Stable Liquid Jets Bouncing off Soft Gels

A liquid jet can stably bounce off a sufficiently soft gel by following the contour of the dimple created upon impact. This new phenomenon is insensitive to the wetting properties of the gels and was observed for different liquids over a wide range of surface tensions, $\gamma =24-72\mathrm{mN}/\mathrm{m}$. In contrast, other jet rebound phenomena are typically sensitive to $\gamma$: only a high $\gamma$ jet rebounds off a hard solid (e.g. superhydrophobic surface) and only a low $\gamma$ jet bounces off a liquid bath. This is because an air layer must be stabilized between the two interfaces. For a soft gel, no air layer is necessary and the jet rebound remains stable even when there is direct liquid-gel contact.

Figure 1

(a) A water jet can bounce off a hydrophilic gelatin gel that is 98.5 wt% water. The inset shows the resulting contact angle of 16° for a $10\mu \mathrm{L}$ water droplet. (b) A soft PDMS gel ($E=1.2\mathrm{kPa}$) can repel both water and soap-water, while a superhydrophobic (SH) surface loses its liquid repellence for soap-water. The corresponding contact angles of $10\mu \mathrm{L}$ water or soap-water droplets shown in the insets are (left to right, top to bottom): 90°, 30°, 150°, and 60°. The SH surface was a hexagonal array of a micropores monolayer of size $\sim 1\mu \mathrm{m}$, with static contact angle for water $\theta =150°$, and contact angle hysteresis $\mathrm{\Delta }\theta =10°$. Detailed methods to fabricate the SH surface and PDMS gels used in this study are described elsewhere [21, 22].

Figure 2

The pressure of the impacting jet creates a dimple of depth $h$ and width $w$ on the PDMS gel, facilitating the jet rebound. Inset I shows the side view of the dimple, inset II shows the eventual breakup of the jet into droplets, while inset III shows the three-phase contact line of an exiting EtOH jet. Note that inset I was taken at a different focal plane from the jet above it, because the refractive index of the PDMS gel/silicone oil introduced an additional optical path length.

Figure 3

(a) An optical fiber with clad diameter of 0.1 mm (inset I shown on the right) was placed coaxial with the needle to couple laser light into the liquid jet. (b) Laser light (red) followed the contour of the silicone oil jet as it bounced off a silicone oil bath, because of a stable air layer that separated the two. (c) In contrast, there was no air layer separating the water jet bouncing off a PDMS gel. Hence, the laser light passed through undeflected into the PDMS gel. A small amount of alumina particles and milk (0.05 wt% and 0.01 wt%, respectively) were added to silicone oil and water jets to act as light scatterers so that the laser path inside the jet could be visualized, with insignificant change to the surface tension (measured $\mathrm{\Delta }\gamma <0.2\mathrm{mN}/\mathrm{m}$).

Figure 4

(a) Dimple width $w$ plotted against $2h\tan {\theta }_i$, where $h$ is the dimple depth and ${\theta }_i$ is the incident angle for liquid jets (diameter $D=0.29–1.1\mathrm{mm}$) impacting PDMS gels (Young’s moduli $E=0.6–1.5\mathrm{kPa}$) at flow rates $Q=5-250\mathrm{ml}/\min$. The liquid used was water, except for the data points labeled with green diamonds, which were obtained for 30 wt% ethanol (surface tension $\gamma =35\mathrm{mN}/\mathrm{m}$). (b) $h$ increases with increasing flow rate $Q$, albeit at different rates depending on exact experimental conditions. (c) The results in (b) can be collapsed into one curve, when $h/D$ is plotted against $\rho U_{\perp }^2/E$, where $\rho$ is the density of the liquid and $U_{\perp }$ is the perpendicular component of the jet speed, i.e., $U\cos {\theta }_i$. (d) The rebound angle ${\theta }_r$ for a fixed ${\theta }_i$ is a function of the ratio $h/D$. The transition from a bouncing jet (inset I) to a trailing jet (inset II) occurred at around $h/D=1.4$.