Coupled fluid‐particle modeling of a slot die coating system

This work seeks to develop a fundamental understanding of particle motion in the slot die coating process through studying the interaction of forces between particles, with the die walls and the fluid phase. Coupled computational fluid dynamics and the discrete element method is employed for evaluating the motion of individual suspended particles near moving surfaces in a complex three‐dimensional flow field, motivated by the flow of particle laden fluid in a slot die coating system, including the presence of free surfaces. Overall, the particles follow the flow streamlines and their final position in the coating depends on the initial entry region of the particles. Particles experiencing adhesion with each other agglomerate in the low velocity regions of the coating gap, and have long residence times near the edge of the die at the end of the feed slot in the coating gap. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1933–1939, 2016     

Simulation of particle migration in free‐surface flows

The migration of particles in free surface flows using the diffusive flux model was investigated. As the free‐surface flows, a planar jet flow and a slot coating flow were chosen. The suspension was assumed to be a Newtonian fluid with a particle concentration dependent viscosity. The governing equations were solved numerically by the finite volume method, and the free‐surface problem was handled by the volume of the fraction model. The result shows that even though the velocity profile is fully developed and becomes flat, the particle distribution never reaches the uniform distribution for both of the cases. It is also shown that the die swell of the free jet is reduced compared to the Newtonian fluid and when the particle loading is 0.5, die contraction is observed. The change in die swell characteristics is purely due to particle migration since the suspension model does not show normal stress differences. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Particle migration and alignment in slot coating flows of elongated particle suspensions

We analyze slot coating flows of elongated particle suspensions and investigate particle concentration and average orientation at the coated film. Shear‐induced particle migration is described by the Diffusive Flux Model, and particle orientation is given by the principal direction of the particle conformation tensor. The conformation evolution and the constitutive equation for the resulting complex liquid are adapted from classical models that describe the behavior of suspensions of cylinders and fibers and polymeric solutions of almost rigid rod‐like molecules. The proposed fully coupled model is applied to slot coating flows, and is solved using the DEVSS‐TG/SUPG finite element method. The results show that the wet coated film is highly nonuniform. Particle concentration and orientation vary along the film thickness and are a strong function of the operating parameters of the process, such as the film thickness‐to‐coating gap ratio and the capillary number of the flow. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3187–3198, 2017     

Analysis of non‐Brownian particle deposition from turbulent liquid‐flow

The deposition of non‐Brownian particles from turbulent liquid‐flow onto channel walls is numerically analyzed. The approach combines Lagrangian particle tracking with a kinematic model of the near‐wall shear layer. For nonbuoyant particles, direct interception is the main deposition mechanism and the deposition velocity scales as the particle diameter (in wall units) to the power of 1.7. When wall/particle hydrodynamic interactions are taken into account, the deposition velocity is significantly reduced and the correction factor scales as the cubic root of the wall roughness to particle diameter ratio. For buoyant particles, sedimentation is usually the predominant deposition mechanism and the hydrodynamic interactions significantly affect the deposition velocity when the drainage characteristic time driven by buoyancy is of the order of the particle residence time close to the wall. Last, a wall‐function for the suspended particles is proposed. © 2015 American Institute of Chemical Engineers AIChE J, 62: 891–904, 2016     

Analysis of slot coating flow under tilted die

Slot coating is a high precision coating method, where the film thickness is controlled by the flow rate fed to the die and the production speed. The range of desirable operating conditions for uniform coating is limited by the shape and locations of upstream and downstream menisci, which are controlled by the pressure gradient within the coating flow. The gradient can be controlled by the shape and orientation of the slot coating die, that is, die configuration. Here, the tilted die, the so‐called angle‐of‐attack configuration is considered. The configuration is similar to underbite and overbite configurations, but it has a sloped die lip due to tilting. Coating flows with such a configuration are examined by computer‐aided analysis using the Galerkin/finite element method. Using steady‐state analysis, the effect of the angle of attack on the upstream meniscus location is discussed. In transient analysis, the amplitude of the thickness variation is predicted under different types of disturbances, namely flow rate and gap oscillations. The analysis shows that die lip configurations affect the thickness uniformity under periodic disturbances. The effect of die tilting can be similar to or different from the underbite/overbite configurations, depending on the type of oscillation. During the analysis, the flow rate apportioning inside the coating flow and decomposing thickness variations into two separating oscillations are useful in understanding the results is found. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1745–1758, 2015     

Particle ordering in colloidal thin films deposited by flow‐coating

The wide applications of two‐dimensionally ordered nanoscale features have stimulated the development of cheap and fast fabrication techniques in recent years. We achieved large area of uniform film of nanoparticles between 49.8 ± 8.7 and 117.6 ± 6.7 nm via flow‐coating. However, the single crystalline domains of a close‐packed monolayer remained limited. That motivated deposition of initially ordered colloidal dispersions, attained through deionized solutions to extend electrostatic double layers for long‐range repulsion. Although the deposition agreed reasonably well with our power‐law model, the initial order was destroyed at high shear. While the particle order was partially preserved during deposition at low shear, the domain size was not particularly extensive due to the high compression of double layers during evaporation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1287–1302, 2014     

Transient response of two‐layer slot coating flows to periodic disturbances

Coating uniformity requirement is becoming more severe as new products come into the market. Coating processes have to be designed not only based on the steady‐state operation but also taking into account how the flow responds to ongoing disturbances on process conditions. These disturbances may lead to thickness variation on the deposited liquid layers that may be unacceptable for product performance. This study extends available transient analysis of single‐layer slot coating to determine the amplitude of the oscillation of each individual coated layer in two‐layer slot coating process in response to small periodic perturbation on different operating parameters. The predictions were obtained by solving the complete transient Navier–Stokes equations for free surface flows. The results show the most dangerous perturbations and how the deposited film thickness variations of each layer can be minimized by changing the geometry of the die lip and liquid viscosities. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1699–1707, 2015     

Automatic detection of contact lines in slot coating flows

Slot coating is a versatile method used to manufacture thin films at high speed. The success of the method lies in controlling a coating flow surrounded by upstream and downstream menisci. The meniscus edges that are in contact with either the die lips or the substrate surfaces are called contact lines. Visualizations of such lines are important in coating flow research because their shapes and locations are sensitive to operating conditions. In this study, we propose a robust image analysis algorithm for images acquired from flow visualizations. The images are dissected into three regions with different characteristics that need to be treated using different pre‐processing techniques. A standard optimal edge detector is then sufficient to capture the contact lines, and post‐processing steps can be simplified. We also highlight two applications of the proposed algorithm: coating windows, and transient behaviors under external disturbances. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2440–2450, 2017     

Response of slot coating flows to periodic disturbances

Slot coating is a common method in the manufacture of a wide variety of products. It belongs to a class of coating method known as premetered coating: in a steady-state operation, the thickness of the coated liquid layer is set by the flow rate fed to the die and the speed of the substrate moving past, and is independent of other process variables. Thus premetered methods are ideal for high precision coating. However, even the best designed slot coating operations are subjected to small oscillations on the process conditions, such as flow rate, vacuum pressure and gap fluctuations. These oscillation may lead to unacceptable variation on the thickness of the deposited liquid layer. The effect of process condition disturbances on the coated layer has to be minimized to assure a wet thickness as uniform as possible.The effect of an imposed periodic perturbation on the liquid flow rate or on the gap clearance in the coated layer thickness is explored in this work by computer-aided analysis. The amplitude of the thickness variation is determined at different process conditions and die configurations by solving the transient, two-dimensional, viscous free surface liquid flow in the coating bead. The system of equations, with appropriate boundary conditions, was solved by the Galerkin/finite element method, and an implicit time integration. The results show the response as a function of the imposed perturbation frequency and of the die geometry. They indicate that the die geometry may be optimized in order to minimize the film thickness oscillation of a slot coating operation.     

Laser monitoring of non‐Newtonian liquids during dip coating

Dip coated films, widely used in the coating industry, are usually measured by capacitive methods with micrometric precision. In this work, interferometric determination of thickness evolution in real time, for the first time to our best knowledge, is applied to volatile non‐Newtonian liquids with several viscosities and distinct dip withdrawing speeds. Thickness evolution during the process depends on time as predicted by a power law model. Comparison with measured results (uncertainty of ± 0.007 μm) showed very good agreement after initial steps of the process. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Filtered two‐fluid models of fluidized gas‐particle flows: New constitutive relations

New constitutive relations for filtered two‐fluid models (TFM) of gas‐particle flows are obtained by systematically filtering results generated through highly resolved simulations of a kinetic theory‐based TFM. It was found in our earlier studies that the residual correlations appearing in the filtered TFM equations depended principally on the filter size and filtered particle volume fraction. Closer inspection of a large amount of computational data gathered in this study reveals an additional, systematic dependence of the correction to the drag coefficient on the filtered slip velocity, which serves as a marker for the extent of subfilter‐scale inhomogeneity. Furthermore, the residual correlations for the momentum fluxes in the gas and particle phases arising from the subfilter‐scale fluctuations are found to be modeled nicely using constitutive relations of the form used in large‐eddy simulations of single‐phase turbulent flows. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3265–3275, 2013     

Rheological behavior and microstructure of bimodal suspensions of core‐shell structured swollen particles

The rheological behavior and microstructure of bimodal suspensions of core‐shell structured swollen particles have been examined with changing volume ratio of two different sized particles. As the volume fraction of large particles increases, the viscosity, degree of shear‐thinning, and the critical shear stress σ_c decreases, while the interparticle distance ξ of the microstructure increases. The suspensions exhibit single mode rheological behavior and have a single diffraction peak in the SAXS profiles. These results suggest that the bimodal suspensions of the core‐shell structured swollen particles behave likely to unimodal suspensions of hard spheres with alloy like single mode microstructure composed of hypothetical intermediate size particle. The relationship between σ_c and ξ can be represented as σ_c = 3kT/4πξ³, which corresponds to the dynamics of the Brownian hard sphere model with ξ being the particle diameter. These findings indicate that the shear‐thinning of the suspensions can be attributed to dynamical competition between the thermal motion and the hydrodynamic motion under shear flow and that the mechanism can be applied to bimodal suspensions of the swollen particles as well as unimodal suspensions of hard spheres. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 102: 2212–2217, 2006     

Experimental investigations of non‐Newtonian/Newtonian liquid‐liquid flows in microchannels

The plug flow of a non‐Newtonian and a Newtonian liquid was experimentally investigated in a quartz microchannel (200‐µm internal diameter). Two aqueous glycerol solutions containing xanthan gum at 1000 and 2000 ppm were the non‐Newtonian fluids and 0.0046 Pa s silicone oil was the Newtonian phase forming the dispersed plugs. Two‐color particle image velocimetry was used to obtain the hydrodynamic characteristics and the velocity profiles in both phases under different fluid flow rates. The experimental results revealed that the increase in xanthan gum concentration produced longer, bullet‐shaped plugs, and increased the thickness of the film surrounding them. From the shear rate and viscosity profiles, it was found that the polymer solution was in the shear‐thinning region while the viscosity was higher in the middle of the channel compared to the region close to the wall. Circulation times in the aqueous phase increased with the concentration of xanthan gum. © 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 3599–3609, 2017     

Deposition of magnetite particles from flowing suspensions under flow‐boiling and single‐phase forced‐convective heat transfer

The deposition rate of colloidal magnetite particles was measured under both single‐phase forced‐convective and flow‐boiling conditions. All measurements were made at alkaline pH where both the heat transfer surface and the surface of the magnetite particles appear to be negatively charged. For single‐phase forced convection, the deposition rate constant is lower than the mass transfer coefficient for colloidal particles, and the difference is attributed to the force of repulsion between the negatively charged surfaces of the particle and substrate. The deposition rate measured under flow‐boiling conditions is lower than that reported for the deposition of colloidal particles at neutral pH. The difference is, again, attributed to the force of repulsion between the particle and substrate. Particle removal rates were significantly lower than deposition rates; analysis using the theory of turbulent bursts suggests a removal efficiency of only 10^?9% for each turbulent burst. The low removal efficiency is consistent with the particle diameter being significantly smaller than the thickness of the laminar sublayer in these tests.     

The effect of shear‐thickening on the stability of slot‐die coating

Slot‐die coating is an economical roll‐to‐roll processing technique with potential to revolutionize the fabrication of nano‐patterned thin films at high throughput. In this study, the impact of shear‐thickening of the coating fluid on the stability of slot‐die coating was investigated. For the coating fluid, a model system fumed silica nanoparticles dispersed in polypropylene glycol was chosen. These dispersions exhibit shear and extensional thickening characterized through steady shear and capillary break‐up measurements. The critical web velocity for the onset of coating defect for different flow rates was measured, while the type of coating defect was visualized using a high speed camera. For the shear thickening particle dispersions, the coating failed through the onset of a ribbing instability. The critical web velocity for the onset of coating defect was found to decrease with increasing particle concentration and increasing fluid viscosity. The minimum wet thickness was studied as a function of capillary number for the particle dispersions and compared with a series of Newtonian fluids with similar viscosities. In all cases, shear‐thickening behavior was found to stabilize coating by reducing the minimum wet coating thickness when compared against a Newtonian fluid with similar viscosity at the same capillary number. Conversely, the shear‐thinning fluids tested destabilized the coating by increasing the minimum wet thickness when compared against a Newtonian at the same capillary number. The impact of shear‐thickening on slot‐die coating was further studied by quantifying the evolution of the ribbing instability with increasing web speed and by conducting tests over a wide range of coating gaps. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4536–4547, 2016     

Effect of volume fraction and particle size on wall slip in flow of polymeric suspensions

For especially highly concentrated suspensions, slip at the wall is the controlling phenomenon of their rheological behavior. Upon correction for slip at the wall, concentrated suspensions were observed to have non‐Newtonian behavior. In this study, to determine the true rheological behavior of model concentrated suspensions, “multiple gap separation method” was applied using a parallel‐disk rheometer. The model suspensions studied were polymethyl methacrylate particles having average particle sizes, in the range of 37–231 μm, in hydroxyl terminated polybutadiene. The effects of particle size and solid particle volume fraction on the wall slip and the true viscosity of model concentrated suspensions were investigated. It is observed that, as the volume fraction of particles increased, the wall slip velocity and the viscosity corrected for slip effects also increased. In addition, for model suspensions in which the solid volume fraction was ≥81% of the maximum packing fraction, non‐Newtonian behavior was observed upon wall slip correction. On the other hand, as the particle size increased, the wall slip velocity was observed to increase and the true viscosity was observed to decrease. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 439–448, 2005     

Fluid‐particle drag in inertial polydisperse gas–solid suspensions

In this article, we extend the low Reynolds number fluid‐particle drag relation proposed by Yin and Sundaresan for polydisperse systems to include the effect of moderate fluid inertia. The proposed model captures the fluid‐particle drag results obtained from lattice‐Boltzmann simulations of bidisperse and ternary suspensions at particle mixture Reynolds numbers ranging from 0 ≤ Re_mix ≤ 40, over a particle volume fraction range of 0.2 ≤ ? ≤ 0.4, volume fraction ratios of 1 ≤ ?_i/?_j ≤ 3, and particle diameter ratios of 1 ≤ d_i/d_j ≤ 2.5. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Ni-W-P镀层的防垢性能

在紫铜基体上制备了化学镀Ni-W-P镀层,X射线衍射结果表明,镀层的结构形态为非晶态。污垢附着实验和池沸腾实验结果表明,低表面自由能的化学镀Ni-W-P镀层使污垢沉积速度降低了52%,在硫酸钙溶液中的传热系数则是紫铜表面的1.7倍。用高速摄影仪观察了沸腾表面的气泡行为,由于传热方式的差别形成了两种不同结构的硫酸钙污垢,紫铜表面为针状垢,而镀层表面是粒状垢。