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.     

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.     

Measurement of dynamic surface tension using helical flow of a viscous liquid in a pool of another viscous liquid inside a micro-channel

Measurement of surface tension (s.t.) and critical micelle concentration (c.m.c.) of a surfactant in dynamic condition is important for several engineering applications, for which, the interface between two or more different phases does not remain constant but alters and replenishes continuously with flow of the fluids so that equilibrium may not be reached between the bulk and the interface. There are however not many methods for measuring these quantities in dynamic experiments which mimics the real dynamic situations. In this report, we present a novel two-phase flow pattern inside a triple-helical micro-channel using which, we show that it may be possible to measure the dynamic s.t. of a liquid. When two immiscible liquids such as oil and water are pumped into it, at a certain range of flow rates, oil flows as the continuous phase, whereas water remains in it as a wavy filament, the wavelength of which varies with the flow rates of oil and water but also on the interfacial tension between these two liquids. We show that wavelength decreases with increase in concentration of a solute attaining a minima at the c.m.c. A simple scaling analysis captures most experimental observations.     

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.     

A generalized continuous surface tension force formulation for phase-field models for multi-component immiscible fluid flows

We present a new phase-field method for modeling surface tension effects on multi-component immiscible fluid flows. Interfaces between fluids having different properties are represented as transition regions of finite thickness across which the phase-field varies continuously. At each point in the transition region, we define a force density which is proportional to the curvature of the interface times a smoothed Dirac delta function. We consider a vector valued phase-field, the velocity, and pressure fields which are governed by multi-component advective Cahn–Hilliard and modified Navier–Stokes equations. The new formulation makes it possible to model any combination of interfaces without any additional decision criteria. It is general, therefore it can be applied to any number of fluid components. We give computational results for the four component fluid flows to illustrate the properties of the method. The capabilities of the method are computationally demonstrated with phase separations via a spinodal decomposition in a four-component mixture, pressure field distribution for three stationary drops, and the dynamics of two droplets inside another drop embedded in the ambient liquid.     

Lattice Boltzmann simulation of viscous fingering phenomenon of immiscible fluids displacement in a channel

In this paper, the viscous fingering phenomenon of two immiscible fluids in a channel is studied by applying the lattice Boltzmann method (LBM). The fundamental physical mechanisms of a finger formation or the interface evolution between immiscible fluids are described in terms of the relative importance of viscous forces, surface tension, and gravity, which are quantifiable via the dimensionless quantities, namely, capillary number, Bond number and viscosity ratio between displaced fluid and displacing fluid. In addition, the effect of wettability on flow behaviour of fluids is investigated for the cases with and without consideration of gravity, respectively. The numerical results provide a good understanding of the mechanisms of viscous fingering phenomenon from a mesoscopic point of view and confirm that the LBM can be viewed as a promising tool for investigating fluid behaviour and other immiscible displacement problems.     

Micro-PIV investigation of the internal flow transitions inside droplets traveling in a rectangular microchannel

This paper discusses the studies on the internal flow field of droplets traveling in a rectangular microchannel by means of microparticle image velocimetry, specifically concentrating on the effects of capillary number, viscosity ratio and interfacial tension. The flow topology is predominantly dependent on the capillary number. It shows that the evident transitions from three pairs of recirculation zones at lower capillary numbers to one pair of recirculation zones near the sidewalls with low velocity in the central area at intermediate capillary numbers, then to a pair of recirculation zones closest to the axial centerline with high velocity in the central area at higher capillary numbers. There are two critical capillary numbers increasing with viscosity ratio in the evolution of flow features. Droplet size only influences two velocity components values other than the flow topology within intervals separated by the critical values. The equilibrium mechanism of viscous friction force and Marangoni stress dominate the internal topological transition in a surfactant added system. The obtained internal fluid phenomena inside droplets are beneficial to provide a guideline for screening of biochemical reaction conditions in the device.     

Micro-droplet formation in non-Newtonian fluid in a microchannel

Micro-droplet formation from an aperture with a diameter of micrometers is numerically investigated under the cross-flow conditions of an experimental microchannel emulsification process. The process involves dispersing an oil phase into continuous phase fluid through a microchannel wall made of apertured substrate. Cross-flow in the microchannel is of non-Newtonian nature, which is included in the simulations. Micro-droplets of diameter 0.76–30 μm are obtained from the simulations for the apertures of diameter 0.1–10.0 μm. The simulation results show that rheology of the bulk liquid flow greatly affects the formation and size of droplets and that dispersed micro-droplets are formed by two different breakup mechanisms: in dripping regime and in jetting regime characterized by capillary number Ca. Relations between droplet size, aperture opening size, interfacial tension, bulk flow rheology, and disperse phase flow rate are discussed based on the simulation and the experimental results. Data and models from literature on membrane emulsification and T-junction droplet formation processes are discussed and compared with the present results. Detailed force balance models are discussed. Scaling factor for predicting droplet size is suggested.     

Thin film evaporation in microchannels with interfacial slip

We investigate the role of interfacial slip on evaporation of a thin liquid film in a microfluidic channel. The effective slip mechanism is attributed to the formation of a depleted layer adhering to the substrate–fluid interface, either in a continuum or in a rarefied gas regime, as a consequence of intricate hydrophobic interactions in the narrow confinement. We appeal to the fundamental principles of conservation in relating the evaporation mechanisms with fluid flow and heat transfer over interfacial scales. We obtain semi-analytical solutions of the pertinent governing equations, with coupled heat and mass transfer boundary conditions at the liquid–vapor interface. We observe that a general consequence of interfacial slip is to elongate the liquid film, thereby leading to a film thickening effect. Thicker liquid films, in turn, result in lower heat transfer rates from the wall to liquid film, and consequently lower mass transfer rates from the liquid film to the vapor phase. Nevertheless, the total mass of evaporation (or equivalently, the net heat transfer) turns out to be higher in case of interfacial slip due to the longer film length. We also develop significant physical insights on the implications of the relative thickness of the depleted layer with reference to characteristic length scales of the microfluidic channel on the evaporation process, under combined influences of the capillary pressure, disjoining pressure, and the driving temperature differential for the interfacial transport.     

Liquid–liquid micro-dispersion in a double-pore T-shaped microfluidic device

For further understanding the dispersion process in the T-shaped microfluidic device, a double-pore T-shaped microchannel was designed and tested with octane/water system to form monodispersed plugs and droplets in this work. The liquid–liquid two-phase flow patterns were investigated and it was found that only short plugs, relative length L/w < 1.4, were produced. Additionally, the droplets flow was realized at phase ratios (F _C /F _D) just higher than 0.5, which is much smaller than that in the single-pore T-shaped microchannels. A repulsed effect between the initial droplets was observed in the droplet formation process and the periodic fluctuation flow of the dispersed phase was discussed by analyzing the resistances. Besides, the effect of the two-phase flow rates on the plug length and the droplet diameter was investigated. Considering the mutual effect of the initial droplets and the equilibrium between the shearing force with the interfacial tension, phase ratio and Ca number were introduced into the semi-empirical models to present the plug and droplet sizes at different operating conditions.     

Fluid flow and heat transfer in the evaporating thin film region

The evaporating thin film region is an extended meniscus beyond the apparent contact line at a liquid/solid interface. Thin film evaporation plays a key role in a highly efficient heat pipe. A detailed mathematical model predicting fluid flow and heat transfer through the thin film region is developed. The model considers the effects of inertial force, disjoining pressure, surface tension, and curvature. Utilizing the order analysis, the model is simplified and can be numerically solved for the thin film profile, interfacial temperature, meniscus radius, heat flux distribution, velocity distribution, and mass flow rate in the evaporating thin film region. The prediction shows that while the inertial force can affect the thin film profile, interfacial temperature, meniscus radius, heat flux distribution, velocity distribution, and mass flow rate, in particular, near the non-evaporating region, the effect can be neglected. It is found that a maximum velocity, a maximum heat flux, and a maximum curvature exist for a given superheat, but the locations for these maximum values are different.     

“From microtiter plates to droplets” tools for micro-fluidic droplet processing

Droplet-based microfluidic allows high throughput experimentation in with low volume droplets. Essential fluidic process steps are on the one hand the proper control of the droplet composition and on the other hand the droplet processing, manipulation and storage. Beside integrated fluidic chips, standard PTFE-tubings and fluid connectors can be used in combination with appropriate pumps to realize almost all necessary fluidic processes. The segmented flow technique usually operates with droplets of about 100–500 nL volume. These droplets are embedded in an immiscible fluid and confined by channel walls. For the integration of segmented flow applications in established research workflows—which are usually base on microtiter plates—robotic interface tools for parallel/serial and serial/parallel transfer operations are necessary. Especially dose–response experiments are well suited for the segmented flow technique. We developed different transfer tools including an automated “gradient take-up tool” for the generation of segment sequences with gradually changing composition of the individual droplets. The general working principles are introduced and the fluidic characterizations are given. As exemplary application for a dose–response experiment the inhibitory effect of antibiotic tetracycline on Escherichia coli bacteria cultivated inside nanoliter droplets was investigated.     

Formation of fully closed microcapsules as microsensors by microfluidic double emulsion

Microcapsules templated from microfluidic double emulsions attract a great attention due to their broad new potential applications. We present a method to form transparent polymer microcapsules in small sizes of ~30 μm with aqueous cores and fully closed shells. We controlled the size ratio of the aqueous core to the polymer shell not only by flow rates of the double emulsions, but also by synergetic interaction between surfactants at the interface of immiscible fluids. We also found that fully closed shells can be formed by generating the double emulsion droplets in a jetting regime, in which the aqueous cores are confined centrally in the double emulsion droplets. We demonstrated the formation of barcodes in these microcapsules for multiplexed bioassays. These transparent microcapsules also have wide and high potentials for the development of various microsensors by functionalizing the liquid-state cores with compounds sensitive and responsive to temperature, light or electromagnetic field.     

Numerical and experimental investigations of the formation process of ferrofluid droplets

This paper reports both experimental and numerical investigations of the formation process of ferrofluid droplets in a flow focusing configuration with and without an applied magnetic field. In the experiment, the homogenous magnetic field was generated using an electromagnet. The magnetic field in the flow direction affects the formation process and changes the size of the droplets. The change in the droplet size depends on the magnetic field strength and the flow rates. A numerical model was used to investigate the force balance during the droplet breakup process. A linearly magnetizable fluid was assumed. Particle level set method was employed to capture the interface movement between the continuous fluid and the dispersed fluid. Results of the droplet formation process and the flow field are discussed for both cases with and without the magnetic field. Finally, experimental and numerical results are compared.     

Modelling droplet motion and interfacial tension in filters collecting liquid aerosols

Extensive experimental investigations have shown some of the differences between the behaviours of the barrel and the clamshell shapes of droplets on filter fibres in flow fields. Realistic flow velocities (such as those used in many industrial filter systems) were utilised. The forces acting are air drag, interfacial tension and gravity. The properties of the interfacial restoring force are modelled, and show agreement with the experimental results, at least in the linear extension region before the onset of oscillatory behaviour of the droplets (induced by instability of the flow field). The model for the oscillatory behaviour is explored, and the natural frequencies of oscillation in the radial and transverse directions are shown to be the same, for the barrel shape. The clamshell shape also has the same natural frequencies, but they are different to those of the barrel shape. The coupling of the radial and transverse oscillation modes is explored for both the barrel and clamshell shape. Some contact angle results are given, both without airflow acting on the droplet and with increasing airflow.     

Droplet coalescence by geometrically mediated flow in microfluidic channels

Microfluidic flow is geometrically mediated at a trifurcating junction allowing periodically formed, equally spaced out emulsion droplets to redistribute and fuse consistently. This is achieved by controlling the ratio between the droplet transport time across the trifurcating junction and the drainage time of the fluid volume separating the droplets t _r/t _d. Three different microfluidic trifurcation geometries have been designed and compared for their droplet fusion efficiencies. Fusion of up to six droplets has been observed in these devices. The fusion of two droplets occurs when t _r/t _d is equal to 1.25 and the number of fused droplets increases with t _r/t _d. When the junction length (d) is 216 μm fusion of 2–6 six droplets are possible however when the junction length is increased to 360 μm fusion of only two droplets is observed.     

Y- and T-junction microfluidic devices: effect of fluids and interface properties and operating conditions

Water-in-oil emulsions were produced in microchannels with Y- and T-junction geometries by individual droplet generation. For each microchannel configuration, the effect of the fluids and interface properties as well as of the process conditions was evaluated. The size of the droplets depended mainly on the relative velocity between continuous and dispersed phases and the relative fluid viscosity between phases. Those variables were related to the shear stress between the phases, which caused the droplet detachment. In addition, the interfacial forces played a minor role in Y-junction, and they had no effect in the droplets formation in T-junction microchannels. In Y-junction, a large variation in the droplet size was observed, depending on the system composition and the operating conditions. At low relative velocity and fluid viscosity, no droplets were generated. In contrast, the process in T-junction resulted in a lower variation of droplets size and the droplets were formed even at less favorable conditions. Such results indicate that the knowledge of the mechanism of droplets generation in each microchannel geometry makes it possible to choose the appropriate configuration according to the type of fluid, and the operating conditions can be adjusted to obtain the desired final emulsion.     

Droplet bistability and its application to droplet control

Novel methods for controlling droplets precisely in the microchannels are presented, which employ microfluidic bifurcation channels with outlet restrictions based on droplet bistability, utilizing the Laplace pressure caused by interfacial tension that arises when a droplet encounters a narrow restriction. The bistable geometry possesses two symmetric branches and restrictions that operate as capillary valves allowing a droplet to be trapped in front of a restriction and released through it when the next droplet arrives at the other restriction. This trap-and-release occurs repeatedly and regularly by the succeeding droplets. Furthermore, a critical flow rate is found to exist, which is necessary for achieving droplet bistability. This occurs only when the apparent Laplace pressure surpasses the pressure drop across the droplet. By adopting a simplified hydrodynamic resistance model, the droplet bistable mechanism is clearly explained, and droplet bistability is shown to enable the simple and precise control of droplets at a bifurcation channel. Thus, precise droplet traffic control is achieved at a bifurcation channel connected with a single inlet channel and two outlet channels using an appropriate channel design that induces droplet bistability. In particular, droplets are distributed at a junction in a manner of perfect alternation or perfect switching between the two outlet channels. This article proposes that bistable components can be used as elaborately embedded droplet traffic signals for red light (trap), green light (release), and turn light (switching) in complex microfluidic devices, where droplets provide both the chemical or biological materials and the processing signal.     

Modelling of annular flow through pipes and T-junctions

This paper describes a computational model for the prediction of isothermal annular two-phase flow in vertical and horizontal intersecting pipes and presents the results of its application to predict phase separation in a horizontal T-junction. The method is based on computational fluid dynamics techniques (CFD) to compute the dispersed core flow simultaneously with the flow of the liquid film along the walls. The core is represented as a dispersed two-phase mixture in which the droplets are tracked using a Lagrangian technique; the wall liquid film is modelled as a thin boundary layer. Full account is made of the interaction between the wall-film and the droplet flow in the core through mass and momentum transfer mechanisms. The method has already been validated against experimental data for fully developed annular flow in vertical and horizontal pipes; there, the predicted film thickness was found to be in satisfactory agreement with data obtained from the literature. The method is now applied to the phenomenon of phase separation occurring in T-junctions where it is found that the predictions for phase split agree quite well with measurements from an independent experiment for a range of phase split ratios. The predictions for wall-film thickness also exhibit similar trends to the data but do not quite match the locations where wall-film thickness peaks occur.     

Fluid dynamic behavior of dispensing small droplets through a thin liquid film

This paper presents a technology for dispensing droplets through thin liquid layers. The system consists of a free liquid film, which is suspended in a frame and positioned in front of a piezoelectric printhead. A droplet, generated by the printhead, merges with the film, but due to its momentum, passes through and forms a droplet that separates on the other side and continues its flight. The technology allows the dispensing, mixing and ejecting of picolitre liquid samples in a single step. This paper overviews the concept, potential applications, experiments, results and a numerical model. The experimental work includes studying the flight of ink droplets, which ejected from an inkjet print head, fly through a free ink film, suspended in a frame and positioned in front of the printhead. We experimentally observed that the minimum velocity required for the 80 pl droplets to fly through the 75 ± 24 μm thick ink film was of 6.6 m s^?1. We also present a numerical simulation of the passage of liquid droplets through a liquid film. The numerical results for different initial speeds of droplets and their shapes are taken into account. We observed that during the droplet–film interaction, the surface energy is partially converted to kinetic energy, and this, together with the impact time, helps the droplets penetrate the film. The model includes the Navier–Stokes equations with continuum-surface-tension force derived from the phase-field/Cahn–Hilliard equation. This system allows us to simulate the motion of a free surface in the presence of surface tension during merging, mixing and ejection of droplets. The influence of dispensing conditions was studied and it was found that the residual velocity of droplets after their passage through the thin liquid film well matches the measured velocity from the experiment.