Direct numerical simulations of thermocapillary migration of a droplet attached to a solid wall

This paper is designated to gain further insight into the physical mechanisms of thermal droplet actuation on a wall through direct numerical simulation. Classical theory states that free droplets in a nonuniform temperature field always move towards the hot side. However, when attaching a droplet to a wall with a nonuniform temperature gradient, lubrication theory explains how such a droplet moves towards the colder side. This paper aims at further investigating and clarifying the physical mechanisms and acting forces in the environment of a nonuniform temperature field and offers some explanations. For the numerical simulations of a droplet attached to a wall with a linear temperature gradient and larger contact angles, the full Navier–Stokes equations and energy equation are solved in a Volume of Fluid framework. The solver is extended with a dynamic contact angle treatment and thoroughly validated. The droplet motion is studied both in two and three dimensions, where a movement towards the cold and the warm side can be observed. The forces acting in such a setting are identified and interpreted. A decomposition of the jump conditions shows that the tangential stress due to the temperature dependent surface tension alone would lead to a motion towards the cold side, whereas the normal component alone would move the droplet to the opposite direction. The differences between two- and three-dimensional simulations show that the problem at hand is clearly three-dimensional.     

A STUDY ON DROPLET VELOCITY OF ETHANOL DURING ELECTROSPRAYING PROCESS AT CONE-JET MODE

研究液滴在静电喷雾下的速度特性是理解喷雾形态的形成及演化的关键.结合锥射流模式下乙醇静电喷雾实验数据,建立了静电喷雾二维轴对称模型.基于离散相液滴运动方程、连续相空气运动方程、电场方程以及用户自定义函数,进行了数值求解,获得了锥射流模式下的乙醇静电喷雾形态、空间电场分布以及液滴速度场分布.考虑了不同空气入口流速的影响,得到了乙醇/空气同轴射流静电喷雾形态的变化规律.结果表明,喷雾外围液滴与空气流场有较强的相互作用,导致喷雾中轴线附近的液滴速度分布变化较小,而在喷雾外围处的液滴速度分布沿径向剧烈变化;随着空气入口速度的增大,乙醇/空气同轴射流静电喷雾形态先趋于发散,当空气入口速度大于喷雾外围液滴轴向速度时,喷雾形态则趋于聚拢.因此,除改变施加电压、液体流量和电极结构外,通过控制空气入口速度来影响喷雾液滴速度场,也可获得不同的静电喷雾效果.     

Motion,deformation, and coalescence of ferrofluid droplets subjected to a uniform magnetic field

In this article, we present the motion, deformation, and coalescence of ferrofluid droplets suspended in a nonmagnetic fluid, subjected to a uniform magnetic field in both vertical and horizontal directions. A coupling between the simplified multiphase lattice Boltzmann method and the self-correcting scheme is constructed to numerically solve the two-dimensional flow field and the magnetostatics equations, respectively. The Cahn-Hilliard equation is employed to seize the diffuse interface between magnetic and nonmagnetic fluids. In order to validate the model, deformation of a ferrofluid droplet suspended in nonmagnetic fluid is simulated as a test case and the results are compared with numerical and experimental results. Furthermore, a detailed analysis on the behavior of falling ferrofluid droplets and the coalescence between a pair of ferrofluid droplets under the effect of different magnetic fields and different droplets configurations are also presented in this article. The results provide significant insight and a better understanding of these phenomena. It is found that for higher values of magnetic bond number and susceptibility, the droplet deformation is significant and the falling process is faster while a reverse behavior is observed for higher values of Eötvös number. Moreover, the magnetic energy density exhibits an interesting behavior in the vicinity of the droplets. It is concentrated between the droplets with a nonuniform distribution when the droplets are close to each other.     

Low-Reynolds-number droplet motion in a square microfluidic channel

In this study, we investigate computationally the low-Reynolds-number droplet motion in a square micro-channel, a problem frequently encountered in microfluidic devices, enhanced oil recovery and coating processes. The droplet deformation and motion are determined via a three-dimensional spectral boundary element method for wall-bounded flows. The effects of the flow rate, viscosity ratio and droplet size on the interfacial dynamics are identified for droplets smaller and larger than the channel size and for a wide range of viscosity ratio. Owing to the stronger hydrodynamic forces in the thin lubrication film between the droplet interface and the solid walls, large droplets exhibit larger deformation and smaller velocity. Under the same average velocity, a droplet in a channel shows a significantly smaller deformation and higher velocity than in a cylindrical tube with the same size, owing to the existence of the corners’ area in the channel which permits flow of the surrounding fluid. A suitable periodic boundary implementation for our spectral element method is developed to study the dynamics of an array of identical droplets moving in the channel. In this case, the droplet deformation and velocity are reduced as their separation decreases; the reduction is influenced by the flow rate, viscosity ratio and more significantly the droplet size.     

PTV investigation of phase interaction in dispersed liquid–liquid two-phase turbulent swirling flow

An investigation of dispersed liquid–liquid two-phase turbulent swirling flow in a horizontal pipe is conducted using a particle tracking velocimetry (PTV) technique and a shadow image technique (SIT). Silicone oil with a low specific gravity is used as immiscible droplets. A swirling motion is given to the main flow by an impeller installed in the pipe. Fluorescent tracer particles are applied to flow visualization. Red/green/blue components extracted from color images taken with a digital color CCD camera are used to simultaneously estimate the liquid and droplet velocity vectors. Under a relatively low swirl motion, a large number of droplets with low specific gravity tend to accumulate in the central region of the pipe. With increasing droplet volume fraction, the liquid turbulence intensity in the axial direction increases while that in the wall-normal direction decreases in the central region of the pipe. In addition, the turbulence modification in the present flow is strongly dependent on the droplet Reynolds number; however, the interaction of droplet-induced turbulences is significant due to vortex shedding, particularly at high droplet Reynolds numbers and higher droplet volume fraction.     

The Motion Behavior of a Group of Charged Droplets in Liquid-Liquid Electrostatic Spray

The droplet sizes and electrical charges under different applied electrical voltages are experimentally measured for a liquid-liquid electrostatic spray system. Considering droplet size and charge distributions, the two-dimensional motion for a group of charged droplets in a liquid-liquid electrostatic atomization system is simulated. From measured droplet size and charge distributions, the simulation can obtain the velocities and positions in a two-dimensional domain for all simulated droplets at different times. The various forces acting on droplet as well as their effects on droplet velocity and trajectory are analyzed and the liquid-liquid electrostatic atomization characteristics are revealed. In addition, for one-dimensional motion trajectory of larger droplet, the comparison between simulation and experiment is also conducted and a general agreement can be obtained.     

A numerical study of droplet motion/departure on condensation of mixture vapor using lattice Boltzmann method

Droplet motion/departure, which is governed by external force acceleration coefficient, droplet radius and surface wettability on solid surfaces under external forces such as gravitational force, play a significant role in characterizing condensation heat transfer, especially when high fractional non-condensable gases (NCG) present. However, due to the challenge in visualizing the vapor/steam velocity field imposed by droplet motion/departure, the detailed mechanism of droplet motion/departure on condensing surfaces has not been completely investigated experimentally. In this study, droplet motion/departures on solid surfaces under external forces and their interactions with steam flow are simulated using two dimensional (2D) multiphase lattice Boltzmann method (LBM). Large external force acceleration coefficient, droplet radius and contact angle, lead to large droplet deformation and high motion/departure velocity, which significantly shortens the droplet residual time on the solid surface. Our simulation shows that steam vortices (lateral velocity) induced by droplet motion/departure can greatly disturb the vapor flow and would be intensified by increasing external force acceleration coefficient, droplet radius, and contact angle. In addition, the location of vortex center shifts in the ascending direction with increase of these factors. The average lateral velocities induced by droplet motion/departure at various conditions are obtained. The mass transfer resistance is substantially reduced owing to the droplet motion/departure, leading to an enhanced heat flux. The experimental results are compared to validate the influence of droplet motion/departure on condensation heat transfer performance, especially for steam–air mixture with the presence of high fractional NCG.     

Thermocapillary migration of liquid droplets in a temperature gradient in a density matched system

An experimental investigation of thermocapillary flow in droplets of a vegetable oil (partially hydrogenated soybean oil) immersed in silicone oil was conducted in a test cell with a heated top wall and a cooled bottom wall. The liquids are nearly immiscible and have equal densities at a temperature below the room temperature, thus providing a simulation of low-gravity conditions by reducing the buoyancy forces. The interfacial tension between the two oils was measured in the temperature range 20–50°C using a capillary tube and d/dT was determined to be negative. Droplets ranging in sizes from 3 mm to 1 cm diameter were injected into the silicone oil. The vertical temperature profile in the bulk liquid (silicone oil) produces temperature variations along the interface which induce variations in the interfacial tension. The flow inside the droplet driven by the resulting interfacial shear stresses was observed using a laser light-sheet flow visualization technique. The flow direction is consistent with the sign of d/dT. The observed maximum surface velocities are compared to the theoretical predictions of Young et al. (1959).For short times after injection, the droplets were driven by this flow towards the hot wall above the matched-density temperature until the droplets reached a point where the forces due to the flow and buoyancy were equal. After longer times, the droplets moved to the cold side due to suspected density changes caused by mass transfer from the droplets to the silicone oil. This was confirmed by tests under isothermal conditions, where it was observed that droplets of all sizes fell to the cold bottom eventually.Thus, even though the thermocapillary flow inside the droplets persisted for long times in spite of the mass transfer, the migration of droplets towards the hot side was eventually affected by uncontrolled buoyancy forces resulting from density changes due to mass transfer. While additional liquids are being tried, it is suggested from the present experience that reduced gravity experiments will probably be necessary to provide unambiguous data for the migration of droplets.     

Hydrodynamics of contact of a falling drop with a liquid free surface

A fine structure of the flows developing during primary contact of freely falling drops with a deep quiescent fluid is studied using the macrophotography and high-speed video filming methods. Water drops falling in water, alcohol, and oil, as well as drops of oil, petroleum, and aqueous solutions of salt or alcohol falling in water are investigated. The work is focused on the visualization of the finespray scattering from the primary contact area. The collisions of small droplets with the surface of the submerging drop are first recorded. The direction of the spray and streamer scattering is determined by the surface tension coefficients of the coalescing liquids. The conditions under which the spray droplets collide with the drop surface are determined.     

Charged droplets evaporation and motion in an electric field

Monodisperse spray evaporation is investigated theoretically when a pure liquid or an electrolyte solution spray is charged and moves through an electric field. The solution of the equations in the case of electrolyte solutions gives the droplet size evolution down to the “equilibrium radius” when the relative humidity is high and down to the saline kernel when the humidity is lower. This solution also gives the dynamic behaviour in an electric field when the droplets are charged and are moving in a gas stream. A non dimensional curve is obtained for a given humidity, molality and temperature, independently of the electric field. With this curve it is possible to predict the droplet evolution only knowing a “middle time” of evaporation, calculated for a given electric force and a given initial radius.