Periodic Precipitation Patterns during Coalescence of Reacting Sessile Droplets

Marangoni-driven spreading of a droplet on a miscible thin liquid layer

HYPOTHESIS

The coalescence of droplets with liquid-gas interfaces of different surface tensions is common in nature and industrial applications, where the Marangoni-driven film spreading is an essential process. Unlike immiscible fluids governed by triple contact line dynamics, the mixing between two miscible fluids strongly couples with the film spreading process, which are expected to manifest distinct power-law relations for the temporal increase in the film radius.

EXPERIMENTS

We experimentally investigate the Marangoni-driven film spreading phenomenon for a droplet with lower surface tension dropping onto a miscible, thin liquid layer. The temporal growth of the film radius was detected by using a novel deep convolutional neural network, the U2-net method. Scaling analysis was performed to interpret the spreading dynamics of the film.

FINDINGS

We find that the film radius exhibits a three-stage power-law relation over time, with the exponent varying from 1/2 to 1/8, and back to 1/2. The diffusion-affected Marangoni stresses in these three stages were derived, and two estimations of viscous stress were considered. Through estimating and balancing the viscous stress with the Marangoni stress, the three-stage power-law relation was derived and validated.

Numerical Study of the Coalescence and Mixing of Drops of Different Polymeric Materials

In this study, we employ direct numerical simulation (DNS) to investigate the solutal hydrodynamics dictating the three-dimensional coalescence of microscopic, identical-sized sessile drops of different but miscible shear-thinning polymeric liquids (namely, PVAc or polyvinyl acetate and PMMA or polymethylmethacrylate), with the drops being in partially wetted configuration. Despite the ubiquitousness of the interaction of different dissimilar droplets in a variety of engineering problems ranging from additive manufacturing to understanding the behavior of photonic crystals, coalescence of drops composed of different polymeric and non-Newtonian materials has not been significantly explored. Interaction of such dissimilar droplets often involves simultaneous drop spreading, coalescence, and mixing. The mixing dynamics of the dissimilar drops are governed by interphase diffusion, the residual kinetic energy of the drops stemming from the fact that coalescence starts before the spreading of the drops have been completed, and the solutal Marangoni convection. We provide the three-dimensional velocity fields and velocity vectors inside the completely miscible, dissimilar coalescing droplets. Our simulations explicate the relative influence of these different effects in determining the flow field at different locations and at different time instances and the consequent mixing behavior inside the interacting drops. We also show the non-monotonic (in terms of the direction of migration) propagation of the mixing front of the miscible coalescing drops over time. We also establish that the overall mixing (on either side of the mixing front) speeds up as the Marangoni effects dictate the mixing. We anticipate that our study will provide an important foundation for studying miscible multi-material liquid systems, which will be crucial for applications such as inkjet or aerosol jet printing, lab-on-a-chip, polymer processing, etc.

Substrate Wettability Influences Internal Jet Formation and Mixing during Droplet Coalescence

The internal dynamics during the axisymmetric coalescence of an initially static free droplet and a sessile droplet of the same fluid are studied using both laboratory experiments and numerical simulations. A high-speed camera captured internal flows from the side, visualized by adding a dye to the free droplet. The numerical simulations employ the volume of fluid method, with the Kistler dynamic contact angle model to capture substrate wettability, quantitatively validated against the image-processed experiments. It is shown that an internal jet can be formed when capillary waves reflected from the contact line create a small tip with high curvature on top of the coalesced droplet that propels fluid toward the substrate. Jet formation is found to depend on the substrate wettability, which influences capillary wave reflection; the importance of the advancing contact angle subordinated to that of the receding contact angle. It is systematically shown via regime maps that jet formation is enhanced by increasing the receding contact angle and by decreasing the droplet viscosity. Jets are seen at volume ratios very different from those accepted for free droplets, showing that a substrate with appropriate wettability can improve the efficiency of fluid mixing.

Enabling Free-Standing 3D Hydrogel Microstructures with Microreactive Inkjet Printing

Reactive inkjet printing holds great prospect as a multimaterial fabrication process because of its unique advantages involving customization, miniaturization, and precise control of droplets for patterning. For inkjet printing of hydrogel structures, a hydrogel precursor (or cross-linker) is printed onto a cross-linker (or precursor) bath or a substrate. However, the progress of patterning and design of intricate hydrogel structures using the inkjet printing technique is limited by the erratic interplay between gelation and motion control. Accordingly, microreactive inkjet printing (MRIJP) was applied to demonstrate a spontaneous 3D printing of hydrogel microstructures by using alginate as the model system. In addition, a printable window within the capillary number-Weber number for the MRIJP technique demonstrated the importance of velocity to realization of in-air binary droplet collision. Finally, systematic analysis shows that the structure and diffusion coefficient of hydrogels are important factors that affect the shape of printed hydrogels over time. Based on such a fundamental understanding of MRIJP of hydrogels, the fabrication process and the structure of hydrogels can be controlled and adapt for 2D/3D microstructure printing of any low-viscosity (<40 cP) reactive inks, with a representative tissue-mimicking structure of a ∼200 μm diameter hollow tube presented in this work.

Marangoni-driven spreading of miscible liquids in the binary pendant drop geometry

When two liquids with different surface tensions come into contact, the liquid with lower surface tension spreads over the other liquid. This Marangoni-driven spreading has been studied for various geometries and surfactants, but the dynamics of miscible liquids in the binary geometry (drop-drop) has hardly been investigated. Here we use stroboscopic illumination by nanosecond laser pulses to temporally resolve the distance L(t) over which a low-surface-tension drop spreads over a miscible high-surface-tension drop. L(t) is measured as a function of time, t, for various surface tension differences between the liquids and for various viscosities, revealing a power-law L(t) ∼ tα with a spreading exponent α ≈ 0.75. This value is consistent with previous results for viscosity-limited spreading over a deep bath. The universal power law L[combining tilde] ∝ t[combining tilde]3/4 that describes the dimensionless distance L[combining tilde] as a function of the dimensionless time t[combining tilde] reasonably captures our experiments, as well as previous experiments for different geometries, miscibilities, and surface tension modifiers (solvents and surfactants). The range of this power law remarkably covers ten orders of magnitude in dimensionless time. This result enables engineering of drop encapsulation for various liquid-liquid systems.

Direct Patterning of Highly Conductive PEDOT:PSS/Ionic Liquid Hydrogel via Microreactive Inkjet Printing

The gelation of poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) has gained popularity for its potential applications in three dimensions, while possessing tissue-like mechanical properties, high conductivity, and biocompatibility. However, the fabrication of arbitrary structures, especially via inkjet printing, is challenging because of the inherent gel formation. Here, microreactive inkjet printing (MRIJP) is utilized to pattern various 2D and 3D structures of PEDOT:PSS/IL hydrogel by in-air coalescence of PEDOT:PSS and ionic liquid (IL). By controlling the in-air position and Marangoni-driven encapsulation, single droplets of the PEDOT:PSS/IL hydrogel as small as a diameter of ≈260 μm are fabricated within ≈600 μs. Notably, this MRIJP-based PEDOT:PSS/IL has potential for freeform patterning while maintaining identical performance to those fabricated by the conventional spin-coating method. Through controlled deposition achieved via MRIJP, PEDOT:PSS/IL can be transformed into different 3D structures without the need for molding, potentially leading to substantial progress in next-generation bioelectronics devices.

Mass Transfer Accompanying Coalescence of Surfactant-Laden and Surfactant-Free Drop in a Microfluidic Channel

The coalescence of two different drops, one surfactant-laden and the other surfactant-free, was studied under the condition of confined flow in a microchannel. The coalescence was accompanied by penetration of the surfactant-free drop into the surfactant-laden drop because of the difference in the capillary pressure and Marangoni flows causing a film of surfactant-laden liquid to spread over the surfactant-free drop. The penetration rate was dependent on the drop order, with considerably better penetration observed for the case when the surfactant-laden drop goes first. The penetration rate was found to increase with an increase of interfacial tension difference between the two drops, an increase of flow rate and drop confinement in the channel (for the case of the surfactant-laden drop going first), an increase of viscosity of the continuous phase, and a decrease of viscosity of the dispersed phase. Analysis of flow patterns inside the coalescing drops has shown that, unlike coalescence of identical drops, only two vortices are formed by asymmetrical coalescence, centered inside the surfactant-free drop. The vortices were accelerated by the flow of the continuous phase if the surfactant-laden drop preceded the surfactant-free one, increasing the rate of penetration; the opposite was observed if the drop order was reversed. The mixing patterns on a longer time scale were also dependent on the drop order, with better mixing being observed for the case when the surfactant-laden drop goes first.

Physics of active emulsions

Phase separating systems that are maintained away from thermodynamic equilibrium via molecular processes represent a class of active systems, which we call active emulsions. These systems are driven by external energy input, for example provided by an external fuel reservoir. The external energy input gives rise to novel phenomena that are not present in passive systems. For instance, concentration gradients can spatially organise emulsions and cause novel droplet size distributions. Another example are active droplets that are subject to chemical reactions such that their nucleation and size can be controlled, and they can divide spontaneously. In this review, we discuss the physics of phase separation and emulsions and show how the concepts that govern such phenomena can be extended to capture the physics of active emulsions. This physics is relevant to the spatial organisation of the biochemistry in living cells, for the development of novel applications in chemical engineering and models for the origin of life.

Ultra-fast precipitation of transient amorphous cerium oxalate in concentrated nitric acid media

Amorphous cerium oxalate precipitates as a primary transient precursor for the crystalline phase by means of a binodal phase separation.