涂层表面形貌形成过程模拟与分析

表面涂层形貌形成过程的定量描述对涂层质量控制效果的提升至关重要,建立了集成蒙特卡罗（Monte Carlo）和计算流体力学（CFD）的混合方法模拟复杂的海量液滴沉积成液膜及其随后的流平过程,并系统研究油漆液滴平均直径、黏度、密度以及表面张力对涂层表面粗糙度、流平速度以及流平时间的影响。模拟结果表明,油漆液滴平均直径增大,涂层初始表面粗糙度增大,流平速度减小,流平时间延长;黏度增大,涂层的初始和最终表面粗糙度增大,流平速度减小,流平时间延长;密度减小,涂层初始表面粗糙度增大,初始流平速度增大,流平时间稍微缩短,对最终表面粗糙度影响不大;表面张力增大,涂层流平速度增大,流平时间缩短,对涂层最终表面粗糙度影响很小。     

The flow of paint coatings: a hydrodynamic analysis

The flow of a viscous liquid film on a plane surface, under the influence of gravity and surface tension, is analysed mathematically, taking into account the initial surface profile of the liquid and any inclination of the underlying surface. The approach adopted is suitable for liquids such as paint where the Reynolds number is extremely low and the viscosity may be shear or time dependent. The surface profile is represented by a complex Fuorier Series and the hydrodynamic analysis centres on the biharmonic equation for the stream function. Two velocity components are derived for each point on an arbitrary initial grid and the displacements are obtained on multiplying by a short time interval from which the next grid is obtained. In this way the progress of the surface profile can be followed. Such a numerical method is eminently suitable for computer graphic simulation.     

FILAMENT SPLITTING BETWEEN SEPARATING PLATES

The breakup of a liquid filament being stretched between two surfaces or plates separating at a constant velocity is analyzed using the nonlinear thin filament equation. Filament breakup is caused by plate movement relative to the average filament velocity and by surface tension-driven flow. The location of filament splitting is strongly dependent upon the initial velocity profile along the filament and the relative importance of surface tension to inertia. An approximate analysis, based on scaling arguments, is presented to estimate the time for filament breakup.     

γ射线透射技术测量气液鼓泡塔内气含率的轴向分布

引　言鼓泡床反应器以其具有良好的传热、传质、相间充分接触和高效的可连续操作等特点在许多领域得到了广泛的应用 ,如氧化、加氢、烷基化、污水处理等工业过程 .在鼓泡反应器中气体以分散相的形式存在 ,轴向气含率分布是反映气泡在鼓泡塔反应器内运动行为的重要参数之一 .虽然采用了各种测量方法对流体力学行为进行了大量研究[1～ 3] ,取得了一定的研究成果 ,但工业过程往往是在高温高压的条件下操作 ,大部分的测量方法难以适应这种条件 ,所以探求新的测试技术尤为重要 .　　γ射线透射技术不仅用于塔设备的故障检测 ,而且用于其他的石油…     

Spreading of an inviscid drop impacting on a liquid film

The evolution of the deforming liquid surface following the impact of a drop onto a film of the same liquid is analysed numerically using a boundary integral method assuming axisymmetric, inviscid flow. Surface tension and gravity are taken into account. At times comparable to, or larger than the impact time scale (based on initial drop radius and impact velocity), the section of the liquid surface bounded by the radially propagating crown or rim is predicted to approach a single central shape independent of film thickness. At times which are much smaller than the impact time scale, jetting behaviour is obtained in the neck region where the drop meets the film when the Weber number is large enough. The jet is found to move close to the film, and this suggests the possibility of bubble entrapment, confirming a previous report in the literature. The present results suggest the occurrence of a train of bubble rings from repeated near-reconnection events as the neck moves radially outwards under jetting conditions.     

混合蒸气冷凝过程中均匀温度面上液滴自发移动现象及特性

在某些混合蒸气的冷凝过程中，传热面温度梯度导致冷凝液浓度及表面张力不平衡，从而驱动冷凝液滴产生自发移动现象。此现象产生的前提为传热面具有整体温度分布，即传热面从一侧表面的相对低温状态，随着表面位置变化逐渐过渡到另一侧的相对高温状态，而本论文在水-酒精混合蒸气的冷凝过程中，观测到在均匀温度传热面上也会发生冷凝液滴自发移动现象。通过对具有和不具有初速度的冷凝液滴在均匀传热面上的不同移动特性进行比较分析，确认了具有明显初速度的冷凝液滴在均匀温度领域产生自发移动现象，而无初速度液滴则产生无序运动（非自发移动）。从而验证了在均匀温度传热面，冷凝液滴自发移动的驱动力为液滴移动同时其周围形成的局部温度分布和局部表面张力不平衡的推测。     

Computational fluid dynamic simulations on liquid film behaviors at flooding in an inclined pipe☆

The complex liquid film behaviors at flooding in an inclined pipe were investigated with computational fluid dynamic (CFD) approaches. The liquid film behaviors included the dynamic wave characteristics before flooding and the transition of flow pattern when flooding happened. The influences of the surface tension and liquid viscosity were specially analyzed. Comparisons of the calculated velocity at the onset of flooding with the available experimental results showed a good agreement. The calculations verify that the fluctuation frequency and the liquid film thickness are almost unaffected by the superficial gas velocity until the flooding is triggered due to the Kelvin–Helmholtz instability. When flooding triggered at the superficial liquid velocity larger than 0.15 m·s?1, the interfacial wave developed to slug flow, while it developed to entrainment flow when it was smaller than 0.08 m·s?1. The interfacial waves were more easily torn into tiny droplets with smaller surface tension, eventual y evolving into the mist flow. When the liquid viscosity increases, the liquid film has a thicker holdup with more intensive fluctuations, and more likely developed to the slug flow.     

Evaporation-induced pattern formation in polymer films via secondary phase separation

The ordered necklace-like or cellular pattern formation has been investigated for ternary polymer solutions in which primary and secondary phase separations were induced by the solvent evaporation. The patterns consisted of regular droplet arrays of various diameters, which arose in the pre-existing polymer phases via the secondary phase separation. The pattern formation was enhanced with increasing air velocity and ambient humidity, while it was suppressed with decreasing initial film thickness. The regular pattern was independent of surface wettability of the solid substrate. We ascribe the morphology change to the evaporation-induced surface tension driven convection, which re-arranged the droplet distributions from disordered to flow-induced ordered patterns.     

Interplay of kinetics and interfacial interactions in breath figure templating - A phenomenological interpretation

Breath Figure BF templating is an attractive technique for the production of polymer films with controlled porosity: upon the exposure to a moist airflow, monodisperse water droplets condense on the surface of evaporating polymer solution into ordered arrays, acting as a template for the final film structure.This work has been focused on polylactic acid (PDLLA), a biocompatible biodegradable polymer, and aims to provide a phenomenological interpretation of BF process based on the role of kinetics and the influence of interfacial tension. The effects of physical and chemical properties of solvents have been evaluated; the contribution of kinetics has been assessed by modifying the rate of film hardening from seconds to minutes, via different experimental set-up. Our experimental observations indicated that the interplay of kinetics and interfacial tension defines the structure of BF films: interfacial forces govern the physical interactions among water, solvent and polymer, but the dynamics of the process and thus the final pore structure is regulated by kinetics.     

DRYING BEHAVIOR OF ACETATE FILAMENT IN DRY SPINNING

Drying behavior of acetate filament in dry spinning is investigated, including the elongational deformation of polymer solution thread in the early stage of drying. Variations of diameter, velocity, temperature, solvent concentration profile in the thread and tension distribution along the threadline in the spinning column, are calculated for spinning conditions encountered commercially by means of the equations of simultaneous momentum, heat and mass transfer between the thread and hot air flow in the spinning column. Concentration and temperature dependencies of the mutual diffusion coefficient from desorption experiment are correlated by the free volume theory. The elongational viscosity is estimated from the shear viscosity data using Krevelen theory. Residual acetone concentratio in the thread and tension at the exit of the spinning column are compared between the calculated results and the experimental data by a commercial apparatus; satisfactory agreement is found. Rapid decreases of temperature and surface concentration of the dope thread after extrusion confine the elongational deformation within several centimeters below the spinnerette. Initial elongational rate and die swell ratio are related to the winding velocity and tension at the exit of the spinning column. The tension is determined mainly by initial viscous force and air drag.     

DRYING BEHAVIOR OF ACETATE FILAMENT IN DRY SPINNING

Drying behavior of acetate filament in dry spinning is investigated, including the elongational deformation of polymer solution thread in the early stage of drying. Variations of diameter, velocity, temperature, solvent concentration profile in the thread and tension distribution along the threadline in the spinning column, are calculated for spinning conditions encountered commercially by means of the equations of simultaneous momentum, heat and mass transfer between the thread and hot air flow in the spinning column. Concentration and temperature dependencies of the mutual diffusion coefficient from desorption experiment are correlated by the free volume theory. The elongational viscosity is estimated from the shear viscosity data using Krevelen theory. Residual acetone concentratio in the thread and tension at the exit of the spinning column are compared between the calculated results and the experimental data by a commercial apparatus; satisfactory agreement is found. Rapid decreases of temperature and surface concentration of the dope thread after extrusion confine the elongational deformation within several centimeters below the spinnerette. Initial elongational rate and die swell ratio are related to the winding velocity and tension at the exit of the spinning column. The tension is determined mainly by initial viscous force and air drag.     

The gap between the measured and calculated liquid–liquid interfacial tensions derived from contact angles

We present our new findings about the causes of discrepancies between the measured and calculated liquid-liquid interfacial tensions derived from contact angles. The calculated ones are based on either the equation developed by Fowkes or that by van Oss, Chaudhury and Good (VCG), while the measured ones are based on the sessile drop, weight-volume by Jańzuk et al. and the axisymmetric drop shape analysis (ADSA) by Kwok and Neumann. Indeed, there are deviations between the calculated and measured results. For an immiscible liquid-liquid or liquid-solid interface, we prefer to employ Harkins spreading model, which requires the interfacial tension to be constant. However, for the initially immiscible liquid-liquid pairs, we propose an adsorption model, and our model requires the interfacial tension to be varying and the surface tensions of bulk liquids at a distance from the interface to remain unchanged. Thus, the difference between the initial and final interfacial spreading coefficients (S_i) equals the equilibrium interfacial film pressure (π_i)_e. According to our findings, the calculated interfacial tension represents the initial value (γ₁₂)_o, which differs from the equilibrium value (γ₁₂)_e obtained experimentally after some time delay. This expected gap at a reasonable time frame is chiefly caused by the equilibrium interfacial film pressure between the two liquids. The initial (or calculated) interfacial tension can be positive or negative, while the equilibrium (or measured) one can reach zero. In fact, the former is shown to have more predictive value than the latter. A negative initial interfacial tension is described to favor miscibility or spontaneous emulsification but it tends to revert to zero instantaneously. Thus, a miscible liquid mixture should have zero interfacial tension. In response to recent papers by Kwok et al., we show that the disagreements between the calculated and measured interfacial tensions are definitely not caused by the failure of the VCG approach. Correct interfacial tensions are calculated for liquid pairs containing formamide or dimethyl sulfoxide (DMSO) by using the dispersion components cited in Fowkes et al.'s later publication. With the corrected surface tension components, the equilibrium interfacial film pressures (π_i)_e's for at least 34 initially immiscible liquid pairs have been calculated. These values are generally lower than the corresponding spreading pressures π_e's obtained by others using the Harkins model. Recently, we established a relationship between these two film pressures with the Laplace equation and found a new criterion for miscibility to be (π_i)_e = π_e.     

规整填料表面液膜流动特性的数值模拟

精馏过程气液两相流运动分布特征对分离效率具有重要影响。为研究规整填料表面液膜流体动力学特性建立了基于VOF方法的CFD分析模型,并基于文献试验结果进行了验证。对液膜随时间和空间的演化分布特征、速度场分布和液相流量影响进行了模拟分析。液膜在波纹顶部下沿聚集形成凸起状波峰,在波纹底部波峰消失,而到达下节波纹上沿时,波峰重新形成;瞬态液膜厚度随时间波动,且沿填料表面液膜平均厚度先减小后保持稳定;发现液相聚集及形成液滴坠落容易导致出现干板区。不同位置液膜速度分布存在明显差异,沿填料表面液膜平均速度先增后减或保持稳定;液膜绕过波纹顶部时会加速,在波纹底部和上沿处会减速。液相流量增大,液膜平均厚度和速度均有所增大。     

Surface nonuniformities in latex paints due to evaporative mechanisms

A model is developed for predicting long‐wavelength nonuniformities in the thickness of drying latex paint films. The model includes the effects of temperature, latex particle volume fraction, surface surfactant density, bulk surfactant density, and several material and environmental factors. After the model is simplified by applying the lubrication approximation, equations for spatially independent base state solutions are derived. The base state solutions describe a drying latex paint film of uniform thickness. The equations for the base states are solved numerically and a linear stability analysis is conducted. This analysis indicates that evaporation, slow surfactant kinetics, low initial surface tension, substrate permeability, and high initial latex particle volume fractions destabilize the uniform film, while fast surfactant kinetics, high initial surface tension, and high viscosity are stabilizing. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1841–1858, 2018     

R32在水平微细圆管内凝结换热的数值模拟

采用VOF模型对R32在内径为1 mm水平圆管内的凝结换热进行了数值模拟.圆管进口饱和蒸气和壁面温度分别为40℃和30℃.假设气相为湍流、液相为层流,考虑重力和表面张力的影响,模拟分析了干度、液膜厚度和轴向速度沿管长的变化.结果表明,沿管轴向顶部液膜先增厚后基本保持不变,管底部液膜持续增厚.表明当量直径在1 mm时重力作用仍不可忽略.传热系数的模拟值随干度的增大而增大;与实验结果相比,模拟值小于实验值,但二者差别在实验误差范围内.     

HOW LIQUIDS SPREAD ON SOLIDS

A theory of the wetting of solids by liquids is put forward. The theory accounts for capillary pressure gradient, gravitational potential gradient, surface tension gradient, disjoining pressure gradient driving forces of flow in thick thin-films and of surface diffusion in thin thin-films. Disjoining pressure stems from the way intermolecular forces aggregate in submicroscopically thin films. For thick thin-films of slowly varying thickness the lubrication approximation to velocity distributions is appropriate. With this approximation the spontaneous, unsteady, two-dimensional spreading of liquid is shown to be governed by a nonlinear convective-diffusion equation for the evolution of the film thickness profile. The predictions of the theory agree with Marmur and Lelah's (1980, 1981) observations of water drops spreading on glass and with Bascom, Cottington and Singleterry's (1964) and Ludviksson and Lightfoot's (1971) observations of oils spreading on high energy surfaces. The theory is used to analyze Derjaguin and co-workers' (1944, 1957, 1970) blowing-off experiments designed to measure thin-film rheology. The theory is also used to buttress the proposition that much contact angle hysteresis is due simply to slow attainment of equilibrium.     

Onset of Rayleigh–Bénard–Marangoni convection with time-dependent nonlinear concentration profiles

Taking into account the effects of the time-dependent nonlinear base concentration profile on the concentration and velocity disturbances in the Rayleigh–Bénard, Bénard–Marangoni, and Rayleigh–Bénard–Marangoni problems, a spatial base-profile influenced frozen-time marginal state analysis has been developed to predict the onset of cellular convection caused by the Rayleigh effect (buoyancy) and Marangoni effect (surface tension gradient). The relations between the base velocity and concentration profiles and the velocity and concentration fluctuations have been established, analogous to the theory of statistical physics which describes the relation between the fluctuating forces and velocities for particles in non-equilibrium systems. Compared with the quasi-static analysis and the initial-value technique, the numerical calculations of this spatial base-profile influenced frozen-time marginal state analysis are straightforward and involve no subjective decisions on either the initial conditions of disturbances or the criterion for the onset time of convection. Using the spatial base-profile influenced frozen-time marginal state analysis, the calculated critical parameters for the onset of convection are in good agreement with the published experimental results.     

气升式内环流反应器内局部气含率径向分布

The local gas holdup profiles in an internal-loop airlift reactor were studied experimentally by using dual electrical conductivity probe under different conditions,including superficial velocity,surface tension and liquid viscosity.The results showed that the radial gas holdup profile has a parabolic shape,which was consistent with the empirical model of Luo.Local gas holdup distribution parameters were obviously influenced by flow regime and almost remained unchanged in the same flow regime.In the gas distributor region,the profiles were steeper in the homogenous flow regime than in the heterogeneous flow regime.However,in the stable region,there was an inverse change trend in two flow regimes.The increase of surface tension,superficial velocity and liquid viscosity made the profile of local gas holdup steeper in two flow regimes.     

The velocity field characteristics of high-viscosity fluids falling film flow down clamped channels

The complexity of falling film flow has been studied in many industrial applications. In this work, the velocity field of high-viscosity fluids falling film flow down clamped channels was investigated numerically and experimentally. The results show that the numerical simulation results are consistent with the experimental results, and the characteristics of the velocity field are related to the fluid properties, operating conditions, and structure of the clamped channels. When the fluid viscosity is greater than or equal to 10 Pa ⋅ s, the type of velocity field changes into I shape, U shape, and V shape. While the fluid viscosity drops to 0.89 Pa ⋅ s, the viscous force cannot resist the inertial force and gravity, resulting in a cardioid velocity field. By adjusting the structure of the clamped channels and operating conditions, the tension of the liquid film can be changed, and the velocity distribution of the liquid film can be manipulated. Significantly, under the fluctuating curtain flow, the liquid film coalesces and breaks frequently, which enlarges the surface area of the liquid film and strengthens the surface renewal frequency. Hence, this form of falling film flow can be applied to process intensification of high-viscosity materials.     

Thin film flow over structured packings at moderate Reynolds numbers

A model describing the dynamic evolution of waves on laminar falling wavy films at low to moderate Reynolds numbers (Re<30) over corrugated surfaces is presented. This model is based on the integral balance method, which is used to simplify the analysis by assuming a parabolic velocity profile within the bulk of the film. The predictions of this model are compared to those obtained from a computational fluid dynamics (CFD) code for which no assumptions regarding the film velocity profile are made. The film evolution profiles, obtained via numerical solution of the model equations, are used to calculate the ratio of film interfacial area to that of the substrate. The model predicts suppression of wave growth on a corrugated surface. The model is also used to predict the effect of packing geometry on the flow characteristics, which may improve packing design. Solutions obtained for Re∼200 using the CFD code demonstrate the degree of fluid accumulation within the ‘valleys’ of the structured substrate wherein re-circulation occurs.