Static Droplet Research Articles

Application of improved pseudo-potential model in examination of droplet dynamic on a rotary cylinder with high-density ratio

This work examines the ability of the improved pseudo-potential model in simulating the two-phase flows on the curved surface with the angular velocity. Owing to this purpose, the movement of a two-dimensional droplet on a cylinder is investigated using the lattice Boltzmann method. To calculate the cohesion forces the model of Kupershtokh is used. Also, the distribution functions near the surface are approximated using the bounce-back method with the ability to calculate the surface velocity. After validation, results are presented for two droplets with and without initial velocity. Accordingly, the effects of the capillary number and Galilei number in the static droplet and the effect of Reynolds number and Weber number for a thrown droplet are investigated considering effects of contact angle and angular velocity. Results show that increasing the Galilei number leads to droplet dripping from the cylinder, while the reduction of the capillary number causes the droplet to oscillate before reaching the equilibrium state. Also, at low angular velocities, the dripping of the droplet is accelerated but with a further increase of the angular velocity the droplet completely covers the surface of the cylinder without detaching it. On the other hand, the inertia of the droplet causes more surface wetting, while further increase in the inertia causes the droplet to be fragmented and it removes the surface before complete surface wetting.

Entropy generation analysis of wet-steam flow with variation of expansion rate using NURBS-based meshing technique

In this paper, the entropy generation is introduced as a criterion to analyze the impact of variation of expansion rate in a two-dimensional viscous wet-steam flow through stationary cascades of a steam turbine. In addition, for the first time the NURBS-based mesh generation method is introduced and assessed in the field of wet-steam flow. In the mentioned method, the computational grid with “curved” boundaries is generated by non-uniform rational B-spline (NURBS) surface that describes the geometry of the cascade. The results, which are validated against well-established experiments, reveal that compared to the typical H-type grid, employing the generated NURBS-based mesh significantly reduce the computational error of numerical simulation. According to the obtained results, the prediction errors of static pressure distribution and droplet average radius are reduced by 31% and 78.44%, respectively. Furthermore, it is observed that decreasing the expansion results in moving the nucleation zone toward downstream of the blade and increasing the rate of droplets nucleation. Additionally, the liquid mass fraction as well as the amount of entropy and total entropy generation in the fluid flow increases.

Ratio analysis of two mechanisms of static droplet evaporation driven by pressure difference

When droplet moving in the steam-water separator, the gas pressure will decrease due to flow resistance and the liquid-vapor equilibrium at the droplet surface will be broken. The droplet evaporates continuously as a result. The fast evaporation mechanism and thermal balance evaporation mechanism are presented for the droplet evaporation at cases of pressure variation. The droplet phase change model due to pressure variation is formulated. Subsequently, the effects of pressure difference on the droplet evaporation characteristics are analyzed. The ratio analysis of the two mechanisms is conducted. The droplet evaporation map over the ratio of two mechanisms is drawn. The numerical results indicate that the pressure difference significantly influences the droplet evaporation characteristics. Under most conditions, the droplet evaporation characteristics are dominated by the combined action of two mechanisms. For large pressure difference and small droplets, the fast evaporation mechanism dominates the evaporation process, and vice versa. With increasing pressure difference between the droplet and the surrounding environment, the droplet evaporates faster and the percentage of fast evaporation mechanism decreases gradually. The present work can lay the foundation for further investigation on the moving droplet evaporation.

Motion of an oil droplet through a capillary with charged surfaces

A model developed by Wilmottet al. (J. Fluid Mech., vol. 841, 2018, pp. 310–350) for the advance of a charged oil droplet along a charged capillary pore is considered. The oil droplet is surrounded by an aqueous phase filling the pore, and the model considers a uniformly curved capillary static droplet front plus an aqueous thin film separating the body of the oil droplet from the capillary wall, with these two regions being joined by a transition region. The methodology follows a classical asymptotic approach proposed by Bretherton (J. Fluid Mech., vol. 10, 1961, pp. 166–188) but incorporates additional electro-osmotic effects (specifically an electro-osmotic disjoining tension) due to the charged surfaces. A number of dimensionless parameters control the model’s behaviour, of which the most important is denoted$\unicode[STIX]{x1D712}^{\prime }$and represents the ratio between the ‘nominal’ thickness of the aqueous film (as determined neglecting any electrostatic effects) and the Debye length within the film, which is sensitive to ion concentrations and hence to salinity. When$\unicode[STIX]{x1D712}^{\prime }$is large, electro-osmotic effects are screened and Bretherton’s classical results are recovered. However as$\unicode[STIX]{x1D712}^{\prime }$decreases, electro-osmotic effects come into play and the film becomes much thicker than Bretherton’s prediction to ensure that screening effects are not altogether lost, and also there is a noticeable increase in the pressure needed to drive the droplet front along. These results apply with minor variations in the case of singly charged surfaces (charge on either oil or on the capillary wall), oil and wall surfaces with like charges, or oil and wall surfaces with opposite but unequal charges. However in the case of opposite and equal charges, the system’s behaviour changes dramatically. There is now a conjoining electro-osmotic pressure rather than a disjoining tension, the film becomes thinner than the analogous Bretherton film, and the pressure needed to drive the droplet front along decreases. Surprisingly in this case, for sufficiently small$\unicode[STIX]{x1D712}^{\prime }$, the work done by the conjoining pressure can exceed the work done against viscous dissipation, meaning the pressure required to drive the droplet front is not just smaller than in Bretherton’s predictions but also slightly less than would be estimated based on capillary forces alone. Although the main effect of reducing salinity is to increase Debye length and hence reduce$\unicode[STIX]{x1D712}^{\prime }$, salinity also affects surface charges. A situation is explored whereby reducing salinity affects charges, producing a switch from disjoining tensions to conjoining pressures and back again: this leads to a non-monotonic response in film thickness and pressure required to drive the droplet front along.

Slippery Properties and the Robustness of Lubricant-impregnated Surfaces

Inspired by nepenthes pitcher plants, Lubricant-Impregnated Surfaces (LISs) are surfaces with lubricant infused in the textures which form slippery interfaces. In this paper, we investigated slippery properties and the robustness of LISs with different micro-texture topologies (i.e., no textures, micro-pillar textures and micro hole textures), including original LISs and LISs rinsed by water. We measured the static contact angle, sliding angle and droplet motions on the LISs, using a contact angle instrument and a Particle Image Velocimetry (PIV) system. Similar contact angles and small sliding angles were observed on all original LISs, which indicated that an oil-layer existed on each LIS’s interface. After rinsed by water, the sliding angle increased obviously and the slip velocity decreased, which meant that the LISs slippery properties deteriorated in different degrees. Among all the LISs in our experiments, LIS with micro pillar textures has the best slippery performance and robustness before and after rinsed. We found that the LISs’ slippery properties were closely related to the states of the oil-layer on the interface, which were changed after rinsed. For the LIS with micro pillar textures, a thin layer of lubricant can sustain on the interface even after rinse, which made the droplet slide smoothly on the surface, with a lower sliding angle and a larger sliding velocity. This indicates that the proper micro-texture will enhance the slippery property and make it last longer.

Superhydrophobic surfaces-based redox-induced electricity from water droplets for self-powered wearable electronics

Making use of water energy is an attractive, renewable and clean way to derive some electronic devices. Although flowing water droplets can be utilized to generate electric signals, the corresponding origins are still unclear due to the fluid-flow-induced various effects, while generating electricity from static water droplets still remains a challenge. Here, we report redox-induced electricity from static water droplets for self-powered wearable electronics, where superhydrophobic surfaces with nanostructures not only can be utilized to enhance the output current, but also can increase the output stability. The fabricated device can deliver an output voltage of about 0.78 V and an output current of about 0.25 mA with a corresponding power density of about 30 mW/cm3 by using a 10-μL water droplet. Only three water droplets can be utilized to directly drive a wearable watch and sustainably power a temperature sensor for monitoring temperature variations of a human hand.

Hydrodynamic control of droplet breakup, immobilization, and coalescence for a multiplex microfluidic static droplet array

Droplet manipulation is an essential technique in droplet-based microfluidics for a versatile assay platform. To improve the assay reliability, the droplet manipulation error should be minimized. Here, we study the droplet behavior for multiplex microfluidic static droplet array (μSDA) formation, including breakup, immobilization, and coalescence. Hydrodynamic resistance control is the basic principle of droplet manipulation for μSDA formation. We show the relationship between droplet dynamics and microfluidic channel design using dimensionless parameters, including capillary number, droplet extension, and the channel resistance ratio. In addition, we identify the critical factor between droplet breakup and non-breakup conditions as a function of the capillary number and initial droplet extension. This critical factor can also be varied by changing the hydrodynamic resistance ratio and entrance geometries of the trap chamber. We show that by using an optimized microfluidic design and optimized flow conditions, an error-free 100 multiplex μSDA is formed through combinatorial coalesce of the droplets via microvalve operation. Our results provide an immediately applicable microfluidic design and a direct guide for device operation parameters as physical properties of samples to improve assay reliability.

Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio

In this paper, a novel lattice Boltzmann (LB) model based on the Allen-Cahn phase-field theory is proposed for simulating axisymmetric multiphase flows. The most striking feature of the model is that it enables to handle multiphase flows with large density ratio, which are unavailable in all previous axisymmetric LB models. The present model utilizes two LB evolution equations, one of which is used to solve fluid interface, and another is adopted to solve hydrodynamic properties. To simulate axisymmetric multiphase flows effectively, the appropriate source term and equilibrium distribution function are introduced into the LB equation for interface tracking, and simultaneously, a simple and efficient forcing distribution function is also delicately designed in the LB equation for hydrodynamic properties. Unlike many existing LB models, the source and forcing terms of the model arising from the axisymmetric effect include no additional gradients, and consequently, the present model contains only one non-local phase field variable, which in this regard is much simpler. In addition, to enhance the model’s numerical stability, an advanced multiple-relaxation-time (MRT) model is also applied for the collision operator. We further conducted the Chapman-Enskog analysis to demonstrate the consistencies of our present MRT-LB model with the axisymmetric Allen-Cahn equation and hydrodynamic equations. A series of numerical examples, including static droplet, oscillation of a viscous droplet, breakup of a liquid thread, and bubble rising in a continuous phase, are used to test the performance of the proposed model. It is found that the present model can generate relatively small spurious velocities and can capture interfacial dynamics with higher accuracy than the previously improved axisymmetric LB model. Besides, it is also found that our present numerical results show excellent agreement with analytical solutions or available experimental data for a wide range of density ratios, which highlights the strengths of the proposed model.

Finite volume Ghost Fluid Method implementation of interfacial forces in PISO loop

In this work, we implement interfacial forces (surface tension, hydrostatic and viscous forces) by enlisting the finite volume discretization of GFM (Ghost Fluid Method) using A-CLSVOF (Algebraic Coupled Level-Set/Volume-of-Fluid) method for the mass conservative, and smooth interface description. The widely used PISO momentum solution to resolve the pressure–velocity coupling is presented along with the present GFM discretization and its placement within the PISO loop. The pressure jump at the interface due to the interfacial forces is made sharp via direct calculation of the modified pressure matrix coefficients corresponding to targeted interfacial cells, and as a source term for the jump value itself. The Level-Set field is enlisted for curvature computation in A-CLSVOF and for the interpolation and weighting of the relative contribution of the capillary force in adjacent for the matrix coefficients in the FV framework. To assess the A-CLSVOF/GFM performance, four canonical cases were studied. In the case of a static droplet in suspension, A-CLSVOF/GFM produces a sharp and accurate pressure jump compared to the traditional CSF implementation of A-CLSVOF. The interaction of viscous and capillary forces is proven to be accurate and consistent with theoretical results for the classical capillary wave. For the linear two-layer shear flow, GFM sharp treatment of the viscosity captured the velocity gradient across the interface and removed the diffusion of the viscous stresses caused by the discontinuous material properties. Finally, the combination of all GFM improvements proposed in this study are compared to experimental findings of terminal velocity for a gaseous bubble rising in a viscous fluid. GFM outperforms CSF with errors of 4.6% and 14.0% respectively.

Phase-field-based lattice Boltzmann model for multiphase ferrofluid flows

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A novel forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and Spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocities in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. At last, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomenon of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Observation of a mixed regime for an impinging droplet on a sessile droplet

This article reports experimental results of the presence of a mixed regime where rebound or coalescence occurs when a liquid droplet with low impact velocity impinges on a static sessile droplet, deposited on a flat aluminum surface. In particular, the present study suggests possible reasons why this mixed occurs with nearly the same probabilities with the use of the sequential images captured by two high-speed cameras from the 767 experimental cases. It is also demonstrated that the mixed regime is substantially affected by static droplet volumes, Weber numbers, and offset distances between impinging and static droplets. In the mixed regime, rebound may occur because a relatively large air-film maintains to prevent film drainage for coalescence. The lubrication theory is utilized to estimate film thickness between two droplets and is compared to the critical film thickness. The upper limit of the Weber numbers in the mixed regime decreases with an increase in the offset distance, owing to a rotational droplet motion causing air-film elongation. The contact time during rebound slightly increases with the static sessile droplet volume. It is observed that the measured contact times increases with a decrease in impact velocity, showing cushioning effect by air-film. On the other hand, a coalescence is observed to intermittently in the mixed regime because the air-film layer existing at the interface has an irregular shape by oscillation of an impinging droplet.

An implicit surface tension model for the analysis of droplet dynamics

A Lagrangian incompressible fluid flow model is extended by including an implicit surface tension term in order to analyze droplet dynamics. The Lagrangian framework is adopted to model the fluid and track its boundary, and the implicit surface tension term is used to introduce the appropriate forces at the domain boundary. The introduction of the tangent matrix corresponding to the surface tension force term ensures enhanced stability of the derived model. Static, dynamic and sessile droplet examples are simulated to validate the model and evaluate its performance. Numerical results are capable of reproducing the pressure distribution in droplets, and the advancing and receding contact angles evolution for droplets in varying substrates and inclined planes. The model is stable even at time steps up to 20 times larger than previously reported in literature and achieves first and second order convergence in time and space, respectively. The present implicit surface tension implementation is applicable to any model where the interface is represented by a moving boundary mesh.

Biocompatible/Biodegradable Electrowetting on Dielectric Microfluidic Chips with Fluorinated CTA/PLGA.

One of the major hurdles in the development of biocompatible/biodegradable EWOD (Electrowetting-on-dielectric) devices is the biocompatibility of the dielectric and hydrophobic layers. In this study, we address this problem by using reactive ion etching (RIE) to prepare a super-hydrophobic film combining fluorinated cellulose triacetate (CTA) and poly (lactic-co-glycolic acid) (PLGA). The contact angle (CA) of water droplets on the proposed material is about 160°. X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM) characterizations indicate that a slight increase in the surface roughness and the formation of CFx (C-F or CF2) bonds are responsible for the super-hydrophobic nature of the film. Alternating Current (AC) static electrowetting and droplet transportation experiments evidence that contact angle hysteresis and contact line pinning are greatly reduced by impregnating the CTA/PLGA film with silicon oil. Therefore, this improved film could provide a biocompatible alternative to the typical Teflon® or Cytop® films as a dielectric and hydrophobic layer.

Scalable static droplet array for biochemical assays based on concentration gradients

Many important biological assays demand rapid and low-cost screening systems. In this study, we present a scalable static droplet array (SDA) that can generate a high-resolution concentration gradient. The system consists of discrete sample dispensing channels, array units, and microvalves for droplet generation and droplet storage. We utilize negative pressure on a suction valve located below array chambers to enhance the capacity of droplet filling. The size of the droplets is controlled by valve actuation time, and array chambers can contain up to 32 droplets with a 20-millisecond valve actuation time. We present various profiles of concentration gradients generated by the combined storage of binary concentrations of droplets. As a proof of concept, we performed an enzymatic inhibition assay for validating our system with IC50 and the Hill coefficient using β–galactosidase (β-gal), di(β-d-galactopyranoside) (FDG) and 2-Phenylethyl β-d-thiogalactoside (PETG), and achieved an IC50 value of 2.18 μM and a Hill coefficient of 1.11, which agrees well with results in the literature. We anticipate that this system will serve as a general assay platform that is capable of high-throughput screening for various biological assays and imaging.

Rational Design of the Nanostructure Features on Superhydrophobic Surfaces for Enhanced Dynamic Water Repellency

Biomimetic surfaces with various extents of liquid adhesion intensely appeal to many researchers due to their academic significance and potential industry applications. The present work aims to discuss the relationship between bouncing dynamics of impact droplets and static liquid adhesion driven by micro/-nanostructure features. Here, we fabricated three types of nanostructure (nanotube, nanomesh, and nanowire) superhydrophobic surfaces based on the TiO2 nanomaterials, and all of these resultant surfaces were endowed with the robust superhydrophobicity, and showed the low liquid adhesion with the sliding angles from 7.5° to 3°. Subsequently, the bouncing dynamics of impact droplets on these surfaces were evaluated and showed remarkable distinctions with different capacity to rebound off. This is explained in that the impact droplet has induced a higher capillary-induced adhesion force interaction as compared to the static droplet on the nanotube structure surface due to the existence of dynamic pressure ...

A computational framework for interface-resolved DNS of simultaneous atomization, evaporation and combustion

A computational framework for interface-resolved direct numerical simulations (DNS) of simultaneous atomization, evaporation and combustion process is proposed. The present work utilizes a level set method to implicitly capture the gas–liquid interface and the ghost fluid method (GFM) to accurately address jump conditions across the interface. Specific care has been devoted to the discretization of the convective term and diffusive term for the species and energy equations. The level set method with a sub-cell resolution of the interface is employed and a semi-Lagrangian scheme for the discretization of the level set equation with an evaporation source term is proposed. The one-step global reaction model of n-heptane is used for the vapor combustion. To the best of our knowledge, this is the first computational framework that has the capability to simulate spray combustion with an interface-resolved method. The present framework has been validated in several cases, including the one-dimensional evaporation and the static droplet evaporation for low ambient temperature, the Stefan problem, the Sucking problem, the evaporation of static and moving droplet for high ambient temperature, and the combustion of static and moving droplet. Finally, the integrated simulation of droplet collision and combustion is performed to evaluate the accuracy and robustness of the present method.

Simulation on a gravity-driven dripping of droplet into micro-channels using the lattice Boltzmann method

Micro-channels are prevalent extensively in microelectronic devices and heat-exchange equipment. In this study, a single-component multiphase (SCMP) pseudo-potential lattice Boltzmann model is employed to investigate the dripping of a droplet driven by gravity into micro-channels in two-dimensional coordinates. The model has capabilities that make it applicable to cases with high density ratios, low viscosities, and tunable surface tension. Tests on static droplets verify these capabilities and exhibit the effect of different parameters. Four typical deformation processes are identified: free falling, attachment, flowing, and dripping. Furthermore, the effects of different parameters, such as wettability of walls, are compared. And the critical values of dimensionless numbers are investigated. The results quantificationally shows that the critical break-up number (Ca) is increasing and the critical dripping number (Bo) is decreasing with the increase of fluid–solid strength on walls.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows.

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Numerical simulation of diffusion process in T-shaped micromixer using Shan-Chen Lattice Boltzmann Method

A multicomponent Lattice Boltzmann Method (LBM) scheme is employed to study the performance of a T-shaped micromixer with obstacles in its main channel. This solution was proposed in order to speed-up the diffusive mixing process which occurs at very low-Reynolds flow regime. The multicomponent LBM was firstly validated against well-documented cases like the simulation of a static droplet and the layered two-dimensional flow in a channel. Then two-dimensional simulations of the T-mixer are conducted with different flow rates and obstacle layouts demonstrating the improvement of the device mixing efficiency induced by this solution. In addition, the results show a very good agreement with a previous study in which a commercial code was adopted and provide guidelines to conveniently place the obstacles in a T-shape micromixer.

Statics and dynamics of liquid barrels in wedge geometries

We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle $\unicode[STIX]{x1D703}_{e}$, confined in a solid wedge geometry of opening angle $\unicode[STIX]{x1D6FD}$. We focus on a mostly non-wetting regime, given by the condition $\unicode[STIX]{x1D703}_{e}-\unicode[STIX]{x1D6FD}>90^{\circ }$, where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales.