Inkjet droplet deposition dynamics into square microcavities for OLEDs manufacturing

The dynamics of inkjet deposition in square microcavities are investigated utilizing a three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann (LB) model with large density ratios. A geometric scheme is considered within the pseudopotential LBM framework to obtain the desired contact angles. The effects of wettability, density ratios, droplet viscosity and impact velocity are explored to reveal the droplet–microcavity interactions. With the contact angles of microcavity increasing, the physical outcomes including the crown-like shape with a small round dot, circular hollow core, uniform film and convex film are identified and analyzed. At a lower density ratio ρ_r?=?11.6, the surrounding denser gas resists the droplet recoiling flow resulting in an increasing hollow core. The appropriate higher droplet viscosity and decreasing impact velocity are preferred which could eliminate the hollow core in the recoiling phase and accelerate the inkjet deposition process straightforward. The revelation of droplet-microcavity dynamics is beneficial for optimizing inkjet deposition process and fabricating uniform OLEDs panels.     

Behavior of microdroplets in diffuser/nozzle structures

This paper investigates the behavior of microdroplets flowing in microchannels with a series of diffuser/nozzle structures. Depending on the imposed flow direction, the serial structures can act either as a series of diffusers or nozzles. Different serial diffuser/nozzle microchannels with opening angles ranging from 15° to 45° were considered. A 2D numerical model was employed to study the dynamics of the microdroplet during its passage through the diffuser/nozzle structures. The deformation of the microdroplet was captured using a level set method. On the experimental front, test devices were fabricated in polydimethylsiloxane using soft lithography. T-junctions for droplet formation, diffuser/nozzle structures and pressure ports were integrated in a single device. Mineral oil with 2% w/w surfactant span 80 and de-ionized water with fluorescent worked as the carrier phase and the dispersed phase, respectively. The deformation of the water droplet and the corresponding pressure drop across the diffuser/nozzle structures were measured in both diffuser and nozzle configurations at a fixed flow rate ratio between oil and water of 30. The results show a linear relationship between the pressure drop and the flow rate. Furthermore, the rectification effect was observed in all tested devices. The pressure drop in the diffuser configuration is higher than that of the nozzle configuration. Finally, the pressure measured results with droplet and without droplet were analyzed and compared.     

Electrokinetic motion of an electrically induced Janus droplet in microchannels

The electrokinetic motion of an electrically induced Janus oil droplet with one side covered with an aluminum oxide nanoparticle film in a circular microchannel was numerically simulated in this paper. The Janus oil droplet is electrically anisotropic as the nanoparticle-covered area carries positive charges and the rest oil–water surface area carries negative charges. A theoretical model was constructed to calculate the electrokinetic velocity of the Janus droplet by considering the force balance on the surface of the Janus droplet at steady state. In the model, the effects of the electric double layer and surface charges on the motion at the oil–water interface are considered. The effects of five parameters on the electrokinetic motion of the Janus droplets were studied: the electric field, the zeta potential ratio of the positively charged side to the negatively charged side of the Janus droplet, the viscosity ratio of the oil phase to the water phase, the nanoparticle coverage of the Janus droplet, and the size ratio of the diameter of the Janus droplet to the diameter of the cylindrical microchannel. The simulation results indicate that the increase in the electrical field, the zeta potential ratio, the viscosity ratio or the nanoparticle coverage leads to faster electrokinetic motion of the Janus droplet. On the other hand, with the increase in size ratio, the electrokinetic velocity of Janus droplet first decreases gradually then increases sharply. The simulated results were compared with the experimental results and good agreement was found.     

Numerical simulation of emergence of a water droplet from a pore into a microchannel gas stream

A numerical investigation on the dynamic behavior of liquid water entering a microchannel through a lateral opening (pore) in the wall is reported in this paper. The channel dimensions, flow conditions and transport properties are chosen to simulate those in the gas channel of a typical proton exchange membrane fuel cell (PEMFC). Two-dimensional transient simulations employing the volume of fluid method are used to explicitly track the liquid–gas interface, and to gain understanding into the dynamics of a water droplet subjected to airflow in the bulk of the microchannel. A series of parametric studies, including the effects of static contact angle, dimensions of the pore, air-inlet velocity, and water-inlet velocity are performed with a particular focus on the effect of hydrophobicity. The simulations show that the wettability of the microchannel surface has a major impact on the dynamics of the water droplet. Flow patterns are presented and analyzed showing the splitting of a droplet for a hydrophobic surface, and the tendency for spreading and film flow formation for a hydrophilic surface. The time evolution of the advancing and receding contact angles of the droplet are found to be sensitive to the wettability when the gas diffusion layer surface is hydrophilic, but independent of wettability when the surface is hydrophobic. The critical air velocity at which a droplet detaches is found to decrease with increasing hydrophobicity and with increasing initial dimension of the droplet. The critical air velocity found in the present study by taking into account the water transport and evolution of the droplet from a pore are found to differ significantly from previous works which consider a stagnant droplet sitting on the surface.     

Contact dynamics of nanodroplets in carbon nanotubes: effects of electric field,tube radius,and salt ions

We report contact dynamics of nanodroplets in carbon nanotubes using molecular dynamics simulations. The effects of electric field, nanotube radius, and salt ions included in the nanodroplets are explored in more detail. For the cases without applied electric field, the droplet fills the cross section of carbon nanotubes with small radius completely. When the tube radius becomes larger, the droplet retracts towards the surface of the nanotube to minimize the surface tension of the droplet and shows wider extension along the axial direction. When an electric field perpendicular to the axial direction of the carbon nanotubes is applied, the position and shape of the droplets are changed which is also related to the tube radius and whether the droplet contains salt ions. Unlike a planar surface, the nanotube limits spreading of the droplets along the radial direction. The variation of the center of mass of the droplets indicates a significant confinement to the position of the droplets in the electric field. For the salty water droplets, a strong electric field induces ejection of small water clusters from the droplet in a nanotube with large radius. As a consequence, the droplet and water clusters are separated and moved to two opposite sides of the nanotube by the electric field.     

Deformation and migration of a leaky-dielectric droplet in a steady non-uniform electric field

This work numerically investigates the dynamics of an initially uncharged droplet freely suspended in another immiscible fluid and influenced by a steady non-uniform electric field. Both the droplet and the suspending fluid are assumed leaky dielectric. A three-dimensional spectral boundary element method is employed. It is validated by comparing with other numerical results and experimental findings for droplet deformation in a uniform electric field. This work reveals the dominant influence of the relative conductivity of fluids on the droplet migration direction in a non-uniform electric field. We have also explored the complicated behavior of the droplet deformation and speed affected by the relative permittivity and conductivity. In addition, the impact of the electric capillary number and viscosity ratio on the droplet dynamics has also been investigated. Results found and numerical algorithms developed in this study pave ways for investigations on droplet motion in an electric field created by co-planar electrodes, which has direct applications in digital microfluidics.     

Generation of droplets in the T-junction with a constriction microchannel

Droplet microfluidics plays an essential role in science and technology with various applications such as chemical engineering, environment, energy and other fields. T-junction with a constriction microchannel is designed for the controlled production of monodisperse microdroplets, which could produce droplets with the same size under a lower flow resistance. The influence of the microchannel structure, operating conditions, and physical properties on the dispersion rules is systematically investigated by combinations of micro-particle image velocimetry (Micro-PIV), high-speed camera and numerical simulation. Compared to the traditional T-junction channel, the T-junction with a constriction microchannel can generate smaller droplets whose size conforms to the size prediction formula of the traditional T-junction channel. It is found that the velocity vector of the T-junction with a constriction microchannel is faster than that in the T-junction channel at each stage of droplet generation. The droplet size is mainly based on the Ca number, the flow rate ratio and viscosity ratio of the continuous phases in our channel, and the range of the index of Ca with the droplet size is found. The constriction width has a significant influence on the dispersion rule, as there is a decreasing tendency for the droplet size with reducing constriction width.     

Droplet arrangement and coalescence in diverging/converging microchannels

We experimentally examine the dynamics of droplet assembly and recombination processes in a two-dimensional pore-model system. Monodisperse trains of droplets are formed by focusing streams of immiscible fluids into a square microchannel that is connected to a diverging/converging slit microfluidic chamber. We focus on the limit of dilute emulsions and investigate the formation and stability of crystal-like structures when droplets are hydrodynamically coupled in the chamber. The minimal distance between droplets and the spread of droplet lattices are measured as a function of initial control parameters and the relationship between droplet velocity and trajectory is discussed. We demonstrate that the onset of coalescence depends on both the capillary number based on the viscosity of the external phase and the droplet concentration. The draining time of the thin film between droplets in apparent contact is found to depend on fluid characteristics. Such property allows us to examine the crossover between non-coalescing and coalescing droplet microflows by varying the residence time of the dispersion in the microfluidic chamber. This work characterizes droplet interaction and coalescence phenomena during multiphase transport in a simple extensional microgeometry.     

Phase-field simulation of impingement and spreading of micro-sized droplet on heterogeneous surface

A numerical investigation on the impingement and spreading of a micro-sized droplet with nonzero impact velocities on a surface with heterogeneous wettability is presented in this paper. The numerical model was implemented through phase-field simulation with finite element formulation. A simple scheme based on interfacial phase-field function gradient was proposed to track the velocity of contact line which was required to specify the dynamic contact angle based on hydrodynamic theory and molecular kinetic approach. For a circular pattern with a higher wettability than the surrounding surface, the impinging droplet final spread diameter decreases with an increasing wettability contrast. The droplet conforms to the circular patterns with smaller diameters up to a threshold, which is dictated by the wettability of the surface surrounding the pattern. Impact velocity of the droplet affects the maximum spread diameter but not the final conformability to a wettability pattern. Impingement and anisotropic spreading of a droplet on a stripe pattern was also demonstrated in a three-dimensional simulation. The high wettability contrast between the inner and outer regions of the stripe pattern confines droplet spreading and elongates the droplet in the direction of the stripe. These simulations demonstrated the conditions for a jetted micro-sized droplet to be confined to a specific area through wettability patterning, which can potentially improve the precision of current inkjet printing technology.     

Nanodroplets on a solid plane: wetting and spreading in a Monte Carlo simulation

The wetting behavior and spreading dynamics of small polymer melt droplets in the course of transition from partial to complete wetting conditions on a flat structureless solid substrate have been studied by dynamic Monte Carlo simulation. From the density profiles of the drops we determine the contact angles at varying strength of the van der Waals surface forces in the whole interval of partial wetting. The validity of Young's equation is then tested whereby the surface tension of the melt/vapor interface is derived independently from interfacial fluctuation analysis, and the surface free energy of the melt at the substrate—from the anisotropy of the local pressure at the wall. The bending rigidity of the melt/vapor interface turns out negative, as recently predicted for short-range interactions.We carry out computer experiments which show that Tanner's law for the kinetics of drop spreading holds also on nanoscopic scales. The observed density profiles of spreading droplets confirm earlier predictions that the central cap-shaped region of the droplets shrinks at the expense of a transition region (“foot”) surrounded by a precursor film which is roughly one monolayer thick. At later times the precursor film breaks into individual polymer chains and advances in typically diffusive manner as found in laboratory experiments.Eventually we investigate the impact of line tension on nanodroplets behavior at varying strength of adhesion and demonstrate that the Gretz equation which incorporates line tension into Young's rule holds even on nanoscale and predicts important properties of the drops subject to droplet size.     

A deformable surface model for real-time water drop animation

A water drop behaves differently from a large water body because of its strong viscosity and surface tension under the small scale. Surface tension causes the motion of a water drop to be largely determined by its boundary surface. Meanwhile, viscosity makes the interior of a water drop less relevant to its motion, as the smooth velocity field can be well approximated by an interpolation of the velocity on the boundary. Consequently, we propose a fast deformable surface model to realistically animate water drops and their flowing behaviors on solid surfaces. Our system efficiently simulates water drop motions in a Lagrangian fashion, by reducing 3D fluid dynamics over the whole liquid volume to a deformable surface model. In each time step, the model uses an implicit mean curvature flow operator to produce surface tension effects, a contact angle operator to change droplet shapes on solid surfaces, and a set of mesh connectivity updates to handle topological changes and improve mesh quality over time. Our numerical experiments demonstrate a variety of physically plausible water drop phenomena at a real-time rate, including capillary waves when water drops collide, pinch-off of water jets, and droplets flowing over solid materials. The whole system performs orders-of-magnitude faster than existing simulation approaches that generate comparable water drop effects.     

Dynamics of droplet transport induced by electrowetting actuation

This study reports on the dynamics of droplets in the capillary regime induced by electrowetting-on-dielectric actuation. The configuration investigated allows for comparing the experimental results with respect to the predictions of Brochard’s theoretical model (Brochard in Langmuir 5:432–438, 1989). Firstly, side-view observations using stroboscopic recording techniques were used to measure and analyse droplet deformations as well as the front and rear apparent contact angles during motion. Secondly, the influence of viscosity on the droplet velocity as a function of the applied voltage was studied. This has revealed that low Reynolds number droplet motion can be described by the simple laminar viscous model of Brochard. Finally, the influence of the dielectric thickness on the droplet dynamics was studied. It is shown that droplet velocity is limited by a saturation effect of the driving electrostatic force and that this phenomenon is very similar to that occurring in static experiments.     

A variational approach to the contact angle dynamics of spreading droplets

The modeling and the numerical representation of the contact line between a two-phase interface and a solid surface are still open problems from the physical, mathematical and numerical point of view. This paper deals with the numerical simulation of the spreading of a single droplet impacting over horizontal dry surfaces. A new variational approach to study the droplet spreading is presented by coupling an interface front-tracking algorithm to the single-fluid finite element formulation of the incompressible Navier-Stokes equations which are solved on a fixed mesh. Standard no-slip boundary conditions near the contact line lead to a singular behavior that in the variational approach is removed by introducing a generalized boundary condition which is the sum of a dissipation term and the dynamical contact angle law. By changing the intensity of the dissipation a large number of boundary conditions around the contact point are modeled, ranging from no-slip to free-slip. Since the impact is over horizontal surfaces, axisymmetric solutions are investigated with high mesh resolutions. A very precise implementation of the capillary force with a volumetric extension of the curvature has been adopted. We have considered a Lagrangian front-tracking method to advect the interface. The marker representing the contact point is simply advected by the computed velocity at the boundary without the need to extrapolate the vector field from the interior and to enforce locally mass-conservation. The model has been tested for the impact and the spreading of a droplet on solid substrates with a different wettability at low Reynolds numbers where the inertial, the viscous and the surface tension forces are all important. A number of droplet impacts with different outcomes, ranging from simple deposition to partial and complete rebound, have been reproduced. However, our simulations indicate that the formulas suggested in the literature for the dynamical contact angle should be modified to simulate a broad class of experiments.     

Predictive model on micro droplet generation through mechanical cutting

We describe the step-by-step formation process of picoliter to femtoliter volume of microdroplets by using a mechanical valve. An experiment-based theoretical model has been proposed through a parametric study of droplet formation in a microchannel with variations of the channel height, the working pressure to drive the liquids in the microchannels, and the viscosity of the dispensed phase. Three steps in the process of droplet generation have been depicted. The present study provides a clear understanding of the droplet generation process based on physical cutting method by using a mechanical valve and could be applied to advanced design for highly flexible droplet-based microfluidic systems. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. W. S. Lee, S. Jambovane and D. Kim contributed equally to this work.     

Guiding of emulsion droplets in microfluidic chips along shallow tracks defined by laser ablation

We demonstrate controlled guiding of nanoliter emulsion droplets of polar liquids suspended in oil along shallow hydrophilic tracks fabricated at the base of microchannels located within microfluidic chips. The tracks for droplet guiding are generated by exposing the glass surface of polydimethylsiloxane (PDMS)-coated microscope slides via femtosecond laser ablation. The difference in wettability of glass and PDMS surfaces together with the shallow step-like transverse topographical profile of the ablated tracks allows polar droplets wetting preferentially the glass surface to follow the track. In this study, we investigate guiding of droplets of two different polar liquids (water/ethylene glycol) with and without surfactant suspended in an oil medium along surface tracks of different depths of 1, 1.5, and 2 \(\upmu\)m. The results of experiments are also verified with computational fluid dynamics simulations. Guiding of droplets along the tracks as a function of the droplet composition and size and the surface profile depth is evaluated by analyzing the trajectories of moving droplets with respect to the track central axis, and conditions for stable guiding are identified. The experiments and numerical simulations indicate that while the track topography plays a role in droplet guiding using 1.5- and 2-\(\upmu\)m deep tracks, for the case of the smallest track depth of 1 \(\upmu\)m, droplet guiding is mainly caused by surface energy modification along the track rather than the presence of a topographical step on the surface. Our results can be exploited to sort passively different microdroplets mixed in the same microfluidic chip, based on their inherent wetting properties, and they can also pave the way for guiding of droplets along reconfigurable tracks defined by surface energy modifications obtained using other external control mechanisms such as electric field or light.     

Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton’s theory to empirical models

The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, Ca, from \(10^{-4}\) to 1 and inner-to-outer viscosity ratios, \(\lambda\), from 0, i.e. a bubble, to high-viscosity droplets. Theoretical asymptotic results obtained in the limit of small capillary number are combined with accurate numerical simulations at larger Ca. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers (\(Ca<10^{-3}\)) agrees well with Bretherton’s scaling for bubbles as long as \(\lambda <1\). For larger viscosity ratios, the film thickness increases monotonically, before saturating for \(\lambda>10^3\) to a value \(2^{2/3}\) times larger than the film thickness of a bubble. At larger capillary numbers, the film thickness follows the rational function proposed by Aussillous and Quéré (Phys Fluids 12(10):2367–2371, 2000) for bubbles, with a fitting coefficient which is viscosity-ratio dependent. This coefficient modifies the value to which the film thickness saturates at large capillary numbers. The velocity of the droplet is found to be strongly dependent on the capillary number and viscosity ratio. We also show that the normal viscous stresses at the front and rear caps of the droplets cannot be neglected when calculating the pressure drop for \(Ca>10^{-3}\).     

Contact line characteristics of liquid–gas interfaces over grooved surfaces

Surface wetting is an important phenomenon in many industrial processes including micro- and nanofluidics. The wetting characteristics depend on the surface tension forces at the three-phase contact line and can be altered by introducing patterned groove structures. This study investigates the effect of the grooves on the transition in the wetting behavior between the Cassie to Wenzel regimes. The experiments demonstrate that the wettability on a patterned surface depends on the spacing factor (S = channel depth/channel width). The spacing factor influences the contact angle, contact angle hysteresis, and the transition characteristics between the Cassie and Wenzel states. It was noted that under certain conditions (S > 1) the droplet behaved as a Cassie droplet, while exhibiting Wenzel wetting the rest of the time on the silicon microchannels tested. This criterion was used to design the groove structures on the sidewall of the proton exchange membrane fuel cell gas channel to remove the water effectively. The water coming from the land region into the gas channel is pulled by the grooves to the top wall where the airflow aided in its removal. Also, the contact angles measured on the surfaces were compared with the classical models that use wetted area, and the contact line model that uses the three-phase contact line length. It was found in our experiments that the contact line model predicts the contact angle on the patterned groove surfaces more accurately than the classical models.     

Generation of uniform-size droplets by multistep hydrodynamic droplet division in microfluidic circuits

A microfluidic system is presented to generate multiple daughter droplets from a mother droplet, by the multistep hydrodynamic division of the mother droplet at multiple branch points in a microchannel. A microchannel network designed based on the resistive circuit model enables us to control the distribution ratio of the flow rate, which dominates the division ratios of the mother droplets. We successfully generated up to 15 daughter droplets from a mother droplet with a variation in diameter of less than 2%. In addition, we examined factors affecting the division ratio, including the average fluid velocity, interfacial tension, fluid viscosity, and the distribution ratio of volumetric flow rates at a branch point. Additionally, we actively controlled the volume of the mother droplets and examined its influence on the size of the daughter droplets, demonstrating that the size of the daughter droplets was not significantly influenced by the volume of the mother droplet when the distribution ratio was properly controlled. The presented system for controlling droplet division would be available as an innovative means for preparing monodisperse emulsions from polydisperse emulsions, as well as a technique for making a microfluidic dispenser for digital microfluidics to analyze the droplet compositions.     

Lagrangian simulation of oil droplets transport due to regular waves

Dispersed oils (i.e., oil droplets) at sea are transported by convection due to waves and buoyancy and by turbulent diffusion. This work follows the common approach in the oil community of using a Lagrangian approach instead of the Eulerian approach. Our focus was on small scale simulation of oil plumes subjected to regular waves. Stokes' theory was used to obtain analytical expressions for wave kinematics. The velocity above the Mean Water Level was obtained using a second order Taylor's expansion of the velocity at the MWL. Five hundred droplets were used to simulate the plume for a duration of 60 wave periods. A Monte Carlo framework (300 simulations) was used to compute theoretical mean and variance of plumes. In addition, we introduced a novel dimensionless formulation, whose main advantage was to allow one to report distances in terms of the wave length and times in terms of the wave period. We found that the Stokes' drift was the major mechanism for horizontal transport. We also found that lighter oils propagate faster but spread less than heavier oils. Increasing turbulent diffusion caused the plume to disperse deeper in the water column and to propagate less forward. The spreading in both vertical and horizontal directions increased with an increase in turbulent diffusion. The increase in wave slope (or wave steepness) caused, in general, an increase in the downward and horizontal transport. In the context of mixing in the water column, the dimensionless formulation showed that small steepness waves with a large turbulent diffusion coefficient could result in essentially the same spreading as large steepness waves with a small turbulent diffusion coefficient.