Wanqiu Zhang

The attraction or repulsion force between two solid objects at a liquid-gas interface (i.e. the lateral capillary interaction force) is generally considered to be highly dependent on both the shapes of the solid surfaces and the relative positions. To challenge this, we propose an exotic capillary system in which the stationary exotic plate piercing the interface can produce a constant capillary interaction force on a partly immersed cylinder at different horizontal positions. This constancy is owing to the counterbalancing of variations in the horizontal components of the surface tension force and the hydrostatic pressure force on the cylinder. Through analysing the meniscus profiles and the capillary interaction force in the proposed exotic capillary system, five types of exotic plate shapes are identified. More importantly, a further analysis indicates that the lateral capillary interaction force in the proposed exotic capillary system remains constant even for different vertical positions of the cylinder. To verify the practicality of our theory, a three-dimensional numerical investigation is conducted, and the results show that the lateral capillary interaction force can remain nearly constant as expected. The proposed capillary system provides new insight into controlling the capillary interaction force. The constant-force regimes suggest passive routes for interfacial transport and micromanipulation, force regulation and suppression of undesired capillary aggregation.

Oscillating sessile droplets on a plane, crucial in industrial applications like inkjet printing, spray cooling, and antifogging, present a long-standing challenge in determining viscous damping. Existing solutions are limited to first-order asymptotic approximations of hemispherical droplets, accounting only for viscous dissipation near the wall. Considering further the bulk dissipation that is usually neglected due to its higher-order effect, we obtain a two-term approximation of decay rates for pinned sessile droplets with different contact angles. We demonstrate that the two-term approximation effectively resolves discrepancies between predicted and observed dampings for viscosities in the range of practical interest, supported by experiments and simulations. The two-term approximation also explains why hydrophobic droplets possess much lower damping than hydrophilic ones, and offers a template for damping prediction formulas with potential viscosity measurement applications.

In this paper, we simulate the process of two-dimensional axisymmetric fluid–structure coupling of a droplet impacting on a flexible disk. The effects of dimensionless disk stiffness (K = 0.1–1000), Weber number (We = 1–500) and contact angle (θ = 130° and 60°) on the dynamics of the droplet impacting on the flexible disk are analysed. The results indicate that there are five typical impact modes for a hydrophobic surface (θ = 130°) and four typical impact modes for a hydrophilic surface (θ = 60°) within the range of considered parameters. The analysis of spreading factor reveals that a part of the energy is transferred to the substrate, which is manifested as a weakening of the droplet spreading, when the substrate deforms downwards due to the droplet impact; the squeezing of the droplet causes a tendency to flow from the centre of the droplet to the edge, which is manifested as an enhancement of the droplet spreading, when the substrate recovers from the downward deformation. The effect of the substrate flexibility on the maximum spreading factor depends on the competition of the two mechanisms above. Based on this, a modified scaling law of β_max has been proposed by introducing the effective Weber number (We_m). The analysis of impact force demonstrates that the peak of the impact force is related to the deflection of the flexible substrate which is different from that of a rigid wall; and three typical processes of impact force variation have been summarised. In addition, unlike the rigid substrate scenario, there is an energy interaction between the droplet and the flexible substrate after impact occurs, which is classified as three typical energy transformation processes.

Direct numerical simulations of the droplet impact on a flat solid surface with an annular part are conducted. We investigate droplet impact on a superhydrophobic substrate with a superhydrophilic annulus to understand the formation conditions of droplets in different states. The location and size of superhydrophilic annulus are carried out through the phase diagram. We describe the formation process of droplets in three different states and the spreading radius with time to catch the rupture time of the film. Two different ruptures occur in the spreading stage or the retraction stage, respectively. The rupture times from these two mechanisms observed numerically are found to be a key factor resulting in partial rebound and lens-shaped/ring-shaped droplets. Finally, the influence of non-dimensional numbers on the formation of the ring-shaped droplet is demonstrated. The Weber number can alter the amplitude of the up and down oscillation on the droplet's upper surface, while the Froude number affects primarily the time to form the central penetrating hole. This gives the guidance and method to control the ring-shaped droplets formation time.

An interesting resurrection phenomenon (including the initial complete submersion, subsequent resurfacing and final rebounding) of a superhydrophobic sphere impacting onto a liquid bath was observed in experiments and direct numerical simulations by Galeano-Rios et al. (J. Fluid Mech., vol. 912, 2021, A17). We investigate the mechanisms of the liquid entry for a superhydrophobic cylinder in this paper. The superhydrophobic cylinder, commonly employed as supporting legs for insects and robots at the liquid surface, can exhibit liquid-entry mechanisms different from those observed with the sphere. The direct numerical simulation method is applied to the impact of a two-dimensional (2-D) superhydrophobic cylinder (modelled as a pseudo-solid) onto a liquid bath. We find that for the impacting cylinder the resurrection phenomenon can also exist, and the cylinder can either rebound (get detached from the liquid surface) or stay afloat after resurfacing. The cylinder impact behaviour is classified into four regimes, i.e. floating, bouncing, resurrecting (resurrecting-floating and resurrecting-bouncing) and sinking, dependent on the Weber number and the density ratio of the cylinder to the liquid. For the regimes of floating and bouncing, the force analysis indicates that the form drag dominates the motion of the cylinder in the very beginning of the impact, while subsequently the surface tension force also plays a role with the contact line pinning on the horizontal midline of the cylinder. For the critical states of the highlighted resurrecting regime, our numerical results show that the rising height for the completely submerged cylinder of different density ratios remains nearly unchanged. Accordingly, a relation between the maximum ascending velocity and the density ratio is derived to predict whether the completely submerged cylinder can resurface.

Interfacial capture of particles and droplets is important in practical applications. Interfacial capture owing to the surface tension force occurs only when the target (particle or droplet) is close to the collector, leading to low efficiency with collector or collector arrays. An elliptical cylinder instead of a common circular cylinder is a method to enhance capture efficiency. We theoretically investigate this situation by modelling the motion of floating particles around a surface-piercing elliptical cylindrical collector at Reynolds numbers of 1–10. Results indicate that, despite a smaller capture width, elliptical cross-sections, especially with smaller aspect ratios, are more efficient in capturing owing to a much smaller contact line perimeter compared with circular cross-sections. The aligned orientation (the major axis is parallel to the flow) is better than the orthogonal orientation (the major axis is perpendicular to the flow) owing to a larger capture width. A larger collector is beneficial to capillary capture but a very large size is adverse. Smaller but heavier floating particles for smaller capillary numbers can be easily captured at lower Reynolds numbers. The aligned orientation has a greater advantage over the circular cross-section and the orthogonal orientation in the capillary capture. This provides a good method for enhancing the capture efficiency of floating particles in applications.

Enhancing the aerodynamic performance of bristled wings is an important topic for small flying robotics. This paper numerically investigates this situation at very low Reynolds numbers by using elliptic cylinders as the bristles instead of circular cylinders. Optimal configuration of the bristled wing with five elliptic cylinders is obtained, which corresponds to the maximum lift. The results show that, compared with the case of circular cylindrical bristles, the aerodynamic performance of the elliptical bristles can be enhanced effectively. The enhancement can be more significant as the aspect ratio of the ellipses increases and the gap width decreases. The bristled wing generates more lift compared to a flat-plate wing with a length five times that of the major axis of an ellipse. For the cases that the attack angle α for the whole wing is equal to those for the elliptical bristles θ, the optimal attack angle for ellipses maximizing the total lift force of the five-bristle model is between 40° and 45°. For α ≠ θ with the Reynold number Re ≪ 0.1, the optimal ellipse attack angle is between 40° and 45°. For α ≠ θ with Re∼ 1, the optimal ellipse attack angle deviates heavier from the range between 40° and 45° at some α values and reaches approximately 32° at α = 20°. This paper can lay a foundation for optimal design of small flying robotics and enhancement of flow through porous structures in future.

A macroscale floating object moving downwards will encounter an increasing buoyancy force exerted by the liquid. However, considering the surface tension and the deformed meniscus, we find an exotic floating object of specific shape that withstands a constant total force exerted by the liquid when it moves vertically and slowly. This constant total force consists of the surface tension force and the hydrostatic pressure force, from which a model to determine the shape of the exotic floating object is proposed. Results show that there exist three types of exotic floating objects in both the two-dimensional symmetric and axisymmetric cases, dependent on their concavity and convexity. To ensure that the menisci around the exotic floating objects can be sustained in practice, the stabilities of these menisci are checked. Apart from the meniscus stabilities (of liquid surfaces), the floating stabilities (of solid objects) are also studied. It is demonstrated that the exotic floating object remains in a critical state of floating stabilities no matter where this object locates vertically, from which a new method to predict the floating stabilities for general floating objects of arbitrary shape is put forward, based on the contact angle and the geometrical parameters at the contact point. With the new method, the floating stabilities can be predicted conveniently, without performing an extra force analysis.