Orthogonal liquid-jet impingement on wettability-patterned impermeable substrates

Liquid-jet impingement on flat impermeable substrates is important for a multitude of applications ranging from electronic-equipment cooling to fuel atomization and erosion of solid surfaces. On a wettable horizontal surface, where a sufficient downstream liquid depth can be sustained after axisymmetric impingement, the jet forms a thin film on the substrate up to a radial distance where the film height suddenly increases, forming a hydraulic jump. On a superhydrophobic surface, where a downstream liquid depth is not naturally sustained, the thin film expands and breaks up into droplets, which are subsequently ejected in a random fashion outward, as carried by their radial momentum. In the present work, a facile, scalable, wettability-patterning approach is presented for delaying or even eliminating droplet breakup in the case of jet impingement on horizontal superhydrophobic surfaces. Analytical expressions for predicting the hydraulic jump and droplet breakup locations are developed to designate the proper wettability patterns that facilitate alteration and control of the postimpingement liquid behavior. The axisymmetric model is extended to evaluate the radial variation of the competing forces responsible for film breakup, and a design criterion for the effective wettability patterns is proposed.

Figure 1

Schematic of sample preparation procedure. (a) Aluminum plates were immersed in $5M$ HCl solution for 4 min. (b) Scanning electron micrograph of the acid-etched sample. (c) Acid-etched samples were passivated in boiling deionized water for 60 min. (d) Scanning electron micrograph of the etched-and-boiled sample. (e) Etched-and-boiled samples were then treated in an ethanolic solution of FAS and kept undisturbed for 8–10 h. (f) The CAD-based design was patterned onto the substrate by laser ablation. (g) The final sample featured superhydrophobic and superhydrophilic domains. (h) Sessile water droplet on the superhydrophobic domain exhibiting a contact angle of ${150}^{\circ }\pm 5^{\circ }$ (scale bar denotes 1 mm).

Figure 2

Schematic of the experimental setup.

Figure 3

Evolution of wettability pattern design (A–C) and corresponding experimental snapshots (at 800 mL/min, right column). (a i) Design A and (a ii) image of jet impingement on a substrate with design A exhibiting film breakup into droplets at radius $R_b\simeq 19$ mm. (b i) Design B and (b ii) image of jet impingement on substrate with design B and $R=16\mathrm{mm}$. A circular hydraulic jump forms at jump radius $R_j\simeq 18$ mm, thus eliminating film breakup into droplets. (c i) Design C and (c ii) image of jet impingement on substrate with $R_i=16\mathrm{mm}$ and $R_o=22\mathrm{mm}$. The film breakup, which occurs at $R_o$, is more orderly than that shown in (a ii). The red $\mathsf{X}$ marks the spot of orthogonal jet impact on all three wettability patterns. The relative positions of $R_b$ [see (a ii)] and $R_j$ [see (b ii)] have also been marked by dashed arrows in (c i).

Figure 4

Schematic illustrating an axisymmetric liquid-jet impingement event on (a) a uniformly hydrophilic surface, forming a hydraulic jump, and (b) a uniformly superhydrophobic surface, resulting in film breakup into droplets.

Figure 5

Radial variation (in the vicinity of the annulus with $R_i=16\mathrm{mm}$ and $R_o=22\mathrm{mm}$) of driving momentum ($\rho \frac{17}{35}{U}^{2}h$) and resistive capillary forces ($\sigma [1+cos(\pi -\varphi \left)\right]$) per unit length at the curved advancing film front for a jet flow rate of 800 mL/min. The blue dashed line ($ABX$) represents the radial variation of momentum force per unit length for a completely superhydrophobic surface, while the blue solid line ($ABYCD$) represents the radial variation of momentum force per unit length when the superhydrophilic annulus is present. The red line (both solid and dashed parts) denotes the maximum value of the resistive capillary force per unit length on the superhydrophobic domain (calculated for $\varphi ={150}^{\circ }$), while the solid green line denotes the same on the superhydrophilic domain ($\varphi =5^{\circ }$). Here $X$ denotes the radial location where the momentum and capillary forces balance, indicating the onset of film breakup on a superhydrophobic surface; $Y$ denotes the location of the hydraulic jump on a superhydrophobic surface with a superhydrophilic annulus. The dashed magenta line (running parallel to the line $ABYX$) represents the radial variation of the momentum force for a flow rate of 1000 mL/min; film breakup is observed at $X_H$ ($\simeq 23$ mm), which exceeds $R_o$. The dashed cyan line, on the other hand, shows the radial variation of momentum for a 600-mL/min jet and the point $X_L$ ($\simeq 15$ mm) denotes the location of film breakup for that flow rate on the superhydrophobic surface; $X_L$ is radially located inside $R_i$. The dashed green line represents the capillary force on a slightly hydrophilic surface ($\varphi ={70}^{\circ }$); the point $X_P$ (at radial distance less than $R_o$) denotes where breakup would be observed for a similar annulus with $\varphi ={70}^{\circ }$ and a jet flow rate of 800 mL/min.

Figure 6

Variation of $(R_b-R_j)/R_j$ with We for five different values of $\varphi$ ranging from ${90}^{\circ }$ to ${170}^{\circ }$; $\varphi$ represents the contact angle on the nonwettable domain. The quantity along the abscissa (We) represents the jet flow rate, while the ratio on the ordinate scales the limiting dimensions of the superhydrophilic annulus of pattern C [Fig. 3(c i)]. The conditions for the experimentally-observed data points are ($A$) $Q=800\mathrm{mL}/\min$, $a=1\mathrm{mm}$, and $\varphi ={150}^{\circ }$; ($B$) $Q=1000\mathrm{mL}/\min$, $a=1\mathrm{mm}$, and $\varphi ={150}^{\circ }$; and ($C$) $Q=1200\mathrm{mL}/\min$, $a=0.9\mathrm{mm}$, and $\varphi ={150}^{\circ }$. All the points lie along a single curve, which can facilitate design decisions for any jet-flow-rate/contact-angle combination.