Deposition Patterns of Two Neighboring Droplets: Onsager Variational Principle Studies

Analysis of Evaporation of Droplet Pairs by a Quasi-Steady-State Diffusion Model Coupled with the Evaporative Cooling Effect

Multidroplet evaporation is a common phase-change phenomenon not only in nature but also in many industrial applications, including inkjet printing and spray cooling. The evaporation behavior of these droplets is strongly affected by the distance between neighboring droplets, and in particular, evaporation suppression occurs as the distance decreases. However, further quantitative information, such as the temperature and local evaporation flux, is limited because the analytical models of multidroplet evaporation only treat vapor diffusion, and the effect of the latent heat transfer through the liquid-vapor phase change is ignored. Here, we perform a numerical analysis of evaporating droplet pairs that linked vapor diffusion from the droplet surface and evaporative cooling. Heat transfer through the liquid and gas phases is also considered because the saturation pressure depends on the temperature. The results show an increase in the vapor concentration in the region between the two droplets. Consequently, the local evaporation flux in the proximate region significantly decreases with decreasing separation distance. This means that the latent heat transfer through the phase change is diminished, and an asymmetrical temperature distribution occurs in the liquid and gas phases. These numerical results provide quantitative information about the temperature and local evaporation flux of evaporating droplet pairs, and they will guide further investigation of multiple droplet evaporation.

Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes

The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.

Applying droplets and films in evaporative lithography

This review covers experimental results of evaporative lithography and analyzes existing mathematical models of this method. Evaporating droplets and films are used in different fields, such as cooling of heated surfaces of electronic devices, diagnostics in health care, creation of transparent conductive coatings on flexible substrates, and surface patterning. A method called evaporative lithography emerged after the connection between the coffee ring effect taking place in drying colloidal droplets and naturally occurring inhomogeneous vapor flux densities from liquid-vapor interfaces was established. Essential control of the colloidal particle deposit patterns is achieved in this method by producing ambient conditions that induce a nonuniform evaporation profile from the colloidal liquid surface. Evaporative lithography is part of a wider field known as "evaporative-induced self-assembly" (EISA). EISA involves methods based on contact line processes, methods employing particle interaction effects, and evaporative lithography. As a rule, evaporative lithography is a flexible and single-stage process with such advantages as simplicity, low price, and the possibility of application to almost any substrate without pretreatment. Since there is no mechanical impact on the template in evaporative lithography, the template integrity is preserved in the process. The method is also useful for creating materials with localized functions, such as slipperiness and self-healing. For these reasons, evaporative lithography attracts increasing attention and has a number of noticeable achievements at present. We also analyze limitations of the approach and ways of its further development.

Conservation-Dissipation Formalism for soft matter physics: I. Augmentation to Doi's variational approach

In the first paper of this series, we prove that by choosing the proper variational function and variables, the variational approach proposed by Doi in soft matter physics is equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including the particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, are carefully examined. Based on our work, a deep connection among the generalized Gibbs relation, the second law of thermodynamics and the variational principle in non-equilibrium thermodynamics is revealed.

Horizontal transportation of a Maltese cross pattern in nematic liquid crystalline droplets under a temperature gradient

Flow and director fields strongly couple with each other in liquid crystalline systems, and herein we discuss the coupling effect in cylindrical and spherical-cap droplets formed by nematic liquid crystal. Applying a temperature gradient to droplets dispersed in a liquid solvent, we observed a crosslike texture in the droplets moved toward the high-temperature side, indicating that the director field was deformed from equilibrium. Additionally, measurement of the flow field revealed that a convective flow was induced in the droplets under temperature gradient. These results suggested that the director deformation in the droplet was induced by convection. By designing a simplified model based on this, we theoretically analyzed the above phenomenon based on Onsager's variational principle. The results show that the phenomenon was well described by a balance of surface energy gradient with viscous and elastic forces.

Vapor-induced motion of two pure liquid droplets

The movement of evaporating liquid droplets on a surface can be triggered by the Marangoni effect arising from heterogeneities in the surface tension or a gradient in the surface energy of the substrate. Here, we show that, on a high energy surface that remains uniform, the motion of two pure liquid droplets can be induced by a gradient in the liquid vapor resulting from evaporation. The droplets always attract each other, moving from the high evaporation side to the low evaporation side, to reduce energy dissipation. By varying the volume of the droplets or the distance between droplets, the motion of the droplets can be effectively controlled.

Capillary force induced air film for self-aligned short channel: pushing the limits of inkjet printing

Ultrashort channels of electrodes are essential for the construction of advanced functional devices with high-level integration and high operation speed. However, the channel length of fabricated electrodes is limited to 20 μm in inkjet printing. Although several methods have been previously proposed to obtain short channels, they require extra processing steps. In this paper, channel self-aligning phenomenon was observed in directly patterned electrodes on unmodified substrate by inkjet printing, when using an interspace defects growing method. Further exploring the underlying mechanism reveals that the capillary force induced air film prevents droplets coalescence, even on a substrate with no temperature differences. The wetting region, which is generated by the receding droplets impingement, will draw droplets closer together at a larger drop space, thus demanding smaller air pressure for coalescence inhibition and contributing to the self-aligning phenomenon of micro-sized droplets released by inkjet printing. Accordingly, an ultrashort channel of 2.38 μm is obtained with relatively smooth boundaries, when electrodes are printed on a slightly heated substrate, which reduces the air pressure between two neighboring droplets. This work will provide a significant reference for future high resolution applications of inkjet printing technology.

Multi-ring Deposition Pattern of Drying Droplets

We propose a theory for the multi-ring pattern of the deposits that are formed when droplets of the suspension are dried on a substrate. Assuming a standard model for the stick-slip motion of the contact line, we show that as droplets evaporate many concentric rings of deposits are formed but are taken over by a solid-circle pattern in the final stage of drying. An analytical expression is given to indicate when the ring pattern changes to a solid-circle pattern during the evaporation process. The results are in qualitative agreement with existing experiments, and the other predictions on how the evaporation rate, droplet radius, and receding contact angle affect the pattern are all subject to an experimental test.

Critical Impact of Solvent Evaporation on the Resolution of Inkjet Printed Nanoparticles Film

We first verify the critical role of solvent evaporation on the resolution of inkjet printing. To confirm our hypothesis, we adjusted the evaporation rate gradient along the surface of adjacent droplets by controlling the drying microenvironment. Uneven solvent evaporation flux caused thermocapillary surface flow inward the space of micrometer-sized droplets and increase the air pressure, which prevented the neighboring droplets from coalescence. When reducing the droplet distance by the solvent evaporation-based method, a uniform profile could be obtained at the same time. This work brings us a step closer to resolving one of the critical bottlenecks to commercializing printed electronic goods.