VOF simulations of the contact angle dynamics during the drop spreading: Standard models and a new wetting force model

Introduction

In this study,a novel numerical implementation for the adhesion of liquid droplets impacting normally on solid dry surfaces is presented. The advantage of this new approach, compared to the majority of existing models, is that the dynamic contact angle forming during the surface wetting process is not inserted as a boundary condition, but is derived implicitly by the induced fluid flow characteristics (interface shape) and the adhesion physics of the gas–liquid-surface interface (triple line), starting only from the advancing and receding equilibrium contact angles. These angles are required in order to define the wetting properties of liquid phases when interacting with a solid surface.

Methodology

The physical model is implemented as a source term in the momentum equation of a Navier-Stokes CFD flow solver as an “adhesion-like” force which acts at the triple-phase contact line as a result of capillary interactions between the liquid drop and the solid substrate. The numerical simulations capture the liquid–air interface movement by considering the volume of fluid (VOF) method and utilizing an automatic local grid refinement technique in order to increase the accuracy of the predictions at the area of interest, and simultaneously minimize numerical diffusion of the interface.

Results

The proposed model is validated against previously reported experimental data of normal impingement of water droplets on dry surfaces at room temperature. A wide range of impact velocities, i.e. Weber numbers from as low as 0.2 up to 117, both for hydrophilic (θ_adv = 10° – 70°) and hydrophobic (θ_adv = 105° – 120°) surfaces, has been examined. Predictions include in addition to droplet spreading dynamics, the estimation of the dynamic contact angle; the latter is found in reasonable agreement against available experimental measurements.

Conclusion

It is thus concluded that theimplementation of this model is an effective approach for overcoming the need of a pre-defined dynamic contact angle law, frequently adopted as an approximate boundary condition for such simulations. Clearly, this model is mostly influential during the spreading phase for the cases of low We number impacts (We < ˜80) since for high impact velocities, inertia dominates significantly over capillary forces in the initial phase of spreading.     

Pressure-coupled vaporization response of n-pentane fuel droplet at subcritical and supercritical conditions

The dynamic response of a liquid fuel droplet to externally impressed pressure oscillations is studied comprehensively over a wide range of mean pressures. Both subcritical and supercritical conditions are considered. The formulation treats a complete set of conservation equations and incorporates real fluid thermodynamics and transport theories. As a specific example, the situation with isolated n-pentane droplets in nitrogen is studied at various forcing frequencies. Results are correlated with the liquid thermal inertial time, instantaneous droplet radius, and oscillation frequency. The magnitude of the vaporization response increases with increasing pressure, mainly due to the decreased enthalpy of vaporization at high pressures. The increased sensitivity of droplet thermophysical properties to ambient flow variations at high pressures also plays a role. The phase angle of the vaporization response function, however, appears to be independent of the ambient pressure. An abrupt increase in the response function takes place when the droplet surface reaches its critical mixing state. A major factor contributing to this phenomenon is the abnormal variations of fluid thermophysical properties near the critical mixing point.     

喷雾冷却液滴冲击壁面过程的数值模拟及分析

以经典流体力学中的自由射流湍流理论和提出的描述喷雾流体的流动情况为基础,从理论分析和数值模拟两个方面,研究了喷雾冷却的过程,并分别进行了液滴冲击物理模型和喷嘴射流模型的模拟,对高温壁面以及空气的降温有着非常重要的意义,以达到强化传热的目的.     

Effect of electrode geometry on droplet velocity in open EWOD based device for digital microfluidics applications

Electro wetting-on-dielectric (EWOD) is an emerging method for handling droplet motion by applying an electric field to an array of electrodes. The dependence of droplet velocities on different electrode configuration in open EWOD system has been investigated in this work. In this paper, open configured EWOD devices with different geometries of electrodes, polydimethylsiloxane (PDMS) as a base layer are designed and fabricated. The electrowetting force is computed by analytical methods as well as by numerical methods and its effect on droplet velocity is studied in detail. The velocity of the droplet is measured by using open image processing tool.     

Study on the relationship between emulsion stability and droplet dynamics of a spontaneous emulsion for chemical enhanced oil recovery

Spontaneous emulsion (SE) has attracted increasing attention, especially in the development of low-permeability reservoirs (with an average throat radius of 0.1–2?µm) for enhanced oil recovery. In this work, based on multiple light scattering principles, the relationship between emulsion stability and the droplet dynamics of SEs was investigated. The results showed that the synergistic effect of surfactant and polymer was crucial for oil emulsification in brine, since the stability of the emulsion was greatly improved. The emulsion stability and droplet dynamics depend on the temperature, concentration, and type of emulsifier. The optimal combination system had the lowest Turbiscan stability index value, and the emulsion stability time was more than 2000s. The average droplet size was 1.50?µm, and the droplet migration rate was 7.21?mm/h. The stability of the emulsion was resulted from the microscopic droplet dynamics. By reducing the migration rate of the droplets, stability of the emulsion can be obtained. Finally, the stability and droplet dynamics mechanism of the system were explained by using a schematic representation of the various equilibriums in the spontaneous emulsification flooding system.     

Ultrasound impact on whey protein concentrate-pectin complexes and in the O/W emulsions with low oil soybean content stabilization

Consumers’ preference for products with reduced levels of fat increased in the last years. Proteins and polysaccharides have an important role due to their functional and interaction properties because, when combined in ratios and pH of higher potential for electrostatic interactions they may act as emulsifiers or stabilizers. This study evaluated the ultrasound impact on the electrostatic interaction between pectin (PEC) and whey protein concentrate (WPC) at different WPC:PEC ratios (1:1 to 5:1), and its effect on the emulsification and stability of emulsions formulated with WPC:PEC blends (1:1, 4:1) at low soybean oil contents (5 to 15%). Zeta potential analysis showed greater interactions between biopolymers at pH 3.5, which was proven in FTIR spectra. Rheology and turbidimetry showed that the ultrasound reduced the suspension viscosity and the size of the biopolymer complexes. Suspensions were Newtonian, whereas the emulsions showed shear-thinning behavior with slight increase in apparent viscosity as a function of oil content, and remained stable for seven days, with small droplets (<8 μm) stabilized and entrapped in a pectin network evidenced by confocal laser microscopy. Sonication was successfully applied to emulsion stabilization, improving the functional properties of WPC:PEC blends and enabling their application as low-fat systems, providing healthier products to consumers.     

Ignition and combustion study of JP-8 fuel in a supersonic flowfield

The ignition and combustion process of fuels in a supersonic combustion chamber plays an important role in the design of hypersonic propulsion system. However, it is a quite complicated process, due to the large variation of inlet air velocity, temperature, oxygen concentration, and shocks in the supersonic combustion chamber. The purpose of this paper is to observe the ignition delay and combustion phenomenon of the JP-8 fuel droplets in a supersonic flowfield experimentally. A shock tube is used as a basic test facility to create a high-speed and high-temperature flowfield as a supersonic combustor. In the experiments, several test parameters are controlled, such as shock velocity, gas temperature, fuel droplet size and distance, initial fuel temperature, and oxygen concentration, etc. The test results show the influence of these parameters on ignition delay, ignition limitation, and detonation. The most important factor in the experiment is the initial fuel temperature effect, which is influenced by the altitude variation during a flight. Received 4 August 1995 / Accepted 12 December 1995     

Microgravity experiments and numerical studies on ethanol/air spray flames

Spray flames are known to exhibit amazing features in comparison with single-phase flames. The weightless situation offers the conditions in which the spray characteristics can be well controlled before and during combustion. The article reports on a joint experimental/numerical work that concerns ethanol/air spray flames observed in a spherical chamber using the condensation technique of expansion cooling (based on the Wilson cloud chamber principle), under microgravity.We describe the experimental set-up and give details on the creation of a homogeneous and nearly monosized aerosol. Different optical diagnostics are employed successfully to measure the relevant parameters of two-phase combustion. A classical shadowgraphy system is used to track the flame speed propagation and allow us to observe the flame front instability. The complete characterization of the aerosol is performed with a laser diffraction particle size analyser by measuring the droplet diameter and the droplet density number, just before ignition. A laser tomography device allows us to measure the temporal evolution of the droplet displacement during flame propagation, as well as to identify the presence of droplets in the burnt gases. The numerical modelling is briefly recalled. In particular, spray-flame propagation is schematized by the combustion spread in a 2-D lattice of fuel droplets surrounded by an initial gaseous mixture of fuel vapour and air.In its spherical expansion, the spray flame presents a corrugated front pattern, while the equivalent single-phase flame does not. From a numerical point of view, the same phenomena of wrinkles are also observed in the simulations. The front pattern pointed out by the numerical approach is identified as of Darrieus–Landau (DL) type. The droplets are found to trigger the instability. Then, we quantitatively compare experimental data with numerical predictions on spray-flame speed. The experimental results show that the spray-flame speed is of the same order of magnitude as that of the single-phase premixed flame. On the other hand, the numerical results exhibit the role played by the droplet radius in spray-flame propagation, and retrieve the experiments only when the droplets are small enough and when the Darrieus–Landau instability is triggered. A final discussion is developed to interpret the various patterns experimentally observed for the spray-flame front.     

The influence of thermal expansion flow on droplet evaporation

It has been demonstrated recently that it follows from conservation of mass that unsteady temperature fields create flow in an incompressible fluid with a temperature-dependent density even in the absence of gravity. The paper studies the influence of thermal expansion flow on spherically symmetric evaporation of an isolated droplet. A model problem of a droplet evaporating at a constant rate is first considered. In this idealized situation one can use the assumption of a thin thermal boundary layer to solve analytically the unsteady moving-boundary heat conduction problem to find the temperature field inside the droplet both with and without the thermal expansion flow. Next evaporation of a fuel droplet in a diesel engine is studied numerically. The heat diffusion equation is solved in the liquid phase while the standard quasi-steady model is used for the gas phase. The results of the calculation show that for high ambient temperatures the influence of the thermal expansion flow on the droplet lifetime can be considerable.     

Droplet combustion in standing sound waves

Interaction between droplet combustion and acoustic oscillation is clarified. As the simplest model, an isolated fuel droplet is combusted in a standing sound wave. Apart from the conventional idea that oscillatory component of flow influences heat and mass transfer and promotes combustion, a new model that a secondary flow dominates combustion promotion is examined. The secondary flow, found by the authors in the previous work, is driven by acoustic radiation force due to Reynolds normal stress, and named as thermo-acoustic streaming. Since the force is described by the same equation as buoyancy, i.e., F = ΔρVg, the nature of the streaming is thought to be the same as natural convection. The flow patterns of the streaming are analyzed and its influence on burning rate of a droplet is predicted. Experimental investigation was mainly done with burning droplets located in the middle of node and anti-node of standing sound waves. This location realizes the strongest streaming. By varying sound pressure level, ambient pressure, and acoustic frequency, the strength of the streaming was controlled. Flame configuration including soot and burning rate were examined. Microgravity conditions were employed to clarify the influence of acoustic field through the streaming, since it is similar to and must be distinguished from natural convection. Experiments using microgravity conditions confirmed the new combustion promotion model and the way to quantify it. By introducing a new non-dimensional number Gr_a, that is the ratio of acoustic radiation force to viscosity, burning rate constants for various ambient and sound conditions are rearranged. As a result, it was found that the excess burning rate (k/k₀ − 1) is proportional to or , for weak sound and for strong sound, respectively.