The spreading of a viscous microdrop on a solid surface

The spreading of a liquid microdrop across a solid surface is examined using the interface formation model. This model allows for variable surface tension at constant temperature and a flow induced Maragoni effect, by incorporating irreversible thermodynamics into the continuum model. The model is solved for small Capillary number and small Reynolds number. This problem has been considered before for much larger drops in Shikhmurzaev (Phys Fluids 9:266, 1997a), which examined the spreading of a drop for ε = τ U _CL/R ≪ 1, where U _CL is the speed of the moving contact line across the solid surface, τ is the surface tension relaxation time of the viscous liquid, and R is a typical length scale for the size of the drop. This paper extends that work by examining ε = O(1), which will be shown to be the appropriate scaling for very small liquid drops, on the scale of micrometres or less.     

Molecular simulations of droplet evaporation by heat transfer

Droplet evaporation by heat transfer is investigated by molecular dynamics simulations for a pure Lennard-Jones fluid. Two different initial conditions are treated: (1) a droplet surrounded by its vapor in equilibrium, (2) a cold droplet surrounded by warm vapor. In both cases heat is transferred from a heat bath. Results are the numbers of droplet molecules N _d and density, drift velocity, and temperature profiles as functions of time. For the small droplets considered N _d depends on the definition of a droplet molecule. The density profiles as function of time show a transition from a droplet with liquid–vapor interface to a cluster of interfacial type and finally to the gas state. The temperature at a given time is nearly constant within the droplets or clusters but strong gradients occur in the gas. In case of evaporation of a cold droplet surrounded by warm vapor we observed initially cooling down of the droplet corresponding to pressure jump evaporation and thereafter slower evaporation because of lower initial state vapor density.     

Droplets coalescence and mixing with identical and distinct surface tension on a wettability gradient surface

The influence of identical and distinct surface tensions on the coalescence and mixing of droplets after a direct collision on a wettability gradient surface (made from a self-assembled monolayer, SAM technique) was investigated. The results indicate that their mixing is driven sequentially by interior convection and diffusion; the convection endures less than 100 ms but dominates more than 60 % of the mixing. If the stationary droplet has a large surface tension (73.28 mN × m^?1), whether the moving droplet has a large surface tension (73.28 mN × m^?1) or a small surface tension (38.63 mN × m^?1), the mushroom-shaped mixing pattern is generated within the coalesced droplet that enhances the convective mixing and also significantly enlarges the interface for mass diffusion. The mixing index of these two cases was greater than 0.8 at 120 s after the collision. For the cases in which the stationary droplet with a small surface tension collided by the moving droplet with a large surface tension, a mixing pattern with a round-head shape developed, which was insufficient to benefit the mixing. When the stationary and moving droplets both had small surface tension, the moving droplet was unable to merge with stationary droplet and had poor mixing quality due to the small surface Gibbs energy of both stationary and moving droplets. For the collision of droplets of identical surface tension, the surface tension affects the coalescence behavior; for the collision of droplets with distinct surface tension, the coalescence behavior and mixing quality depend on the colliding arrangement of stationary and moving droplets.     

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.     

动态粒子组成的椭球体的几何尺寸计算方法

为了研究一种线状高分子材料在另一种高分子基体中熔融断裂后，从椭球变化到球的过程，本文给出了由动态粒子堆积成的密度有涨落椭球体的几何尺寸计算方法，介绍了内坐标与回转半径张量法“扭正”椭球、在椭球体边界上取点、非线性最小二乘法拟合椭球方程三个方面的具体计算方法。本文提出了用27个格子确定边界点的方法。在用耗散粒子动力学模拟椭球体变化到球体的过程中，本文用上述计算方法正确测量了椭球体三个半轴的变化，并用不同密度的体系所得体积值较稳定验证了计算方法的准确性。     

Film drainage mechanism between two immiscible droplets

The interaction between two deformable droplets consists of unique dynamic characteristics that are not present during the interaction of solid bodies. A thin film of surrounding fluid is entrapped between the droplets and then drains out under the influence of an external force before the droplets can adhere or coalesce. The drainage process during the coalescence of two similar droplets has received significant research interest due to the presence of dynamical interactions between the droplets. Surprisingly, the film drainage process between two partial engulfing immiscible droplets has not been studied yet. Using a numerical study, we investigate the film drainage between two partial engulfing immiscible droplets. We vary the interfacial tensions between the droplets and surrounding fluid in wide ranges to observe the film drainage time between the droplets. Based on our simulations, we identified three regimes of fast, intermediate and delayed drainage. We found that the film drainage of two immiscible droplets exhibits additional flow into or out of the film, which does not exist in the film drainage of identical droplets. This additional flow can either increase or decrease the rate of film drainage between the droplets, depending on the interfacial tension of droplets with the surrounding fluid and the interfacial tension of the two immiscible droplets.     

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.     

On the dynamic contact angle in simulation of impinging droplets with sharp interface methods

Effects of dynamic contact angle models on the flow dynamics of an impinging droplet in sharp interface simulations are presented in this article. In the considered finite element scheme, the free surface is tracked using the arbitrary Lagrangian–Eulerian approach. The contact angle is incorporated into the model by replacing the curvature with the Laplace–Beltrami operator and integration by parts. Further, the Navier-slip with friction boundary condition is used to avoid stress singularities at the contact line. Our study demonstrates that the contact angle models have almost no influence on the flow dynamics of the non-wetting droplets. In computations of the wetting and partially wetting droplets, different contact angle models induce different flow dynamics, especially during recoiling. It is shown that a large value for the slip number has to be used in computations of the wetting and partially wetting droplets in order to reduce the effects of the contact angle models. Among all models, the equilibrium model is simple and easy to implement. Further, the equilibrium model also incorporates the contact angle hysteresis. Thus, the equilibrium contact angle model is preferred in sharp interface numerical schemes.     

Development of AFM tensile test technique for evaluating mechanical properties of sub-micron thick DLC films

This paper describes mechanical properties of submicron thick diamond-like carbon (DLC) films used for surface modification in MEMS devices. A new compact tensile tester operating under an atomic force microscope (AFM) is developed to measure Young's modulus, Poisson's ratio and fracture strength of single crystal silicon (SCS) and DLC coated SCS (DLC/SCS) specimens. DLC films with a thickness ranging from 0.11 /spl mu/m to 0.58 /spl mu/m are deposited on 19-/spl mu/m-thick SCS substrate by plasma-enhanced chemical vapor deposition using a hot cathode penning ionization gauge discharge. Young's moduli of the DLC films deposited at bias voltages of -100 V and -300 V are found to be constant at 102 GPa and 121 GPa, respectively, regardless of film thickness. Poisson's ratio of DLC film is also independent of film thickness, whereas fracture strength of DLC/SCS specimens is inversely proportional to thickness. Raman spectroscopy analyses are performed to examine the effect of hydrogen content in DLC films on elastic properties. Raman spectra reveal that a reduction in hydrogen content in the films leads to better elastic properties. Finally, the proposed evaluation techniques are shown to be applicable to sub-micron thick DLC films by finite element analyses.     

A numerical method for two phase flows with insoluble surfactants

In many practical multiphase flow problems, i.e. treatment of gas emboli and various microfluidic applications, the effect of interfacial surfactants, or surface reacting agents, on the surface tension between the fluids is important. The surfactant concentration on an interface separating the fluids can be modeled with a time dependent differential equation defined on the moving and deforming interface. The equations for the location of the interface and the surfactant concentration on the interface are coupled with the Navier–Stokes equations. These equations include the singular surface tension forces from the interface on the fluid, which depend on the interfacial surfactant concentration.A new accurate and inexpensive numerical method for simulating the evolution of insoluble surfactants is presented in this paper. It is based on an explicit yet Eulerian discretization of the interface, which for two dimensional flows allows for the use of uniform one dimensional grids to discretize the equation for the interfacial surfactant concentration. A finite difference method is used to solve the Navier–Stokes equations on a regular grid with the forces from the interface spread to this grid using a regularized delta function. The timestepping is based on a Strang splitting approach.Drop deformation in shear flows in two dimensions is considered. Specifically, the effect of surfactant concentration on the deformation of the drops is studied for different sets of flow parameters.     

Characterization of layer-by-layer nano self-assembled carbon nanotube/polymer film sensor for ethanol gas sensing properties

This paper reported a multi-wall carbon nanotubes (MWNTs)/polymer film-based sensor for ethanol gas detection. The film sensor was fabricated using layer-by-layer self-assembly method on the substrate with interdigital electrodes structure. The surface morphology of the self-assembled membranes shows a high strength, dense and random network structures, and the electrical properties of MWNTs/polymer film sensor were investigated. Its ethanol gas-sensing properties with varying gas concentration are characterized at room temperature. The experiment results shown that carboxylic groups attached on the MWNTs surface and the expansion of polyelectrolyte interlayer lead to a prompt response and sensitive resistance change when the sensor exposed to ethanol gas, indicating the unique advantages of layer-by-layer self-assembly of MWNTs/polymer film sensors in prospective application.     

Three-dimensional deformation analyses of the ultra-thin liquid film surface (linearized analyses for the steady state)

Long wave theory, which is the time evolution equation for the shape and deformation of thin liquid films and includes surface tension and surface forces such as van der Waals forces, was used to examine steady and three-dimensional deformations of ultra-thin but continuous liquid films. As liquid film deformations caused by gas pressures and shear stresses at the gas–liquid interface are usually very small, the linearized long wave equation, which is obtained for infinitesimal deformations, was employed to predict the steady-state liquid surface deformations produced by gas pressures and shear stresses. As the velocity of the solid increases and the liquid film thickness decreases, the deformation decreases and is nearly constant along solid running direction almost everywhere except at the applied position of the pressure and shearing stresses. The results obtained using the linearized equation agrees well with those obtained using the nonlinear equation and the calculation time is greatly reduced.     

Effect of vacuum venting and mold wettability on the replication of micro-structured surfaces

Micro injection molding enables the manufacture of micro-scale features with good accuracy at high production rates. However, the replication of complex micro and nano features is still challenging hindering the development of new functional surface topographies. The marked thermal gradient between injected polymer and mold surface and the reduced dimensions promote a rapid drop of melt temperature that causes the incomplete filling of the micro features. This study aims to investigate the combined effects of vacuum venting and mold wettability on the replication of micro-structured surfaces. A low-viscosity polystyrene and a cyclic olefin copolymer were selected and their wetting properties were evaluated. The results showed that a polymer with high wetting properties and an elevated viscosity dependence on temperature improves the replication of the micro features. Moreover, high interfacial effects can be exploited to significantly enhance the filling ratio when applying vacuum venting.

     

Parallelised production of fine and calibrated emulsions by coupling flow-focusing technique and partial wetting phenomenon

The capacity of microfluidic technology to fabricate monodisperse emulsion droplets is well established. Parallelisation of droplet production is a prerequisite for using such an approach for making high-quality materials for either fundamental or industrial applications where product quantity matters. Here, we investigate the emulsification efficiency of parallelised drop generators based on a flow-focusing geometry when incorporating the role of partial wetting in order to make emulsion droplets with a diameter below 10 μm. Confinement intrinsically encountered in microsystems intensifies the role played by interfaces between liquids and solids. We thus take advantage of partial wetting to enhance the maximum confinement accessible due to liquid flow focusing. We compare the performances brought by partial wetting to more established routes such as step emulsification. We show that the step configuration and the partial wetting regime are both well suited for being parallelised and thus open the way to the production of fine and calibrated emulsions for further applications. Finally, this new route of emulsification that exploits partial wetting between the fluids and the channel walls opens possibilities to the formation of substantially smaller droplets, as required in many fields of application.     

Micro-hydrodynamics of immiscible displacement inside two-dimensional porous media

In this paper, a Boolean lattice-gas model based on field mediators proposed by Santos and Philippi (Phys Rev E 65:046305, 2002) is used for the simulation of fluid–fluid interface displacement inside two-dimensional simplified porous media. A new procedure is introduced to allow the simulation of different viscosity ratios on the framework of lattice-gas models. The model is verified by simulating the spreading of a liquid drop on a solid surface and by comparing the simulation results with experimental spreading data. Some important basic physical mechanisms occurring at the pore scale are simulated and compared qualitatively with experimental visualizations. The break-off phenomenon of the fluid–fluid interface is observed in bifurcations, when a wetting (or non-wetting) fluid is displacing a non-wetting (or wetting) fluid. The role of break-off is shown to be different in imbibition and drainage processes in agreement with experimental results. Finally, the influence of wettability on the displacement efficiency is investigated in two-dimensional random arrays of disks.     

Deformation characteristics of ultra-thin liquid film considering temperature and film thickness dependence of surface tension

Thermocapillary deformations of an ultra-thin liquid film caused by temperature distribution were three-dimensionally analyzed using the unsteady and linearized long wave equation considering the temperature and film thickness dependence of surface tension. The temperature and film thickness dependence equation for the surface tension of a liquid was firstly established. The temperature dependence of the surface tension was obtained experimentally using a surface tensiometer and the film thickness dependence was obtained theoretically from the corrected van der Waals pressure equation for a symmetric multilayer system. Time evolutions of depression and groove of the ultra-thin liquid film caused by local heating were obtained quantitatively.     

Temporal analysis of power law liquid jets

In this paper we investigate the breakup mechanisms of power law liquid jets. The viscosity of the liquid is represented the Carreau-Yasuda model, and the surface tension of the liquid jet has a variation (gradient) along the jet axial direction. The surface tension gradient may be introduced by the thermal disturbance of the jet surface as it comes of out an orifice. The Carreau-Yasuda fluid has a power law viscosity bounded by two plateaus, the higher plateau at zero strain rate, μ₀, and the lower plateau at the infinite strain rate, μ_∞. The governing equation for the surface profile of the liquid jet is derived in the forms of a partial differential equation (PDE), as well as an ordinary differential equation (ODE). The PDE and ODE are solved for various cases of Carreau-Yasuda fluid to study the effect of fluid properties on jet breakup. The effects of various parameters on the instability behavior are studied in comparison with two Newtonian jets with upper and lower bound viscosities, μ₀ and μ_∞. A number of quantitative conclusions and sensitivities on the instability behavior of non-Newtonian jets are investigated. It is found that the jet breakup mechanism depends on the properties of the fluid as well as the wave number of the thermal disturbance that causes the surface tension gradient. In contrast to the Newtonian liquid where the jet surface profile has the same frequency as the surface tension gradient, the nonlinear nature of the Carreau-Yasuda constitutive behavior may enable the jet surface profile at frequencies higher than that of the surface tension gradient. This leads to significant surface profile oscillation within one wavelength of the surface tension gradient and the generation of small satellite drops. It is worth noting that at a small wave number the breakup time for the Carreau-Yasuda fluid maybe shorter than that of the Newtonian jet with μ_∞, although the Newtonian jet has a lower viscosity.     

Assembly of Cu nanoparticles in a polyacrylamide grafted poly(vinyl alcohol) copolymer matrix and vapor-induced response

A vapor-sensitive electroconductive film was designed and assembled by inserting Cu²⁺ particles into a polyacrylamide grafted poly(vinyl alcohol) (PAM-g-PVA) in virtue of a complexation between Cu²⁺ and PVA even PAM, as well as the establishment of inter- and intramolecular attractions between polymer matrices, which were in turn reduced into Cu nanoparticles by sodium hypophosphite as a reducing agent. The PAM-g-PVA graft copolymer was prepared via a simple free radical polymerization reaction initiated by a redox reaction. The resistance responsiveness of the film samples to various organic vapor surroundings was investigated. The responsive magnitude, response time and recovery properties depend on the molecular weight of the graft polymer or the PAM chain length and initial resistances of the film samples or Cu particle contents upon exposed to ether and petroleum ether vapor, etc. The structure and morphologies of the PAM-g-PVA/Cu were characterized by a Fourier transform infrared spectroscope and a transmission electron microscope. The response mechanism of the PAM-g-PVA/Cu films to solvent vapors was accounted for by a swelling theory and an interaction between solvent vapor molecules and nanocomposites as well as the type and strength of interaction that each solvent vapor exhibits on the material.