Line tension of sessile droplets: Thermodynamic considerations

Chemo-elasto-electro free energy of non-uniform system in the diffuse interface context

In the present work, we propose an alternative approach for deriving the free energy formulation of a non-uniform system. Compared with the work of Cahn and Hilliard (1958 J.Chem. Phys.28258-67), our approach provides a more comprehensive explanation for the individual energy contribution in a non-uniform system, including entropy, interaction energy, and internal energy. By employing a fundamental mathematical calculus, we reformulate the local composition within the interface region. Utilizing the reformulated local composition as well as classic thermodynamic principles, we establish formal expressions for entropy, interaction energy, and the internal energy, which are functions of both composition and composition gradients. We obtain a comprehensive free energy expression for a non-uniform system by integrating these energy density formulations. The obtained free energy expression is consistent with the formula type of Cahn and Hilliard and prodives more deeper physical interpretation. Moreover, using the same approach, we derive formulations for elastic energy and electric potential energy in a non-uniform system. However, the proposed approach encounters a limitation in the special case of a non-uniform fluid contacting a solid substrate. Due to the significant difference in the length scales between the solid-fluid and fluid-fluid interfaces, the wall free energy formulation based on the aforementioned concept is unsuitable for this multi-scale system. To address this limitation, we reformulate the wall free energy as a function of the average composition over the solid-fluid interface. Additionally, the previous derivation relies on an artificial treatment of describing the composition variation across the interface by a smooth monotone function, while the true nature of this variation remains unclear. By utilizing the concept of average composition, we circumvent the open question of how the composition varies across the interface region. Our work provides a thorough understanding for the construction of free energy formulations for a non-uniform system in condensed matter physics.

Wetting Effect Induced Depletion and Adsorption Layers: Diffuse Interface Perspective

When a multi-component fluid contacts arigid solid substrate, the van der Waals interaction between fluids and substrate induces a depletion/adsorption layer depending on the intrinsic wettability of the system. In this study, we investigate the depletion/adsorption behaviors of A-B fluid system. We derive analytical expressions for the equilibrium layer thickness and the equilibrium composition distribution near the solid wall, based on the theories of de Gennes and Cahn. Our derivation is verified through phase-field simulations, wherein the substrate wettability, A-B interfacial tension, and temperature are systematically varied. Our findings underscore two pivotal mechanisms governing the equilibrium layer thickness. With an increase in the wall free energy, the substrate wettability dominates the layer formation, aligning with de Gennes' theory. When the interfacial tension increases, or temperature rises, the layer formation is determined by the A-B interactions, obeying Cahn's theory. Additionally, we extend our study to non-equilibrium systems where the initial composition deviates from the binodal line. Notably, macroscopic depletion/adsorption layers form on the substrate, which are significantly thicker than the equilibrium microscopic layers. This macroscopic layer formation is attributed to the interplay of phase separation and Ostwald ripening. We anticipate that the present finding could deepen our knowledge on the depletion/adsorption behaviors of immiscible fluids.

Wetting and Contact-Angle Hysteresis: Density Asymmetry and van der Waals Force

A droplet depositing on a solid substrate leads to the wetting phenomenon, such as dew on plant leaves. On an ideally smooth substrate, the classic Young's law has been employed to describe the wetting effect. However, no real substrate is ideally smooth at the microscale. Given this fact, we introduce a surface composition concept to scrutinize the wetting mechanism via considering the liquid-gas density asymmetry and the fluid-solid van der Waals interaction. The current concept enables one to comprehend counterintuitive phenomenon of contact-angle hysteresis on a smooth substrate and increase of contact angle with temperature as well as gas bubble wetting.

Evolution dynamics of thin liquid structures investigated using a phase-field model

Liquid structures of thin-films and torus droplets are omnipresent in daily lives. The morphological evolution of liquid structures suspending in another immiscible fluid and sitting on a solid substrate is investigated by using three-dimensional (3D) phase-field (PF) simulations. Here, we address the evolution dynamics by scrutinizing the interplay of surface energy, kinetic energy, and viscous dissipation, which is characterized by Reynolds number Re and Weber number We. We observe special droplet breakup phenomena by varying Re and We. In addition, we gain the essential physical insights into controlling the droplet formation resulting from the morphological evolution of the liquid structures by characterizing the top and side profiles under different circumstances. We find that the shape evolution of the liquid structures is intimately related to the initial shape, Re, We as well as the intrinsic wettability of the substrate. Furthermore, it is revealed that the evolution dynamics are determined by the competition between the coalescence phenomenology and the hydrodynamic instability of the liquid structures. For the coalescence phenomenology, the liquid structure merges onto itself, while the hydrodynamic instability leads to the breakup of the liquid structure. Last but not least, we investigate the influence of wall relaxation on the breakup outcome of torus droplets on substrates with different contact angles. We shed light on how the key parameters including the initial shape, Re, We, wettability, and wall relaxation influence the droplet dynamics and droplet formation. These findings are anticipated to contribute insights into droplet-based systems, potentially impacting areas like ink-jet printing, drug delivery systems, and microfluidic devices, where the interplay of surface energy, kinetic energy, and viscous dissipation plays a crucial role.