Droplets on chemically patterned surface: A local free-energy minima analysis

Wetting Behavior of Inkjet-Printed Electronic Inks on Patterned Substrates

In inkjet printing technology, one important factor influencing the printing quality and reliability of printed films is the interaction of the jetted ink with the substrate surface. This short-range interaction determines the wettability and the adhesion of the ink to the solid surface and is hence responsible for the final shape of the deposited ink. Here, we investigate wetting morphologies of inkjet-printed inks on patterned substrates by carefully designed experimental test structures and simulations. The contact angles, the surface properties, and drop shapes, as well as their influence on the device variability, are experimentally and theoretically analyzed. For the simulations, we employ the phase-field method, which is based on the free energy minimization of the two-phase system with the given wetting boundary conditions. Through a systematic investigation of printed drops on patterned substrates consisting of hydrophilic and hydrophobic areas, we report that the printed morphology is related not only to the designed layout and the drop volume but also to the printing strategy and the wettability. Furthermore, we show how one can modify the intrinsic wettability of the patterned substrates to enhance the printing quality and reliability. Based on the present findings, we cast light on the improvement of the fabrication quality of thin film transistors.

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.

Transitional Electrodes in Electrowetting-Based Droplet Dispensing

Digital microfluidic systems based on electrowetting-on-dielectric technology, particularly valuable in producing and manipulating microdroplets steadily and consistently, have experienced notable advancements in recent years. In this paper, experimental characterizations reveal that simply adding one transitional electrode between the reservoir and the splitting electrode improves the volumetric consistency and reproducibility for droplet dispensing. The volumetric coefficient variation of the consecutively dispensed droplets from a non-refilling reservoir decreases by 1% after the addition of one transitional electrode, with no extra external apparatus. This work provides a straightforward yet effective approach to the improvement of digital microfluidic systems and micro total analysis systems.

Wetting Effect on Patterned Substrates

A droplet deposited on a solid substrate leads to the wetting phenomenon. A natural observation is the lotus effect, known for its superhydrophobicity. This special feature is engendered by the structured microstructure of the lotus leaf, namely, surface heterogeneity, as explained by the quintessential Cassie-Wenzel theory (CWT). In this work, recent designs of functional substrates are overviewed based on the CWT via manipulating the contact area between the liquid and the solid substrate as well as the intrinsic Young's contact angle. Moreover, the limitation of the CWT is discussed. When the droplet size is comparable to the surface heterogeneity, anisotropic wetting morphology often appears, which is beyond the scope of the Cassie-Wenzel work. In this case, several recent studies addressing the anisotropic wetting effect on chemically and mechanically patterned substrates are elucidated. Surface designs for anisotropic wetting morphologies are summarized with respect to the shape and the arrangement of the surface heterogeneity, the droplet volume, the deposition position of the droplet, as well as the mean curvature of the surface heterogeneity. A thermodynamic interpretation for the wetting effect and the corresponding open questions are presented at the end.

Equilibrium droplet shapes on chemically patterned surfaces: theoretical calculation, phase-field simulation, and experiments

HYPOTHESIS

Droplet wetting on a solid substrate is affected by the surface heterogeneity. Introducing patterned wettability on the solid substrate is expected to engender anisotropic wetting morphologies, thereby manipulating droplet wetting behaviors. However, when the droplet size is comparable with that of the surface heterogeneity, the wetting morphologies cannot be depicted by the quintessential Cassie's theory but should be possible to be predicted from the perspective of thermodynamics via surface energy minimization.

METHODS

Here, we investigate the equilibrium droplet shapes on chemically patterned substrates by using an analytical model, phase-field simulations, and experiments. The former two methods are sharp and diffuse interface treatments, respectively, which both are based on minimizing the free energy of the system. The experimental results are obtained by depositing droplets on chemically patterned glass substrates.

FINDINGS

Various anisotropic wetting shapes are found from the three methods. Excellent agreement is observed between different methods, showing the possibility to quantify the anisotropic wetting droplet morphologies on patterned substrates by present methods. We also address a series of non-rotationally symmetric droplet shapes, which is the first resport about these special wetting morphologies. Furthermore, we reveal the anisotropic wetting shapes in a quasi-equilibrium evaporation process.

Wetting transition and phase separation on flat substrates and in porous structures

In contrast to the wetting phenomenon of pure substance phase, we here concentrate on the wetting behavior of immiscible fluids with two components via numerical simulations. We investigate the energetic contribution, the wall energy and the surface excess energy, to the wetting behavior of liquid solutions varying with temperature. This investigation is in accordance with Cahn's wetting transition theory, where the surface composition plays a vital role. By analyzing the energetic contributions, we reveal two different physical mechanisms of complete wetting: (i) surface tension driven complete wetting, where the wetting microstructure is achieved via the outward spreading of the triple junction, and (ii) diffusion induced complete wetting, where the wetting film is achieved through a direct deposition of the solute on the substrate. The former one is consistent with the classic theory of Young's law, and the latter one is an alternative mechanism. To indicate the broad multiplicity of the microstructural arrangements, we take porous structures to exemplarily elucidate the formation of alternative perfect wetting structures. Differing from the wetting on a flat substrate, we show that the surface composition varying with temperature leads to a distinct wetting phenomenon in porous structures. The present findings provide an alternative interpretation for complete wetting and are expected to be exploited for designing more effectively and efficiently superhydrophilic structures.

How do chemical patterns affect equilibrium droplet shapes?

By utilizing a proposed analytical model in combination with the phase-field method, we present a comprehensive study on the effect of chemical patterns on equilibrium droplet morphologies. Here, three influencing factors, the droplet sizes, contact angles, and the ratios of the hydrophilic area to the hydrophobic area, are contemplated. In the analytical model, chemical heterogeneities are described by different non-linear functions. By tuning these functions and the related parameters, the analytical model is capable of calculating the energy landscapes of the system. The chemically patterned surfaces display complex energy landscapes with chemical-heterogeneity-induced local minima, which correspond to the equilibrium morphologies of the droplets. Phase-field (PF) simulations are accordingly conducted and compared with the predicted equilibrium morphologies. In addition, we propose a modified Cassie-Baxter (CB) model to delineate the equilibrium droplet shapes. In contrast to the classic CB model, our extension is not only restricted to the shape with a spherical cap. Both the energy landscape method and the modified CB model are demonstrated to have a good agreement with the PF simulations.