Gas-cushioned droplet impacts with a thin layer of porous media

Abstract

The pre-impact gas cushioning behaviour of a droplet approaching touchdown onto a thin layer of porous substrate is investigated. Although the model is applicable to droplet impacts with any porous substrate of limited height, a thin layer of porous medium is used as an idealized approximation of a regular array of pillars, which are frequently used to produced superhydrophobic and superhydrophilic textured surface. Bubble entrainment is predicted across a range of permeabilities and substrate heights, as a result of a gas pressure build-up in the viscous-gas squeeze film decelerating the droplet free-surface immediately below the centre of the droplet. For a droplet of water of radius 1 mm and impact approach speed 0.5 m s −1 the change from a flat rigid impermeable plate to a porous substrate of height 5 µm and permeability 2.5 µm 2 reduces the initial horizontal extent of the trapped air pocket by 48%, as the porous substrate provides additional pathways through which the gas can escape. Further increases in either the substrate permeability or substrate height can entirely eliminate the formation of a trapped gas pocket in the initial touchdown phase, with the droplet then initially hitting the top surface of the porous media at a single point.Droplet impacts with a porous substrate are qualitatively compared to droplet impacts with a rough impermeable surface, which provides a second approximation for a textured surface. This indicates that only small pillars can be successfully modelled by the porous media approximation. The effect of surface tension on gas-cushioned droplet impacts with porous substrates is also investigated. In contrast to the numerical predictions of a droplet free-surface above flat plate, when a porous substrate is included the droplet free-surface touches down in finite time. Mathematically this is due to the regularization of the parabolic degeneracy associated with the small gas-film-height limit the gas squeeze film equation, by non-zero substrate permeability and height, and physically suggests that the level of surface roughness is a critical parameter in determining the initial touchdown characteristics.

The air entrapment under a drop impacting on a nano-rough surface

“…2) is fairly invariant to the surface roughness studied herein with the air escaping in the gaps between the roughness asperities. This behavior fits well with the findings of van der Veen et al 37 and Hicks and Purvis, 38 who both observed that for impacts onto arrays of micropillars, the centerline height remained essentially unaffected by the presence of the micropillars. Interferometric measurements were not possible for the lowest and highest velocity impacts onto the 4 times coated surfaces.…”

“…Drop impacts onto regular micropillar arrays have been studied to better understand the macro-dynamics of bouncing, sticking and splashing, [27][28][29][30][31][32][33] the heat transfer characteristics, 34,35 and how the micropillars affect the formation of the central dimple as the droplet approaches the surface. [36][37][38] Tsai et al 36 looked at impacts onto micropillars and noted that a central bubble was entrapped and the droplet penetrated the micropillars to fully wet the surface in the region around the central bubble for high Weber numbers. Van der Veen et al 37 varied the height, width and spacing of the micropillars and concluded that the height of the micropillars has little effect on the height and radius of the entrapped air disc, but as the packing density of the pillars increases, the height of the dimple with respect to the bottom of the pillars increases as well.…”

“…This is mainly due to the potentially trapped air not being able to easily escape between the pillars. Similarly, Hicks and Purvis 38 theoretically studied inviscid drop impacts onto porous surfaces using micropillar arrays as an analog for the porous surface. They reported that as the substrate permeability increased, the radial extent and disc height were decreased.…”

LNG-solid impacts with gas cushioning and phase change

“…For Γ = 0, the normal stress balance (22) implies the liquid and gas pressure are equal across the interface, and hence the free-surface position and gas pressure are additionally coupled using equation (21). The evolution of this coupled system of equations, from an initial free-surface profile of f (x, t) = − 1 2 x 2 − t and gas pressure of p g (x, t) = 0 at large negative times, is computed numerically using the method outlined in Hicks & Purvis [21]. Throughout the impact f (x, t) ∼ − 1 2 x 2 − t and p g (x, t) → 0 as |x| → 0.…”

Preface to the sixth special issue on “Practical Asymptotics”

“…The cost of computational studies may prohibit numerical simulations at a number of parameter values which limits, for example, the optimization of prototypes. There still exists a number of practical problems which are tractable for approximate analytical methods but inaccessible to computation.The special issue invites research articles addressing the following problems: drag coefficients in low Reynolds number flow [6], ice formation on a cold surface due to the impact of a supercooled water droplet [7], droplet impacts with a porous medium [8], the propagation of fronts in a discrete reaction-diffusion equation [9], fluidsolid interactions [10] and geothermal heat exchangers [11]. The analyses comprise a range of perturbation methods, including a hybrid asymptotic-numerical method, matched asymptotic expansion and WKBJ methods, all of which demonstrate the importance of asymptotics in real-world applications.…”