Maurice H. W. Hendrix

A tiny air bubble can be entrapped at the bottom of a solid sphere that impacts onto a liquid pool. The bubble forms due to the deformation of the liquid surface by a local pressure buildup inside the surrounding gas, as also observed during the impact of a liquid drop on a solid wall. Here, we perform a perturbation analysis to quantitatively predict the initial deformations of the free surface of a liquid pool as it is approached by a solid sphere. We study the natural limits where the gas can be treated as a viscous fluid (Stokes flow) or as an inviscid fluid (potential flow). For both cases we derive the spatiotemporal evolution of the pool surface, and recover some of the recently proposed scaling laws for bubble entrapment. On inserting typical experimental values for the impact parameters, we find that the bubble volume is mainly determined by the effect of gas viscosity.

A force balance model has been developed to predict the terminal velocity of a sub-millimetric bubble as its rises in water under buoyancy. The dynamics of repeated collisions and rebounds of the bubble against a horizontal solid surface is modeled quantitatively by including forces due to buoyancy, added mass, drag, and hydrodynamic lubrication—the last arises from the drainage of water trapped in the thin film between the solid surface and the surface of the deformable bubble. The result is a self-contained, parameter-free model that is capable of giving quantitative agreement with measured trajectories and observed collisions and rebounds against a solid surface as well as the spatio-temporal evolution of the thin film during collision as measured by interferometry.

When a drop impacts a surface, a dimple can be formed due to the increased air pressure beneath the drop before it wets the surface. We employ a high-speed color interferometry technique to measure the evolution of the air layer profiles under millimeter-sized drops impacting hydrophobic micropatterned surfaces for impact velocities of typically 0.4 m s⁻¹. We account for the impact phenomena and show the influence of the micropillar spacing and height on the air layer profiles. A decrease in pillar spacing increases the height of the air dimple below the impacting drop. Before complete wetting, when the impacting drop only wets the top of the pillars, the air–droplet interface deforms in between the pillars. For large pillar heights the deformation is larger, but the dimple height is hardly influenced.

Nanoscale interfaces among liquids, solids and gases determine the macroscopic dynamics of a bubble (e.g. the terminal rise velocity and bouncing behavior). Here high-speed interferograms of liquid films created from rising and bouncing bubbles are compared against mobile and immobile interface models. Quantitative agreement of the thin film dynamics with lubrication theory is obtained. Bubbles in deionized water display mobile and immobile dynamics behavior: bubble–surface interactions suggest a mobile interface but its rise velocity is reduced by the immobile bubble interface at the rear.

Collisions between millimeter-size bubbles in water against a glass plate are studied using high-speed video. Bubble trajectory and shape are tracked simultaneously with laser interferometry between the glass and bubble surfaces that monitors spatial-temporal evolution of the trapped water film. Initial bubble bounces and the final attachment of the bubble to the surface have been quantified. While the global Reynolds number is large ($\sim${}102), the film Reynolds number remains small and permits analysis with lubrication theory with tangentially immobile boundary condition at the air-water interface. Accurate predictions of dimple formation and subsequent film drainage are obtained.

The dynamics of water drop impact at high impinging velocity onto superhydrophobic substrates is experimentally investigated. The solid substrate—comprised of regular and hydrophobic micropillars—is transparent, thereby facilitating close-up, top-or-bottom-view, high-speed imaging. With a sufficient impact velocity, instead of a completely-bouncing “Fakir” droplet, wetting splashing can occur, with an entrapped air bubble at the centre surrounded by a wetted area as well as an emission of satellite droplets during the advancing phase of spreading lamella. A large portion of the lamella travels upon air and subsequently recoils due to surface tension, forming a partial rebound on the central wet spot. We present and discuss quantitative results of the entrapped air bubble, the central wetted area, and the maximal spreading lamella as the impact velocity is increased. We further vary the lattice periodicity of the micro-patterns and find its profound influence on the macroscopic flow. More specifically, directional splashing can emerge, emitting secondary droplets in certain directions which are associated with the lattice. Directional splashing can be suppressed to a gentle spreading by decreasing the periodicity of the lattice and, furthermore, can be tuned to a completely-wetting splashing in the diagonal directions of the lattice by a larger periodicity, offering opportunities to control the wetting process. Finally, the elimination of directional splashing by reducing air pressure suggests that the underlying air is squeezed outwards by the falling droplet upon the solid boundary whereby the air flow is affected, leading to different splashing behavior.