Slot coating flows of non‐colloidal particle suspensions

Slot coating is used in the manufacturing of functional films, which rely on specific particle microstructure to achieve the desired performance. Final structure on the coated film is strongly dependent on the suspension flow during the deposition of the coating liquid and on the subsequent drying process. Fundamental understanding on how particles are distributed in the coated layer enables optimization of the process and quality of the produced films. The complex coating flow leads to shear‐induced particle migration and non‐uniform particle distribution. We study slot coating flow of non‐colloidal suspensions by solving the mass and momentum conservation equations coupled with a particle transport equation using the Galerkin/Finite element method. The results show that particle distribution in the coating bead and in the coated layer is non‐uniform and is strongly dependent on the imposed flow rate (wet thickness). © 2016 American Institute of Chemical Engineers AIChE J, 63: 1122–1131, 2017     

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     

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     

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     

Increasing nano‐particle dispersion ratio in the bubble stretching‐based technique

We present a new method to increase nano‐particle migration rate in bubble stretching‐based technique. Vibration created by the inflation and shrinking process of bubbles is used. Process parameters can be adjusted to increase the probability of collision between the nano‐particles and the bubble wall. In effect, particles sufficiently migrate to the bubble wall, increasing both particle migration rate and dispersion ratio. Our measurement show that: (1) particle diameter, initial bubble radius, and initial bubble pressure strongly influence the migration of particles; (2) with appropriate parameters, nano‐particles can quickly and efficiently migrate to the bubble wall through this new method. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

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     

A second-order-moment–Monte-Carlo model for simulating swirling gas–particle flows

A second-order moment (SOM) gas-phase turbulence model, combined with a Monte-Carlo (MC) simulation of stochastic particle motion using Langevin equation to simulate the gas velocity seen by particles, is called an SOM–MC two-phase turbulence model. The SOM–MC model was applied to simulate swirling gas–particle flows with a swirl number of 0.47. The prediction results are compared with the PDPA measurement data and those predicted using the Langevin-closed unified second-order moment (LUSM) model. The comparison shows that both models give the predicted time-averaged flow field of particle phase in general agreement with those measured, and there is only slight difference between the prediction results using these two models. In the near-inlet region, the SOM-MC model gives a more reasonable distribution of particle axial velocity with reverse flows due to free of particle numerical diffusion, but it needs much longer computation time. Both models underpredict the gas and particle fluctuation velocities, compared with those measured. This is possibly caused by the particle–wall and particle–particle interaction in the near-wall region, and the effect of particles on dissipation of gas turbulence, which is not taken into account in both models.     

Experimental investigation of particle migration in suspension flow through bifurcating microchannels

Experimental measurements of velocity and concentration profiles were carried out to study transport of non‐colloidal suspension in bifurcating micro channels for both diverging and converging flow conditions using a combination of mirco‐particle image velocimetry and particle tracking velocimetry techniques. Migration of particles across the streamline was observed and symmetric velocity and concentration profile in the inlet branch becomes asymmetric in the daughter branches. Further migration of particles toward the center of the channel in the outlet branch make the profiles again symmetric. The evolution of velocity and concentration profiles was observed to be different in the symmetric and asymmetric bifurcation channels. The comparison of the streamlines for the fluid and the particles showed significant deviation near the bifurcation region. This may explain why there is unequal flow and particle partitioning during flow of suspension in asymmetric bifurcating channels as reported in many previous studies. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2293–2307, 2018     

Verification of filtered two‐fluid models for gas‐particle flows in risers

The effect of solid boundaries on the closure relationships for filtered two‐fluid models for riser flows was probed by filtering the results obtained through highly resolved kinetic theory‐based two‐fluid model simulations. The closures for the filtered drag coefficient and particle phase stress depended not only on particle volume fraction and the filter length but also on the distance from the wall. The wall corrections to the filtered closures are nearly independent of the filter length and particle volume fraction. Simulations of filtered model equations yielded grid length independent solutions when the grid length is ～half the filter length or smaller. Coarse statistical results obtained by solving the filtered models with different filter lengths were the same and corresponded to those from highly resolved simulations of the kinetic theory model, which was used to construct the filtered models, thus verifying the fidelity of the filtered modeling approach. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

二维环形Couette设备中剪切引起的二维圆形固粒迁移的动态数值模拟

The shear-induced migration of neutrally-buoyant non-colloidal circular particles in a two-dimensional circular Couette flow is investigated numerically with a distributed Lagrange multiplier based fictitious domain method.The effects of inertia and volume fraction on the particle migration are examined.The results indicate that inertia has a negative effect on the particle migration.In consistence with the experimental observations,the rapid migration of particles near the inner cylinder at the early stage is observed in the simulation,which is believed to be related to the chain-like clustering of particles.The migration of circular particles in a plane Poiseuille flow is also examined in order to further confirm the effect of such clustering on the particle migration at early stage.There is tendency for the particles in the vicinity of outer cylinder in the Couette device to pack into concentric rings at late stage in case of high particle concentration.     

Investigation of styrene‐assisted free‐radical grafting of glycidyl methacrylate onto high‐density polyethylene using response surface method

In this study, the free‐radical grafting of glycidyl methacrylate (GMA) onto high‐density polyethylene (HDPE) in the presence of styrene, as a comonomer, is investigated using a Brabender internal mixer. To optimize grafting level of GMA onto HDPE, response surface method (RSM) was exploited. Using RSM method of experimental design, it was possible to investigate the individual effects of various variables including dicumyl peroxide (DCP) concentration, GMA content, as well as reaction time, and their interactions on grafting efficiency. The fitted quadratic model obtained from statistical analysis is expressed by an approximating function to investigate the final torque as a responding variable over the experimental range of the independent variables. The grafting yield of GMA onto HDPE for the prepared samples was determined using titration/back‐titration technique and Fourier transform infrared spectroscopy (FTIR). According to the torque–time diagrams, increasing the DCP content led to an increase in GMA grafting yield. Also, it was found that the reaction time imparts minor effect on the final processing torque, and there exists an interaction between DCP and GMA content. The results of melt flow index (MFI) test showed that increasing the reaction time at constant DCP and GMA content enhances the MFI values of the samples, due to the more probability of chain scission phenomenon. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Development of a hybrid shrinking‐core shrinking‐particle model for entrained‐flow gasifiers

Slagging entrained‐flow gasifiers operate above the melting temperature of the ash. As slag is highly nonwetting on the surface of char (carbon) particles, it is likely that it will agglomerate into one or several slag droplets and some of these droplets can detach from the char particles. If the slag exists in the form of droplets on the char surface rather than as a solid shell around the unreacted char particle, a shrinking particle model would be more physically realistic representation in comparison to the widely used shrinking core model (SCM). In the early section of the gasifier, the temperature remains below the ash melting temperature and, therefore, the SCM is more appropriate in this region. With this motivation, a novel hybrid shrinking‐core shrinking‐particle model has been developed. The model provides spatial profile of a number of important variables that are not available from the traditional SCM. © 2015 American Institute of Chemical Engineers AIChE J, 62: 659–669, 2016     

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     

DEM‐CFD modeling of particle systems with long‐range electrostatic interactions

To investigate dynamic behaviors of monocharged particle systems, a direct truncation (DT) method and a hybrid particle‐cell (HPC) method are implemented into the discrete element method coupled with computational fluid dynamics (DEM‐CFD) with defined cutoff distances. The DT method only considers electrostatic interactions between particles within the cutoff distance while the HPC method computes electrostatic interactions in the entire computational domain. The deposition process of monocharged particles in a container in air was simulated using the developed DEM‐CFD. It was found that using the DT method, the macrostructure, evolution of granular temperature, and radial distribution function of the particle system were sensitive to the specified cutoff distance. In contrast, using the HPC method, these results were independent of the specified cutoff distance, as expected. This implies that, although electrostatic interactions between particles with large separation distances are weak, they should be considered in DEM‐CFD for accurate modeling of charged particle systems. © 2015 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 61: 1792–1803, 2015     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

Liquid‐particle surface properties on spouted bed coating and drying performance

Polymeric coating has been applied to particles for several reasons, which goes from enhancing product esthetics to control the release of chemicals. Spouted beds are among the equipments widely used to coat particles. Its choice is justified by the cyclic movement of the particles in stable spouting resulting in product homogeneity and good solid–fluid contact with high heat and mass transfer rates. Also, the spouted bed with inert particles is an alternative to drying pastes due to its low cost and applicability to low scale production. This work presents results of coating and drying efficiencies for different systems that combine 04 different solids and 03 formulations of suspensions. Materials having different surface tension were chosen and suspensions with varying surface tensions were formulated, resulting in different wettabilities (quantified by contact angles measurements). The results show the direct influence of these properties on the coating and drying performances.     

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