Three‐dimensional simulation of microchip encapsulation process

A finite element simulation of moving boundaries in a three‐dimensional inertiafree, incompressible flow is presented. A control volume scheme with a fixed finite element mesh is employed to predict fluid front advancement. Fluid front advancement and pressure variation in a flow domain similar to the mold cavity used for microchip encapsulation are predicted. The predicted fluid front advancement and pressure variation are in good agreement with the corresponding experimental results. As the difference in the thicknesses of mold cavities above and below the microchip is changed, the weld line location and pressure variation during mold filling are found to change significantly.     

Three‐dimensional numerical analysis of injection‐compression molding process

Injection‐compression molding (ICM) process, combining conventional injection molding (CIM) process with compression molding, has been widely used in the manufacturing of optical media and optical lenses. Most of previous numerical studies regarding ICM process employ the Hele‐Shaw approximation, which is appropriate for thin cavity geometry only. This work presents a three‐dimensional numerical analysis system using a stabilized finite element method (FEM) and an arbitrary Lagrangian‐Eulerian (ALE) method for more rigorous modeling and simulation of ICM process of three‐dimensional geometry. The developed system is verified by comparing the results with existing experimental data as well as simulation data obtained from commercial software. Then, the system is adopted for simulations of ICM process of an optical lens, which is a practical example of three‐dimensional geometry. According to the simulation results, three‐dimensional flow characteristics are found to be significant especially during compression stage because of the squeezing nature of the flow. The results are then compared with those of CIM process, showing that ICM process results in reduced and more uniform distributions of the generalized shear rate and shear stress of the final part. Basic parametric studies are also carried out to understand effects of processing conditions, such as compression velocity and compression gap. POLYM. ENG. SCI.,2011. © 2011 Society of Plastics Engineers     

Three‐dimensional nonisothermal simulation of a coat hanger die

We studied the nonisothermal flow of Carreau fluid in a coat hanger die. A general three‐dimensional finite volume code was developed for the purpose of flow analysis. The pressure distribution and velocity distribution were obtained in addition to the temperature distribution. The results illustrated that the highest temperature occurred more by the center of manifold than by the die‐lip region. In the regions where the die gap was small relatively, the wall temperature played a key role in the determination of the temperature distribution in the melt. However, in the manifold, the viscous dissipation was the key factor that determined the temperature distribution in the melt where the heat conduction was relatively poor because of the thicker gap. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101:2911–2918, 2006     

Three‐dimensional simulation of primary and secondary penetration in a clip‐shaped square tube during a gas‐assisted injection molding process

This article proposes a generalized Newtonian model to predict the three‐dimensional gas penetration phenomenon in the GAIM process, where the gas and melt compressibility are both taken into account and hence the primary and secondary penetrations in GAIM processes are able to be quantitatively predicted. Additionally, an incompressible model requiring no outflow boundary is also presented to emphasis the influence of gas compressibility on the primary penetration. Based on a finite volume discretization, the proposed numerical model solves the complete momentum equation with two front transport equations, which are employed to track the gas/melt and air/melt interfaces. The modified Cross‐WLF model is adopted to describe the melt rheological behavior. The two‐domain modified Tait equation is exploited to represent the melt compressibility, while a polytropic model is employed to express the gas compressibility. The proposed schemes are quantitatively validated by the gas penetration characteristics in a clip‐shaped square tube, where good prediction accuracy is obtained. The influences of five major molding parameters, such as the injection pressure, mold temperature, melt temperature, delay time, and melt material on the gas penetration characteristics in the same clip‐shaped square tube via the proposed numerical approach are extensively presented and discussed. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Three‐dimensional direct simulation of a droplet impacting onto a solid sphere with low‐impact energy

In this paper, a numerical model is developed for direct simulation of droplet impinging onto a spherical surface on a fixed Eulerian mesh. The model couples the level‐set method and the interfacial cell immersed boundary method to the single‐fluid formulation of the Navier–Stokes equations which are solved by a finite‐volume projection technique. Moving contact lines are modelled here with a simple static contact angle model. The model is shown to converge, and to agree with previous work in the literature. The model is then applied to investigate the impact behaviour of a droplet onto solid sphere of different diameters at low Weber number and low Reynolds number. The simulation results show that the droplet used in present study seems to deposit on different spherical surfaces through oscillating. The simulated results also suggest that the impacted‐sphere size has a significant effect on the impact dynamics of the droplet. A local breakage phenomenon may be found in the centre of the droplet collision with a smaller sphere during the first recoiling stage. A regime map is then established to provide quantitative analysis for the breakage mode of the current impacting process.     

Gas assisted injection molding of a handle: Three‐dimensional simulation and experimental verification

Methods implemented in a three‐dimensional finite element code for the simulation of gas assisted injection molding are described, and predictions compared with the results of molding trials. The emphasis is on prediction of primary gas penetration and plastic wall thickness, including the effects of cooling during a delay before gas injection. For the latter, time dependent heat transfer coefficients at the cavity surface are used, determined in a separate analysis of transient heat conduction through the plastic and the mold tool to the circulating coolant. This shows how the initial value of 25,000 W/m²K falls by about an order of magnitude during the first few seconds of cooling, and also how values vary from cycle to cycle as steady periodic conditions are approached. For a tubular handle molded in polystyrene, with melt flow modeled by a Cross WLF model, comparisons of simulations with sectioned parts show excellent prediction of wall thickness and its variation circumferentially and in bends. The increase in wall thickness due to cooling during a gas delay is accurately modeled, as is the occurrence of a blow out. POLYM. ENG. SCI. 45:1049–1058, 2005. © 2005 Society of Plastics Engineers     

Dynamic characteristics of plug‐assist thermoforming process

Plug‐assist thermoforming is a well‐known technique in polymer processing because of its interesting features. The dynamic value of driving‐force for the stretching process is determined based on equilibrium equation. This amount of force is required for applying to a plug to stretch a sheet. It is used for calculation of the required theoretical work and power of a plug‐assist thermoforming process. By using a nonlinear viscoelastic rheological model in the proposed mathematical model, its validity was examined by performing experimental tests on ABS sheets. POLYM. ENG. SCI., 2009. © 2008 Society of Plastics Engineers     

Three‐dimensional dielectric characterization of polymer films

Polymer films are widely used in electronic packaging applications due to their low dielectric constant and ease of fabrication. These films often exhibit anisotropic electrical and thermomechanical properties, due to orientation of polymer chains, which need to be evaluated for performance and reliability modeling of electronic packages. This article presents a dual‐capacitor technique to measure the anisotropic dielectric permittivities of such films. Results are reported for in situ measurements for several spin‐coated polymeric films, some of which exhibit different permittivities in the in‐plane (x and y) and the through‐plane (z) directions (transversely isotropic), and free‐standing liquid crystalline Vectran films which exhibit orthotropic permittivities. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 2328–2334, 2001     

Three‐dimensional simulation of multi‐material injection molding: Application to gas‐assisted and co‐injection molding

This paper presents an overview of the results obtained at the Industrial Materials Institute (IMI) on the numerical simulation of the gas‐assisted injection molding and co‐injection molding. For this work, the IMI's three‐dimensional (3D) finite element flow analysis code was used. Non‐Newtonian, non‐isothermal flow solutions are obtained by solving the momentum, mass and energy equations. Two additional transport equations are solved to track polymer/air and skin/core materials interfaces. Solutions are shown for different thin parts and then for thick three‐dimensional geometries. Different operating conditions are considered and the influence of various processing parameters is analyzed.     

Three‐dimensional simulation on multilayer parison shape at pinch‐off stage in extrusion blow molding

We tried to predict the multilayer parison shape at pinch‐off stage in extrusion blow molding by nonisothermal and purely viscous non‐Newtonian flow simulation using the finite element method (FEM). We assumed the parison deformation as a flow problem. The Carreau model was used as the constitutive equation and FEM was used for calculation method. Multilayer parison used in this simulation was composed of high‐density polyethylene (HDPE) as inner and outer layers and low‐density polyethylene (LDPE) of which viscosity is five times lower than HDPE as a middle layer. We discussed multilayer parison shape in pinch‐off region. The results obtained are as follows; the parison shape of each layer was clearly visible in the pinch‐off during the mold closing. In addition, the distribution of parison thickness ratios for each layer was located for a large deformation near the pinch‐off region. The melt viscosity for each layer has an influence on the melt flow in the pinch‐off region. In a comparison with an experimental data of parison thickness ratios, the simulation results are larger than the experimental data. These simulation results obtained are in good agreement with the experimental data in consideration of the standard deviations. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Three‐dimensional numerical simulation of coalescence and interactions of multiple horizontal bubbles rising in shear‐thinning fluids

The dynamics of multiple horizontal bubbles rising from different orifice arrangements in shear‐thinning fluids was simulated numerically by three‐dimensional Volume of Fluid method. The effects of bubble size, rheological properties of shear‐thinning fluids, and orifice structure arrangements on multiple bubbles interaction and coalescence were analyzed, and the mechanisms of bubble coalescence and breakup were fully discussed and elucidated. The variation of bubble rising velocity during coalescence process and freely rising processes for different orifice arrangements was also deeply investigated. The critical initial horizontal intervals for coalescence of multiple horizontal bubbles with various orifice arrangements were attained by simulation, which could serve as the critical criterion of bubble coalescence or noncoalescence. Furthermore, the critical bubble interval was predicted based on the film drainage model, the prediction accords well with the simulation result and is quite conducive for the design and optimization of perforated gas–liquid contact equipment. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3528–3546, 2015     

Three‐dimensional flow measurements in a static mixer

Laminar heat and mass transfer are central to a wide range of industrial processes, encompassing (thermal) processing of viscous fluids, compact equipment for process intensification, and emerging microfluidic devices. Many of these applications incorporate the “static‐mixing principle” (stirring of a throughflow by internal elements) for mixing and heat‐transfer enhancement. Investigations on static mixers primarily concern numerical simulations. Experimental studies, on the other hand, are relatively rare and to date restricted to visualization of mixing patterns or integral quantities as for example, pressure drop and heat‐transfer coefficients. The present study expands on this by quantitative experimental analysis of three‐dimensional (3‐D) flow fields and streamline patterns in a representative static mixer using 3‐D particle‐tracking velocimetry. This necessitates tackling of (internal) refractions and reflections caused by the complex mixer geometry. Comparison of experimental results with numerical predictions reveals a good agreement. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1746–1761, 2013     

Three‐dimensional polymer flow in the calender bank

The velocity and pressure field that forms within the gap of a calender is numerically calculated. The numerical calculations are based on a decoupled calculation method for the free surface of the bank. The transport equations for mass and momentum are solved numerically. The position of the free surface of the bank is determined by shifting it until it matches a streamline. The resulting three‐dimensional velocity field gives the vortex patterns within the volume of the bank for fluids with non‐Newtonian and Newtonian rheological behavior. The shape of the free surface of the bank and its position are determined by the gap height, the circumferential speed of the rolls, the speed ratio, the feed mass flow into the gap and the rheological behavior of the polymer. Additionally, there are special requirements to be considered that determine the product quality, such as the thickness of the produced sheet, its uniformity and surface appearance, air inclusions and the mixing of the polymer. The calendering process itself requires limited operating windows for the variation of the process parameters in order to meet the product quality requirements. These operating windows are discussed and graphically plotted. Polym. Eng. Sci. 44:1642–1647, 2004. © 2004 Society of Plastics Engineers.     

Three‐dimensional simulations of biofilm growth in porous media

Biofilm growth occurs in a variety of random porous media in a range of industrial processes; prediction of its growth and subsequent influence on hydrodynamics is hence desirable. In this study, we present the first numerical 3D pore‐scale model of biofilm growth in porous media, based on a lattice Boltzmann simulation platform complemented with an individual‐based biofilm model (IbM). We use it to explore the coupled interaction between nutrient mass transport, biofilm growth, and hydrodynamics. Biofilm is shown to be very effective at reducing the permeability of porous media, particularly under nutrient limited conditions. We conclude with a direct comparison of 3D and 2D biofilm growth simulations in porous media and show the necessity of performing the simulations in 3D. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Three‐dimensional mapping of crystalline ceramic waste form materials

This work demonstrates the use of synchrotron‐based, transmission X‐ray microscopy (TXM) and scanning electron microscopy to image the 3‐D morphologies and spatial distributions of Ga‐doped phases within model, single‐ and two‐phase waste form material systems. Gallium doping levels consistent with those commonly used for nuclear waste immobilization (e.g., Ba_1.04Cs_0.24Ga_2.32Ti_5.68O₁₆) could be readily imaged. The analysis suggests that a minority phase with different stoichiometry/composition from the primary hollandite phase can be formed by the solid‐state ceramic processing route with varying morphology (globular vs. cylindrical) as a function of Cs content. The results presented in this work represent a crucial step in developing the tools necessary to gain an improved understanding of the microstructural and chemical properties of waste form materials that influence their resistance to aqueous corrosion. This understanding will aid in the future design of higher durability waste form materials.     

Three‐dimensional color prediction modeling of single‐ and double‐layered woven fabrics

In this research, the three‐dimensional structural and colorimetric modeling of three‐dimensional woven fabrics was conducted for accurate color predictions. One‐hundred forty single‐ and double‐layered woven samples in a wide range of colors were produced. With the consideration of their three‐dimensional structural parameters, three‐dimensional color prediction models, K/S‐, R‐, and L*a*b*‐based models, were developed through the optimization of previous two‐dimensional models which have been reported to be the three most accurate models for single‐layered woven structures. The accuracy of the new three‐dimensional models was evaluated by calculating the color differences ΔL*, ΔC*, Δh°, and ΔE_CMC(2:1) between the measured and the predicted colors of the samples, and then the error values were compared to those of the two‐dimensional models. As a result, there has been an overall improvement in color predictions of all models with a decrease in ΔE_CMC(2:1) from 10.30 to 5.25 units on average after the three‐dimensional modeling.     

Three‐dimensional electrospun micropatterned cellulose acetate nanofiber surfaces with tunable wettability

Three‐dimensional polymer nanofibrous mats with tunable wettability have been fabricated using a single step non‐conductive template assisted electrospinning process. Cellulose acetate nanofibers are electrospun over a nylon mesh, which acts as the template. The as‐deposited fiber mat is removed from this template to produce a free standing three‐dimensional micropatterned nanofibrous mat. By simply varying the template mesh dimensions, the fraction of the air‐liquid interface can be changed which allows control of the wetting mechanics. It is shown that the water contact angle can be varied from about 30° for a planar network to about 140° for a patterned mat implying a complete transition from hydrophilic to hydrophobic behavior. Furthermore, upon stretching the fiber mat loses its pattern irreversibly and reducing the contact angle from 140° to 110° with increasing stretching. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44709.     

Three‐dimensional anisotropic moisture absorption in quartz‐reinforced bismaleimide laminates

The three‐dimensional anisotropic moisture absorption behavior of quartz‐fiber‐reinforced bismaleimide (BMI) laminates is investigated by collecting 21 months of experimental gravimetric data. Laminates of six, twelve, and forty plies and various planar aspect ratios are used to determine the three‐dimensional anisotropic diffusion behavior when exposed to full immersion in distilled water at 25°C. The long‐term moisture absorption behavior deviates from the widely used Fickian model, but can be accurately captured by the three‐dimensional, anisotropic hindered diffusion model (3D HDM). Excellent agreement is achieved between experimental gravimetric data and the 3D HDM for all laminate thicknesses. Recovered model parameters are shown to slightly vary with laminate thickness due to the small changes in the cured‐ply thickness. However, model parameters identified for a given laminate thickness are observed to accurately predict the absorption behavior of samples with different planar dimensions. Equilibrium moisture content of 1.72, 1.69, and 1.84% and corresponding diffusion hindrance coefficients of 0.807, 0.844, and 0.671 are recovered for six, twelve, and forty‐ply laminates, respectively, thus confirming strong non‐Fickian behavior. Moisture absorption parameters may be determined successfully at 16.5 months of immersion, before reaching approximately 85% of the equilibrium moisture content at 21 months. Subsequent gravimetric measurements up to 21 months are consistent with the predicted long‐term behavior. POLYM. ENG. SCI., 54:137–146, 2014. © 2013 Society of Plastics Engineers     

Three‐dimensional simulation of the time‐dependent fluid flow and fouling behavior in an industrial hollow fiber membrane module

A novel three‐dimensional CFD model has been developed on the basis of fluid flow in the shell and lumen sides, and permeation and fouling behavior in the porous membrane zone. The simulated 25‐min dead‐end outside‐in filtration process showed that the energy consumed by the inlet manifold decreases during the constant pressure filtration. The velocity and pressure distributions in the module change with time. Flux distribution both in the axial and radial directions becomes increasingly more uniform, so does the cake distribution. Flux distribution and cake distribution inter‐adjust each other in different modes. A correlation equation has been developed to describe the relationship between the volumetric flow rate and accumulated water production. The correlation equation with simple experiment enables the dynamic evolution of energy consumed by shell inlet manifold to be presented, which can be the criterion of how well the shell inlet manifold or module has been designed. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2655–2669, 2018