Effect of solutal Marangoni convection on motion, coarsening, and coalescence of droplets in a monotectic system

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.

Brownian motion of droplets induced by thermal noise

Brownian motion (BM) is pivotal in natural science for the stochastic motion of microscopic droplets. In this study, we investigate BM driven by thermal composition noise at submicro scales, where intermolecular diffusion and surface tension both are significant. To address BM of microscopic droplets, we develop two stochastic multiphase-field models coupled with the full Navier-Stokes equation, namely, Allen-Cahn-Navier-Stokes and Cahn-Hilliard-Navier-Stokes. Both models are validated against capillary-wave theory; the Einstein's relation for the Brownian coefficient D^{*}∼k_{B}T/r at thermodynamic equilibrium is recovered. Moreover, by adjusting the co-action of the diffusion, Marangoni effect, and viscous friction, two nonequilibrium phenomena are observed. (I) The droplet motion transits from the Brownian to Ballistic with increasing Marangoni effect which is emanated from the energy dissipation mechanism distinct from the conventional fluctuation-dissipation theorem. (II) The deterministic droplet motion is triggered by the noise induced nonuniform velocity field which leads to a novel droplet coalescence mechanism associated with the thermal noise.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest. For microstructures composed of polymer-rich clusters in a polymer-poor matrix, the mobility and viscosity contrasts do not impede domain growth; rather, they change the transient concentration of the polymer-rich phase, altering the shape of the discrete domains. This effect introduces several complexities to the coarsening process, including percolation inversion of the polymer-rich and polymer-poor phases-a phenomenon normally attributed to viscoelastic phase separation.

Janus Droplet Formation via Thermally Induced Phase Separation: A Numerical Model with Diffusion and Convection

Microscale Janus particles have versatile potential applications in many physical and biomedical fields, such as microsensor, micromotor, and drug delivery. Here, we present a phase-field approach of multicomponent and multiphase to investigate the Janus droplet formation via thermally induced phase separation. The crucial kinetics for the formation of Janus droplets consisting of two polymer species and a solvent component via an interplay of both diffusion and convection is considered in the Cahn-Hilliard-Navier-Stokes equation. The simulation results of the phase-field model show that unequal interfacial tensions between the two polymer species and the solvent result in asymmetric phase separation in the formation process of Janus droplets. This asymmetric phase separation plays a vital role in the establishment of the so-called core-shell structure that has been observed in previous experiments. By varying the droplet size, the surface tension, and the molecular interaction between the polymer species, several novel droplet morphologies are predicted in the development process of Janus droplets. Moreover, we stress that the hydrodynamics should be reckoned as a non-negligible mechanism that not only accelerates the Janus droplet evolution but also has great impacts on the coarsening and coalescence of the Janus droplets.

Investigation of Equilibrium Droplet Shapes on Chemically Striped Patterned Surfaces Using Phase-Field Method

We systematically investigate the equilibrium shapes of droplets deposited on a set of chemically striped patterned surfaces by using an Allen?Cahn-type phase-field model. Varying the widths of the stripes d, the volume V, as well as the initial positions of the droplets, we release the droplets on the top of the surfaces and observe the final droplet shapes. It is found that there are either one or two equilibrium shapes for a fixed ratio of d/ V^1/3 and each equilibrium shape corresponds to an energy minimum state. The aspect ratio of the droplets ? shows a periodic oscillation behavior with a decreasing amplitude as d/ V^1/3 decreases, similar to the stick?slip?jump movement of a slowly condensing droplet on a chemically striped patterned surface. Additionally, by comparing the movements of slowly evaporating and condensing droplets, we have observed a hysteresis phenomenon, which reveals that the final shapes of droplets also rely on the moving paths. Through modifying the dynamic contact angle boundary condition, the contact line movements of droplets under condensation and evaporation, which are far from equilibrium, are addressed.

Progress Report on Phase Separation in Polymer Solutions

Polymeric porous media (PPM) are widely used as advanced materials, such as sound dampening foams, lithium-ion batteries, stretchable sensors, and biofilters. The functionality, reliability, and durability of these materials have a strong dependence on the microstructural patterns of PPM. One underlying mechanism for the formation of porosity in PPM is phase separation, which engenders polymer-rich and polymer-poor (pore) phases. Herein, the phase separation in polymer solutions is discussed from two different aspects: diffusion and hydrodynamic effects. For phase separation governed by diffusion, two novel morphological transitions are reviewed: "cluster-to-percolation" and "percolation-to-droplets," which are attributed to an effect that the polymer-rich and the solvent-rich phases reach the equilibrium states asynchronously. In the case dictated by hydrodynamics, a deterministic nature for the microstructural evolution during phase separation is scrutinized. The deterministic nature is caused by an interfacial-tension-gradient (solutal Marangoni force), which can lead to directional movement of droplets as well as hydrodynamic instabilities during phase separation.

Three orthogonal ultrasounds fabricate uniform ternary Al-Sn-Cu immiscible alloy

The production of Al based monotectic alloys with uniform microstructure is usually difficult due to the large density difference between the two immiscible liquid phases, which limits the application of such alloys. Here, we apply three orthogonal ultrasounds during the liquid phase separation process of ternary Al_71.9Sn_20.4Cu_7.7 immiscible alloy. A uniform microstructure consisting of fine secondary (Sn) phase dispersed on Al-rich matrix is fabricated in the whole alloy sample with a large size of 30 × 30 × 100 mm. The numerical calculation results indicate that the coupled effect of three ultrasounds promotes the sound pressure level and consequently enlarges the cavitation zone within the alloy melt. The strong shockwaves produced by cavitation prevent the (Sn) droplets from coalescence, and keep them suspended in the parent Al-rich liquid phase. This accounts for the formation of homogeneous composite structures. Thus the introduction of three orthogonal ultrasounds is an effective way to suppress the macrosegregation caused by liquid phase separation and produce bulk immiscible alloys with uniform structures.