI, we investigate slide electrification at the onset of drop sliding and at low sliding velocities ≤ 1 cm s−1. The novelty of eDoFFI is the simultaneous measurements of the drop discharging current and the friction force acting on the drop. The eDoFFI tool facilitates control on drop length and width using differently shaped rings. Hereby, slide electrification experiments with the defined drop length-to-width ratios >1 and <1 are realized. We find that width of the drop is the main geometrical parameter which determines drop discharging current and charge separation. We combine Kawasaki–Furmidge friction force equation with our finding on drop discharging current. This combination facilitates the direct measurement of surface charge density (σ) deposited behind the drop. We calculate σ ≈ 45 μC m−2 on Trichloro(1H,1H,2H,2H-perfluorooctyl)silane (PFOTS) and ≈20 μC m−2 on Trichloro(octyl)silane (OTS) coated glass surfaces. We find that the charge separation by moving drops is independent of sliding velocity ≤ 1 cm s−1. The reverse sliding of drop along the same scanline facilitates calculation of the surface neutralization time constant. The eDoFFI links two scientific communities: one which focuses on the friction forces and one which focuses on the slide electrification of drops.

1. Advancing and receding contact line velocity.In the main section, pertaining to Figure 1, we record a current signal only when the receding contact line starts moving.We measured a current signal after approx.0.3 seconds from the Electronic Supplementary Material (ESI) for Soft Matter.This journal is © The Royal Society of Chemistry 2024 start of advancing contact line motion.Figure S1 show velocities for the advancing and receding contact line at the onsets and during drop sliding along all three passes.For a 7 µL drop advancing contact line displaces first and receding contact line moves with a delay of approx.0.3 seconds.The maxima in friction force and discharging current is observed when the velocity of advancing and receding contact lines are equal to the stage velocity of 2 mm/s.After that, the drop foot print rearranges to a definite shape.This rearrangement results in a decrease in friction force and indicates a transition regime.Then a constant shape of the drop with a constant foot print is reached which results in a constant current and friction signal.The contact line velocity data was smoothened by 5 points moving average for the better visualization.
2. Force and contact line velocities for each pass.iii We plot the friction force and contact line velocities for all 3 independent drop motions (Fig S2 a,b,c).We find that the drop friction reaches maxima when the advancing and receding contact line velocity of the drop becomes equal.
3. Individual current profile.In the main text, we find that the drop discharging current is proportional to width rather than drop length or the receding contact line length.It seems confusing that the charges separate at the receding contact line but it scales with drop width.We anticipate that the azimuthal contact   The benefit of using a side ring is that it helps us to control the drop shape.However, the attachment of the ring on the side creates an additional moment on the capillary.To measure friction force, the deflection of the sensor while the drop is sliding is measured from the vii reference image.We take the reference image when no drop is attached to the rinig (Fig S6a).
When a 160 µL drop is attached to the ring which results in a lengthier drop, it results in bending of the capillary, δ 1 (Fig S6b).The δ 1 = 1 mm and corresponding spring constant of the capillary is 553 ± 12.5 µN/mm.This results in the force offset of ≈ 600 µN.The bending is caused by the surface tension forces acting on the ring.The net surface tension force on the ring acts at an offset from the fixed capillary axis.This offset creates an additional moment on the capillary axis.The moment results in bending which is opposite to the capillary deflection in the forward drop sliding, and it favors the deflection during reverse drop sliding.Similarly, δ 2 deflection is measured for the ring which results in wider drops (Fig S6d).The spring constant for the capillary having ring resulting in wider drops is 500 ± 11 µN/mm.Hence, we estimate a force offset of 90 µN.
7. Friction force on sliding drops with ring capillaries.The actual value of friction force is altered due the presence of the additional moment (section S6).For the ring which results in lengthier drop, the presence of ring creates a force offset of 600 µN (spring constant 1 × δ 1 ).And for the ring which results in wider drops, we estimate a force offset of 90 µN (spring constant 2 × δ 2 ).To mitigate the effect of this additional moment viii on our actual force measurements, we consider rings with the drop as a reference images.For instance, the image shown in figure S6b is taken as a reference image for force measurements for drop sliding with the ring resulting in lengthier drops.Similarly, the image shown in figure S6d is taken as the reference image for the force measurements for the drop sliding with the rings which results in wider drops.For forward motion using ring resulting in lengthier and wider drops, we measure force of around 810 µN and 300 µN respectively on a 160 µL drop (Fig S7a).During reverse sliding, we measure force magnitude of 170 µN and 600 µN for rings resulting in lengthier drops and wider drops respectively (Fig S7b).Laroche et al., reported that by preshaping a sessile drop in a way such that the length to width ratio increases, the static drop friction can be reduced 2 .Our observation is similar to the observation made by the authors.
We observe a reduction in static friction force from 800 µN to 300 µN by increasing the drop length to width ratio (Fig S7a)    The figure S9 shows the key components of eDoFFI.First, we shield the capillary by wrapping two layers of aluminium foil.This aluminium foil is connected to the ground by amplifier casing.To further shield current measurements from ambient electromagnetic disturbances, we wrap two layers of aluminium foil in the space between amplifier top and XY stage (not shown in the image).This foil acts as a faraday cage and is connected to the building ground. x

Figure S1 .
Figure S1.The advancing and receding contact line velocities for a 7 µL drop sliding at 2 mm/s speed over the distance of 40 mm.The surface is PFOTS on glass.a) The advancing and receding contact line velocities for a drop (pass 1) over a sliding distance of 40 mm.b) The velocities for 2 nd drop (pass 2) c) The velocities for the 3 rd drop (pass 3).The insets show the onsets of sliding for drops, respectively.

Figure S2 .
Figure S2.The friction force (blue & right y-axis), advancing (black) and receding (orange) contact line velocity (left y-axis) for each drop motion.The data corresponds to a 7 µL milli-Q water drop sliding at 2 mm/s speed on a PFOTS coated glass surface.(a) The force and contact line velocities data corresponding to the 1 st drop (pass 1).(b) The force and contact line velocity data for the 2 nd drop (pass 2).(c) The force and contact line velocity data for the 3 rd drop (pass 3).

Figure S3 .
Figure S3.The drop discharging current signals at the onset of drop sliding for 7 µL water drops sliding at 2 mm/s.(a) The discharging current signal at the onset of drop sliding for the 1 st drop (pass 1).(b) The discharging current signal at the onset of 2 nd drop sliding (pass 2).(c)The discharging current signal at the onset of 3 rd drop sliding (pass 3).

Figure
Figure S4.(a) A sketch depicting a possible distribution of negative charges (green) at the receding contact line of the drop in a top view.The sketched drop foot print resembles to the actual drop foot print when a drop slides on eDoFFI setup.(b) The aniciptaed surface charge density along the receding contact line of the drop.
angle distribution possibly leads to a variation in the surface charge density along the receding contact line length (Fig S4) 1 .v 5. Discharging current during forward and reverse sliding.

Figure S5 .
Figure S5.The discharging current signal for a 160 µL drop sliding over the distance of 40 mm on a PFOTS coated glass surface at a velocity of 2 mm/s.The current signal for (a) forward sliding with the elliptical ring which results in a larger drop length or length to width ratio of more than 1.(b) The current signal during the reverse sliding of the same drop along the respective scanline.The current signal during (c) forward sliding, and (d) reverse sliding for drops sliding with elliptical ring which results in wider drops or drop length to width ratio of less than 1.The measurements are performed on 3 independent drops using respective ring configurations.The signal is obtained at the amplification factor of 10 9 filtered with 30Hz low pass filter.

Figure S6 .
Figure S6.The images show additional torque acting on the capillary due to side attachment of the rings.The scale bars are 5 mm.(a) The reference image or no deflection image for the elliptical ring which results in lengthier drop.(b) Idle image when a 160 µL drop is attached to the ring.δ 1 is the deflection due to surface tension force on the ring.(c) Reference image for the capillary with the ring which results in wider drops.(d) Idle image when a drop of 160 µL volume is attached to the ring.δ 2 is the deflection caused by the surface tension force on the ring.

Figure S7 .
Figure S7.The friction force on a 160 µL drop displaced at 2 mm/s on a PFOTS/glass surface with both the elliptical ring capillaries.(a) The force on the drops during forward sliding.The blue data points are the forces on the drop sliding with ring which results in drop length to width ratio of less than 1.And the red data points are forces on the drops having drop length to width ratio of more than 1.(b) The force on the drops during reverse sliding.For these friction force measurements, the reference or no deflection image is when the drop is attached to the capillary (Fig S6b,d). .
8. Calculation of surface neutralization time constant.

Figure S8 .
Figure S8.To calculate the time constant for the surface neutralization, we first calculate the time required by the drop to complete the drop motion along a scanline.

Figure S9 .
Figure S9.The experimental setup (eDoFFI) used for friction force and discharging current measurements.