On jet impingement and thin film breakup on a horizontal superhydrophobic surface

Abstract

When a vertical laminar jet impinges on a horizontal surface, it will spread out in a thin film. If the surface is hydrophobic and a downstream depth is not maintained, the film will radially expand until it breaks up into filaments or droplets. We present the first analysis and model that describes the location of this transition for both isotropic and anisotropic structured superhydrophobic (SH) surfaces. All surfaces explored are hydrophobic or SH, where the SH surfaces exhibit an apparent slip at the plane of the surface due to a shear free condition above the air filled cavities between the structures. The influence of apparent slip on the entire flow field is significant and yields behavior that deviates notably from classical behavior for a smooth hydrophilic surface where a hydraulic jump would form. Instead, break up into droplets occurs where the jet’s outward radial momentum is balanced by the inward surface tension force of the advancing film. For hydrophobic surfaces, or SH surfaces with random micropatterning, the apparent slip on the surface is uniform in all directions and droplet breakup occurs in a circular pattern. When alternating rib/cavity microstructures are used to create the SH surface, the apparent slip varies as a function of the azimuthal coordinate, and thus, the breakup location is elliptically shaped. The thin film dynamics are modeled by a radial momentum analysis for a given jet Weber number and specified slip length and the location of breakup for multiple surfaces over a range of jet Weber numbers and realistic slip length values is quantified. The results of the analysis show that the breakup radius increases with increasing Weber number and slip length. The eccentricity of the breakup ellipse for the rib/cavity SH structures increases with increasing Weber number and slip length as well. A generalized model that allows prediction of the transition (break-up) location as a function of all influencing parameters is presented. Model results are compared to experimental measurements with very good agreement.

Orthogonal liquid-jet impingement on wettability-patterned impermeable substrates

“…Unlike a circular hydraulic jump, the liquid thin film breaks up into droplets that are ejected randomly from the rim due to their high momentum. This phenomenon has also been observed by other researchers [17,40] while studying jet impingement on superhydrophobic surfaces.…”

“…Predicting the slip velocity requires estimation of the slip length at the surface, as discussed in Refs. [40,46]. A previous study by Joseph et al [68] suggested that the effective slip length [44], b ef f , is related to the lateral length scale between the surface structures, L, through b ef f = αL, where α 0.28 leads to the best fitting of the experimental results.…”

“…The analysis and modeling of the radially-expanding thin film on the surface follows the work of Prince et al [40] closely and is briefly summarized here. We consider a vertical liquid jet of speed V , with a volumetric flow rate Q, kinematic viscosity ν, and radius a impinging on a superhydrophobic horizontal surface, as illustrated in Fig.…”

“…A radial momentum balance at the location of breakup is governed by the equilibrium between the momentum flux of the spreading thin film and the pressure jump at its edge. Here, the momentum flux of the droplets leaving the film is neglected, which has been shown to be a good approximation [40]. Substituting ∆P from Eq.…”

“…A downstream depth cannot be maintained on a superhydrophobic surface unless it is forced. Hence, the radially expanding thin film becomes unstable after some distance and breaks up into filaments or droplets [40]. Those droplets do not adhere to the surface; instead, they are rapidly ejected due to their outward momentum, resulting in a significant loss of liquid.…”