Deposition pattern of interacting droplets

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.

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.

Cooperative evaporation in two-dimensional droplet arrays

The evaporation of a sessile drop in a gaseous environment may be critical to many practical applications. Evaporation dynamics of interacting sessile droplets is strongly influenced by the proximity of adjacent droplets. We study the effects of droplet-droplet vapor-mediated interactions on the evaporation lifetime of two-dimensional arrays of sessile water droplets. We observe that the presence of neighboring droplets acts as a mode of vapor accumulation which slows down the evaporation process. By considering an arbitrarily configured two-dimensional array of droplets, here we provide a simple generalized theoretical limit to their lifetime in an evaporating state. Using a scaling analysis, we put forward that the sessile droplet lifetime in a two-dimensional array is a linear function of the extent of confinement for various surface wettability and droplet geometric parameters (contact angle and contact radius). Notwithstanding the geometrical and physical complexity of the effective confinement generated due to their cooperative interactions, we show that the consequent evaporation characteristics may be remarkably insensitive to the topographical details of the overall droplet organization for a wide range of droplet-substrate combinations. With subsequent deployment of particle-laden droplets, however, our results lead to the discovery of a unique pathway towards tailoring the internal flows within the collective system by harnessing an exclusive topologically driven symmetry-breaking phenomenon, yielding a strategy of patterning particulate matters around the droplet array.

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.

Two-component marangoni-contracted droplets: friction and shape

When a mixture of propylene glycol and water is deposited on a clean glass slide, it forms a droplet of a given apparent contact angle rather than spreading as one would expect on such a high-energy surface. The droplet is stabilized by a Marangoni flow due to the non-uniformity of the components' concentrations between the border and the apex of the droplet, itself a result of evaporation. These self-contracting droplets have unusual properties such as absence of pinning and the ability to move under an external humidity gradient. The droplets' apparent contact angles are a function of their concentration and the external humidity. Here we study the motion of such droplets sliding down slopes and compare the results to normal non-volatile droplets. We precisely control the external humidity and explore the influence of the volume, viscosity, surface tension, and contact angle. We find that the droplets suffer a negligible pinning force so that for small velocities the capillary number (Ca) is directly proportional to the Bond number (Bo): Ca = Bo sin α with α the angle of the slope. Lastly we study the successive shapes the droplets take when sliding at larger and larger velocities.

Engineering Interfacial Processes at Mini-Micro-Nano Scales Using Sessile Droplet Architecture

Evaporating sessile functional droplets act as the fundamental building block that controls the cumulative outcome of many industrial and biological applications such as surface patterning, 3D printing, photonic crystals, and DNA sequencing, to name a few. Additionally, a drying single sessile droplet forms a high-throughput processing technique using low material volume which is especially suitable for medical diagnosis. A sessile droplet also provides an elementary platform to study and analyze fundamental interfacial processes at various length scales ranging from macroscopically observable wetting and evaporation to microfluidic transport to interparticle forces operating at a nanometric length scale. As an example, to ascertain the quality of 3D printing we must understand the fundamental interfacial processes at the droplet scale. In this article, we review the coupled physics of evaporation flow-contact-line-driven particle transport in sessile colloidal droplets and provide methodologies to control the same. Through natural alterations in droplet vaporization, one can change the evaporative pattern and contact line dynamics leading to internal flow which will modulate the final particle assembly in a nontrivial fashion. We further show that control over particle transport can also be exerted by external stimuli which can be thermal, mechanical oscillations, vapor confinement (walled or a fellow droplet), or chemical (surfactant-induced) in nature. For example, significant augmentation of an otherwise evaporation-driven particle transport in sessile droplets can be brought about simply through controlled interfacial oscillations. The ability to control the final morphologies by manipulating the governing interfacial mechanisms in the precursor stages of droplet drying makes it perfectly suitable for fabrication-, mixing-, and diagnostic-based applications.

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.

Convection inside condensing and evaporating droplets of aqueous solution

We experimentally study the fluid convection inside a condensing droplet of aqueous NaCl solution and compare it with that of an evaporating droplet. The droplets are sandwiched between two horizontal hydrophobic surfaces and surrounded by a reservoir with solution of different concentration. Condensation and evaporation of the droplets occur due to the vapor pressure difference between the droplet and the reservoir solution. The micro-PIV technique has been used to study the velocity field inside the droplets. Buoyancy driven Rayleigh convection is observed inside both the condensing and evaporating droplets. In the condensing droplet, water condenses on the liquid-air interface creating a low density region near the interface. There is upward movement of fluid along the condensing interface towards the top region of the droplet which recirculates back from the center region of the droplet in the downward direction. In contrast, the fluid moves in the downward direction along the interface in the case of an evaporating droplet with an upward plume like flow at the center region of the droplet. Both evaporating and condensing droplets show a recirculating loop inside the droplets of opposite direction.

Hydrodynamics of Two Interacting Liquid Droplets of Aqueous Solution inside a Microchannel

We experimentally investigated the effect of a neighboring liquid droplet on fluid convection inside a liquid droplet of aqueous solution present inside a microchannel using the microscale particle image velocimetry technique. There is no physical contact between the two droplets, and the solute concentrations of the two droplets are set at different values. Vapor concentration near the interface of the two droplets is different due to the difference in solute concentration. Water vapor evaporates from the low-concentration droplet having higher vapor pressure and condenses on the high-concentration droplet having lower vapor pressure. Evaporation and condensation induce Rayleigh convection inside the two droplets. Flow pattern shows circulating loops inside both liquid droplets. The circulations at the interacting adjacent interface of the two droplets are opposite to each other. The strength of flow inside the liquid droplets decreases with time due to decrease in the difference of solute concentration between the two droplets. The flow strength inside the two interacting droplets is also a function of separation distance between the droplets. The flow strength inside the droplets decreases with increase in separation distance.

Vapor-Induced Motion of Liquid Droplets on an Inert Substrate

Evaporating droplets are known to show complex motion that has conventionally been explained by the Marangoni effect (flow induced by the gradient of surface tension). Here, we show that the droplet motion can be induced even in the absence of the Marangoni effect due to the gradient of the evaporation rate. We derive an equation for the velocity of a droplet subject to the nonuniform evaporation rate and nonuniform surface tension placed on an inert substrate, where the wettability is uniform and unchanged. The equation explains the previously observed attraction-repulsion-chasing behaviors of evaporating droplets.

Deposition Patterns of Two Neighboring Droplets: Onsager Variational Principle Studies

When two droplets containing nonvolatile components are sitting close to each other, asymmetrical ring-like deposition patterns are formed on the substrate. We propose a simple theory based on the Onsager variational principle to predict the deposition patterns of two neighboring droplets. The contact line motion and the interference effect of two droplets are considered simultaneously. We demonstrate that the gradients of evaporation rate along two droplets is the main reason for forming asymmetrical deposition patterns. By tracing the relative motion between the contact line and the solute particles, we found that the velocities of solute particles have no cylindrical symmetry anymore because of the asymmetrical evaporation rate, giving the underlying mechanism of forming asymmetrical patterns. Moreover, controlling the evaporation rate combined with varying the contact line friction, fan-like and eclipse-like deposition patterns are obtained. The theoretical results of pinned contact line cases are qualitatively consistent with the pervious experimental results.

Confinement-induced alterations in the evaporation dynamics of sessile droplets

Evaporation of sessile droplets has been a topic of extensive research. However, the effect of confinement on the underlying dynamics has not been well explored. Here, we report the evaporation dynamics of a sessile droplet in a confined fluidic environment. Our findings reveal that an increase in the channel length delays the completion of the evaporation process and leads to unique spatio-temporal evaporation flux and internal flow. The evaporation modes (constant contact angle and constant contact radius) during the droplet lifetime however exhibit global similarity when normalized by appropriate length and timescales. These results are explained in light of an increase in vapor concentration inside the channel due to greater accumulation of water vapor on account of increased channel length. We have formulated a theoretical framework which introduces two key parameters namely an enhanced concentration of the vapor field in the vicinity of the confined droplet and a corresponding accumulation lengthscale over which the accumulated vapor relaxes to the ambient concentration. Using these two parameters and modified diffusion based evaporation we are able to show that confined droplets exhibit a universal behavior in terms of the temporal evolution of each evaporation mode irrespective of the channel length. These results may turn out to be of profound importance in a wide variety of applications, ranging from surface patterning to microfluidic technology.

Inkjet printing of TiO2/AlOOH heterostructures for the formation of interference color images with high optical visibility

This paper describes a practical approach for the fabrication of highly visible interference color images using sol-gel ink technique and a common desktop inkjet printer. We show the potential of titania-boehmite inks for the production of optical heterostructures on various surfaces, which after drying on air produce optical solid layers with low and high refractive index. The optical properties of the surface heterostructures were adjusted following the principles of antireflection coating resulting in the enhancement of the interference color optical visibility of the prints by as much as 32%. Finally, the presented technique was optimized following the insights into the mechanisms of the drop-surface interactions and the drop-on-surface coalescence to make it suitable for the production of even thickness coatings suitable for printing at a large scale. We propose that the technology described herein is a promising new green and sustainable approach for color printing.

Insights into Vapor-Mediated Interactions in a Nanocolloidal Droplet System: Evaporation Dynamics and Affects on Self-Assembly Topologies on Macro- to Microscales

Particle-laden droplet-based systems ranging from micro- to nanoscale have become increasingly popular in applications such as inkjet printing, pharmaceutics, nanoelectronics, and surface patterning. All such applications involve multidroplet arrays in which vapor-mediated interactions can significantly affect the evaporation dynamics and morphological topology of precipitates. A fundamental study was conducted on nanocolloidal paired droplets (droplets kept adjacent to each other as in an array) to understand the physics related to the evaporation dynamics, internal flow pattern, particle transport, and nanoparticle self-assembly, primarily using optical diagnostic techniques [such as micro-particle image velocimetry (μPIV)]. Paired droplets exhibit contact angle asymmetry, inhomogeneous contact line slip, and unique single-toroid microscale flow, which are unobserved in single droplets. Furthermore, nanoparticles self-assemble (at the nanoscale) to form a unique variable-thickness (microscale) tilted dome-shaped structure that eventually ruptures at an angle because of evaporation at a nanopore scale to form cavities (miniscale). The geometry and morphology of the dome can be further fine-tuned at a macro- to microscale by varying the initial particle concentration and substrate properties. This concept has been extended to a linear array of droplets to showcase how to custom design two-dimensional drop arrangements to create controlled surface patterns at multiple length scales.