Droplet levitation over a moving wall with a steady air film

Abstract

In isothermal non-coalescence behaviours of a droplet against a wall, an air film of micrometre thickness plays a crucial role. We experimentally study this phenomenon by letting a droplet levitate over a moving glass wall. The three-dimensional shape of the air film is measured using an interferometric method. The mean curvature distribution of the deformed free surface and the distributions of the lubrication pressure are derived from the experimental measurements. We vary experimental parameters, namely wall velocity, droplet diameter and viscosity of the droplets, over a wide range; for example, the droplet viscosity is varied over two orders of magnitude. For the same wall velocity, the air film of low-viscosity droplets shows little shape oscillation with constant film thickness (defined as the steady state), while that of highly viscous droplets shows a significant shape oscillation with varying film thickness (defined as the unsteady state). The droplet viscosity also affects the surface velocity of a droplet. Under our experimental conditions, where the air film shape can be assumed to be steady, we present experimental evidence showing that the lift force generated inside the air film balances with the droplet’s weight. We also verify that the lubrication pressure locally balances with the surface tension and hydrostatic pressures. This indicates that lubrication pressure and the shape of the free surface are mutually determined. Based on the local pressure balance, we discuss a process of determining the steady shape of an air film that has two areas of minimum thickness in the vicinity of the downstream rim.

Surfing of drops on moving liquid–liquid interfaces

“…According to the predictions, the film thickness increases with the air film velocity at a larger rate for small drops. Sawaguchi et al (2019), in similar measurements, found that the thickness of the air film was evenly distributed at the bottom of low viscosity drops, while large oscillations were observed for high viscosity drops. Sreenivas et al (1999) who studied the levitation of drops at a hydraulic jump suggested that the force needed to balance the weight of the drop was W = f L µ a vL y L 2…”

“…It was, however, shown that the drops do not always stay at the hydraulic jump steadily but oscillate (Pirat et al 2010), which is not conducive to the study of the dynamics of the trapped film. Similarly, steady drop floating was achieved by releasing drops on the inner surface of a rotating cylinder coated with a thin layer of the same liquid as in the drop (Davis et al 1980;Thoroddsen & Mahadevan 1997;Lhuissier et al 2013;Sawaguchi et al 2019). Whether the drops can levitate on the surface or not depends a lot on the impact conditions.…”

“…However, no calculated results were given. Based on the lubrication theory, Sawaguchi et al (2019) found the 2D pressure distribution in the trapped film for a steadily floating drop. As the drop shape is controlled by the balance between the inner pressure of the drop given by the weight, the outer pressure in the film and the Laplace force, the film pressure can also be calculated if the local drop surface curvature is known.…”

“…In many industrial applications where the drop is levitated over an interface, including oil petroleum transportation and oil-water separation (Rommel et al 1993), the drops are surrounded by another liquid and the fluid interface is significantly deformed when the drop approaches it because of gravity. In most of the previous investigations, drops were generated in air and approached the interfaces of liquid films with air (Lhuissier et al 2013;Castrejón-Pita et al 2016;Sawaguchi et al 2019). In such cases, drop levitation can be realized only when the interface have high speed and the liquids have large viscosity.…”

Extended Reynolds lubrication model for incompressible Newtonian fluid

“…For a spherical two-particle system, the lubrication forces have been well described in the Stokes regime [12][13][14][15][16]. On the other hand, more general lubrication between objects of nonspherical geometries may be described by a small deformation approximation [17], the Benny-Lin equation for small perturbation in film flow on an inclined plane [18,19], or by the Reynolds lubrication equation [20] which shows that the pressure is independent of the wall-normal direction even for deformable particles such as biological cells [21,22] and bubbles or droplets [23]. Figure 1 shows a two-dimensional schematic of a narrow gap between two moving solid surfaces.…”