Rebound of large jets from superhydrophobic surfaces in low gravity

We experimentally investigate the phenomena of large liquid jet rebound, a mode of fluid transfer following oblique jet impacts on superhydrophobic substrates. We initially seek to describe the jet rebound regimes in tests conducted in the weightless environment of a drop tower. A parametric study reveals the dependence of the flow structure on the relevant dimensionless groups such as Reynolds number and Weber number defined on the velocity component perpendicular to the substrate. We show that significantly larger diameter jets behave similarly as much smaller jets demonstrated during previous terrestrial investigations in some parameter ranges while the flow is fundamentally different in others. Level-set numerical predictions are provided for comparisons where practicable. Simple models are developed predicting landing geometry and the onset of instability that are found to yield good agreement with experiments and simulations. Improving our understanding of such jet rebound opens avenues for unique transport capabilities.

Figure 1

Schematic of oblique jet impact with landing flow and rebound from a hydrophobic substrate: (a) top view, (b) profile view, and (c) cross-sectional view of the landing flow at the point of maximum width $w$ with bounding rims identified by radius $r$.

Figure 2

Time-averaged images from drop tower tests of landing flows with the predicted convergence angle $\beta$ overlaid. Tests: (a) ${\varphi }_i=15.1^{\circ }$, ${\mathrm{We}}_{\perp }=1.50$ (D1), (b) ${\varphi }_i=18.3^{\circ }$, ${\mathrm{We}}_{\perp }=10.05$ (D3), and (c) ${\varphi }_i=33.5^{\circ }$, ${\mathrm{We}}_{\perp }=37.12$ (D4). The blurred landing flow boundary in (c) is the result of droplets leaving the landing flow rim.

Figure 3

Photograph of the Dryden Drop Tower at Portland State University.

Figure 4

Partial cutaway view of drop tower experiment rig with critical items identified.

Figure 5

Numerical convergence study for the shape of the landing area for various grid resolutions. The numerical results shown are obtained for dimensionless meshes of different resolutions: $d_j/\mathrm{\Delta }=4.8$ (black), 9.6 (blue), and 19.2 (red).

Figure 6

Top view still images taken from drop tower test footage of oblique impacts of a water jet with a superhydrophobic ($\theta ={158}^{\circ }$) substrate in a nearly weightless environment. Regimes include (a) stable, ${\varphi }_i=15.1^{\circ }$, ${\mathrm{We}}_{\perp }=1.50$ (D1), (b) unstable, ${\varphi }_i=18.3^{\circ }$, ${\mathrm{We}}_{\perp }=10.05$ (D3), and (c) fishbone, ${\varphi }_i=33.5^{\circ }$, ${\mathrm{We}}_{\perp }=37.12$ (D4). Light dashed lines indicate the location where the jet leaves the substrate. Dark dashed lines outline the stable rebounded jet profile which does not change with time. Scale bar is $1\mathrm{cm}$.

Figure 7

Regime map illustrating the observed dependence of flow structures emerging from the oblique impact of a rebounding jet from a superhydrophobic substrate. Marker size is proportional to the diameter of the jet, and black bold markers represent numerical simulations. The horizontal line at $\mathrm{Re}=3000$ marks the approximate transition to turbulent flow for the incident jet, and the vertical line at ${\mathrm{We}}_{\perp }=17.5$ marks the predicted onset of splashing behavior [Eq. (12) with $C_1=1/2$; the fit coefficient $C_1=1/2$ is justified by Fig. 9]. The shaded region represents the extent of Celestini et al. [6].

Figure 8

Still images of a tangent jet taken from drop tower test footage in (a) 1-g before the drop and (b) low-g following the drop package release. In 1-g the jet attaches to the substrate and advances as a rivulet (dashed line). In low-g the growing varicose perturbations deflect the jet away from the substrate (dashed curved segments). The downstream jet in (b) is not in contact with the substrate.

Figure 9

Normalized landing flow width $w/d_j$ as a function of ${\mathrm{We}}_{\perp }$. Gray line indicates a maximum normalized landing flow width of $w/d_j\sim 2$ for stable rebounds. Marker size is proportional to $d_j$, and black bold markers represent simulations.

Figure 10

(a) Top and profile views of time-averaged composite image and (b) sketch of the landing region for the double rivulet jet collision regime (D5). The landing flow film splits producing a third “terminal rim.” The two edge rivulets rebound from the substrate at the point of intersection with the terminal rim only to collide and coalesce downstream forming a single rebounding jet. The triangular void in the flow observed from above is outlined with a dashed line in (a).

Figure 11

Still images taken from drop tower test footage of a normal jet impingement in 1-g (a) before the drop and low-g (b) after the drop package release. In 1-g the fluid leaving the downstream edge of the landing flow feeds a puddle of height $\sim 2l_c$. In low-g a low Weber number “jet” is formed which may exhibit dripping behavior, emitting large droplets, and producing a large attached blob. Large attached blob (a) and incoming jet (b) are outlined with a dashed black line.

Figure 12

Profile and top view comparisons of numerics with drop tower tests for $d_j=6$ mm jet. Comparisons include (a) stable, ${\varphi }_i=15.1^{\circ }$, ${\mathrm{We}}_{\perp }=1.50$ (D1), (b) unstable, ${\varphi }_i=18.3^{\circ }$, ${\mathrm{We}}_{\perp }=10.05$ (D3), and (c) fishbone, ${\varphi }_i=33.5^{\circ }$, ${\mathrm{We}}_{\perp }=37.12$ (D4).

Figure 13

Images from drop tower tests showing the impact of a liquid jet with a concave superhydrophobic substrate. The jet velocity increases from left to right increasing the intact length of the rivulet. The curvature of the substrate suppresses the rebound of the jet. Dashed lines show the rivulet intact length.