Fei 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.

We explore the instability and oscillation dynamics of barrel-shaped droplets on cylindrical fibres, contributing to a deeper understanding of fibre–droplet interactions critical to both natural systems and industrial applications. Unlike sessile droplets on flat surfaces, droplets on fibres exhibit unique behaviours due to the curvature of the fibre, such as transitions from axisymmetric (barrel) to non-axisymmetric (clamshell) shapes governed by droplet volume, contact angle and fibre radius. Using a linear inviscid theory, we compute the frequency spectrum of barrel-shaped droplets and identify stability thresholds for the barrel-to-clamshell transition by examining the first rocking mode, with a focus on the role of contact line conditions. This analysis resolves experimental anomalies concerning the stability of half-barrel-shaped droplets on hydrophobic fibres. Our findings also reveals diverse frequency spectra: droplets on thin fibres exhibit Rayleigh–Lamb-like spectral features, while those on thicker fibres show reduced sensitivity to azimuthal wavenumber. Interestingly, the instability of sectoral modes on thick fibres resembles the Rayleigh–Plateau instability of static rivulets, with fibre curvature slightly reducing growth rates at small axial wavenumbers but increasing them at larger ones.

The contact line of droplets on real surfaces is typically irregular and often assumes an elliptical shape. This geometric irregularity causes significant differences in resonance frequencies between droplets on ideal and real surfaces. We experimentally investigate how elliptical contact lines affect the first-order mode resonance frequencies of sessile droplets. The elliptical contact lines are controlled through the aspect ratio γ (semi-minor to semi-major axis). For droplets with fixed volume and wetting area, decreasing γ induces splitting of the first-order mode into two distinct modes along the major and minor axes. The resonance frequency along the major axis decreases progressively with reduced γ, showing stronger frequency reduction at lower γ values. We propose a simplified harmonic oscillator model to interpret these observations. This model yields an explicit expression for the resonance frequency along the major axis that aligns well with experimental data, particularly for smaller droplets. This work advances the understanding of droplet dynamics on real surfaces and enhances techniques for manipulating droplets in technological and scientific applications.

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.

Despite the widespread occurrence of pendant drops in nature, there is still a lack of combined studies on their dynamic and static stability. This study focuses on the dynamic and static stability of elongated drops with either a free or pinned contact line on a plane. We first examine static stability for both axisymmetric and non-axisymmetric perturbations subject to volume or pressure constraints. The stability limits for volume and pressure disturbances (axisymmetric) correspond to the maximum volume and pressure of the drops, respectively. Drops with free contact lines are marginally stable to non-axisymmetric perturbations because of their horizontal translational invariance, whereas pinned drops are stable. The linear dynamic stability is then investigated numerically through a boundary element model, restricted to volume disturbances. Results show that when the stability limit is reached, the first zonal mode has a zero frequency, suggesting that the thresholds for static and dynamic stability are essentially equivalent. Furthermore, natural frequencies experience sharp changes as the stability limit is approached. Another zero frequency mode associated with the horizontal motion of the centre of mass is also revealed by the numerical results, reflecting the horizontal translational invariance of drops with free contact lines. Finally, the frequency spectrum modified by gravity is explored, resulting in the identification of five gravity-induced frequency shift patterns. The frequency shifts break the spectral degeneracy for hemispherical drops with free contact lines, leading to various spectral orderings according to polar and azimuthal wavenumbers.