Wind- and gravity-forced drop depinning

Liquid drops adhere to solid surfaces due to surface tension but can depin and run back along the surface due to wind or gravity forcing. This work develops a simple mechanistic model for depinning by combined gravity and high-Reynolds-number wind forcing and tests that model using water drops on a roughened aluminum surface. On noninclined surfaces, drops depin at a constant critical Weber number ${\text{We}}_{\mathrm{crit}}=7.9$ for the present wettability conditions. On inclined surfaces, ${\text{We}}_{\mathrm{crit}}$ decreases linearly with the product of the Bond number and the width-to-height aspect ratio of the unforced drop. The linear slope is different in distinct wind- and gravity-dominated forcing regimes above and below ${\text{We}}_{\mathrm{crit}}=4$. Contact-line shapes and drop profile shapes are measured at depinning conditions but do not adequately explain the differences between the two forcing regimes.

Figure 1

Wind tunnel and experimental rig for drop stability experiments.

Figure 2

Boundary velocity and turbulence intensity profiles.

Figure 3

Initial drop-dimension measurements.

Figure 4

Critical run-back velocity $U_{\mathrm{crit}}$ as a function of drop volume $V$. The vertical gray line is at $V=175\mu \mathrm{L}$, the boundary between the low- and high-Bond-number regimes.

Figure 5

Critical run-back angle for gravity-forced drops $U=0$. The vertical gray line is at $V=175\mu \mathrm{L}$, the boundary between the low- and high-Bond-number regimes.

Figure 6

Critical Weber number as a function of drop aspect ratio times Bond number.

Figure 7

Mean and standard deviation of drop contact lines for initial drop placements and final subcritical drop measurements. Contact lines are shown for (a) wind-forced drops and (b) gravity-only drops. Solid curves are mean contact-line locations. Shaded areas indicate one standard deviation.

Figure 8

Final subcritical drop profiles for each surface inclination angle. Mean profiles for drops that depin in the wind-dominated forcing regime are shown with solid lines; drops that depin due to gravity-dominated forcing are shown with dashed lines. Shaded areas indicate one standard deviation.