Heat Transfer in Porous Green Bodies During Binder Removal by Minimum Time Heating Cycles

Heat transfer in ceramic green bodies is examined during rapid binder removal cycles predicted by a variational calculus algorithm. Both the heat transfer and the mass transfer problems are described by one-dimensional spatial models, for which analytical solutions are available. During the minimum time heating cycles, the temperature difference within the green body is shown to depend on the thermal diffusivity, on the permeability, on the threshold pressure at which failure of the green body occurs, and on a number of other kinetic and transport parameters. The temperature difference within the green body is smallest during the early part of the minimum time heating cycle, when the constraint on pressure buildup within the green body limits the rate at which the temperature can be increased.     

Determination of the Minimum Time for Binder Removal and Optimum Geometry for Three-Dimensional Porous Green Bodies

A model is developed to optimize two aspects of the thermal removal of binder from green ceramic components. The model, which accounts for flow in porous media arising from the thermal decomposition of binder in three-dimensional bodies with anisotropic permeability, describes the pressure within the body as a function of position, time, and temperature during the heating cycle. The model is used with variational calculus to predict the heating profile that minimizes the cycle time for the thermal removal of binder. The model is also used to determine which body geometry maximizes the buildup of pressure in parallelepipeds, a common shape of multilayer ceramic capacitors.     

Minimum Time Heating Cycles for Diffusion‐Controlled Binder Removal from Ceramic Green Bodies

An algorithm based on variational calculus has been developed to predict the minimum time heating cycle (MTHC) for thermal binder removal from a ceramic green body when diffusion, as described by the free volume theory, is the governing mass transport mechanism. The algorithm uses a previously derived analytic solution for the diffusant concentration, which was obtained from the governing reaction–diffusion differential equation. Either a constraint on diffusant concentration or on the equilibrium pressure of diffusant is used to predict the MTHC for both a stationary binder model and a shrinking core binder model. For these four cases, the dependence of the MTHC has been determined on a number of model parameters, including the threshold concentration or pressure, the body size, and the reaction order of the binder degradation kinetics. The algorithm determines two important aspects of the MTHC, namely, the starting temperature of the heating cycle and how temperature varies with time during the cycle. The duration and shape of the temperature‐versus‐time heating schedule, whether increasing, decreasing, or almost constant, depends sensitively on parameters in the model.     

Determination of Binder Decomposition Kinetics for Specifying Heating Parameters in Binder Burnout Cycles

The decomposition kinetics of poly(vinyl butyral) binder from barium titanate multilayer ceramic capacitors with platinum metal electrodes were analyzed by thermogravimetric analysis as a function of the heating rate. The activation energy and pre-exponential factor for the decomposition kinetics were determined from two types of integral equations, from the Redhead method, and from the variation in heating rate method. The accuracy of the kinetic parameters determined from these methods was then evaluated for describing the observed rate of binder decomposition. Although the individual models yielded very different kinetic parameters, all were capable of describing the experimental data within ±15% accuracy. The kinetic parameters were then used in a coupled transport and kinetic model for describing the buildup of pressure within the ceramic green body as a function of the heating cycle. A methodology based on calculus of variations was also developed to predict the minimum duration for the binder burnout cycle.     

A process control algorithm for reaction-diffusion minimum time heating cycles for binder removal from green bodies

Minimum time heating cycles have been simulated for binder removal from ceramic green bodies where the product of binder decomposition exits the green body via diffusion. The model consists of the reaction-diffusion partial differential equation, ordinary differential equations describing the reaction kinetics and a heating function, and algebraic equations, one of which imposes a constraint on concentration or pressure to avoid failure of the green body. Two solution approaches were compared: an earlier approximate method based on the pseudo-steady state assumption combined with a variational calculus algorithm and a new approach based on the finite element method combined with a process control algorithm. The agreement between the two solution strategies reinforces the validity of the pseudo-steady state approximation and the utility of the process control methodology. The latter, which was also applied to problems in which no approximate solution was obtainable, is thus a general method for obtaining minimum time heating cycles.     

Minimum time heating cycles for diffusion‐ versus permeability‐controlled binder removal from ceramic green bodies

A comparison of minimum time heating cycles (MTHCs) was conducted for binder removal from ceramic green bodies for two mass transfer mechanisms: diffusion and gas permeability. The MTHCs were determined by combining approximate analytic solutions to the governing reaction‐diffusion and reaction‐gas permeability equations with a variational calculus algorithm containing a constraint on pressure buildup within the green body. Both the temperature‐time profile and duration of the MTHCs were sensitive to the operative transport process as well as to a number of model parameters including the pressure constraint, the total furnace pressure, the reaction kinetics, the gas permeability, and the diffusivity as described by the free volume theory. Strategies were identified which are most effective for decreasing the cycle time for each mass transfer mechanism.     

Determination of rapid heating cycles for binder removal from open pore green ceramic components

Abstract

Rapid heating cycles have been determined for the thermal removal of binder from open pore green ceramic components. The samples are multilayer green bodies with barium titanate as the dielectric, and the binder consists of poly(vinyl butyral) and dioctyl phthalate. The kinetics of binder decomposition, the gas permeability of the green body and the conditions at failure of the green body were determined from a combination of experiments and modelling. These results were then used with an algorithm based on variational calculus to develop successful rapid heating cycles without causing failure of the component.     

Binder Burnout from Layers of Alumina Ceramics Under Centrifugal Force

The effect of centrifugal force on the delamination of layered green body during binder burnout has been studied in terms of internal gas pressure resulting from gas flow kinetics in porous media. Here, a sheet of nano-particle of γ-alumina was prepared by tape casting using polyvinyl butyral (PVB, binder) and dibutyl phthalate (DBP, plasticizer). Because of the fine pore structure (average pore size of 25 nm), molecular flow kinetics was applied to estimate internal pressure arising from evolved gases. Assuming that delamination is related to internal pressure, the interfacial strength of the layer was estimated. This strength was modified by applying a compressive pressure controlled by a centrifugal force. Because of the increased interfacial strength, delamination was suppressed, even during rapid heating. The compressive pressure required increased proportionally with increasing heating rate, a tendency that agreed with the expectation based on the gas flow kinetics in porous media.     

Modeling of the Pressure Distribution in Three-Dimensional Porous Green Bodies during Binder Removal

A model is developed to describe flow in porous media from the thermal decomposition of binder in three-dimensional bodies with anisotropic permeability. The model is able to describe the pressure within the body as a function of position, time, and temperature during the heating cycle. The results from numerical solution of the un-steady-state partial differential equation are compared to those obtained from an analytical solution to the steady-state equation. Under many conditions that are representative of binder removal, the analytical solution provides a reasonable representation of the numerical solution. A criterion is also developed to determine when the analytical solution is valid. Scaling relationships for the buildup of pressure in terms of the dimensions of the body, the rate of reaction, and the permeability are also derived.     

The Effect of Cook‐Off on the Bulk Permeability of a Plastic Bonded Explosive

Plastic bonded explosives when exposed to prolonged heating environments undergo a variety of changes that affect their bulk chemical, thermophysical, and mechanical properties. During slow heating conditions, referred to as cook‐off, the thermal behavior of the polymeric binder plays an important role in the transformations of these composite energetic materials. The recently introduced Darcian flow hypothesis for PBX‐9501 implies that, during preignition, temperature gradients will lead to pressure gradients which in turn will drive convection of decomposition gases throughout the explosive, thus affecting ignition time and location. Here, we focus on the cook‐off behavior of PBX‐9501 and investigate its effects on bulk permeability to gases produced as a result of thermal decomposition. The concept of Darcian convection through porous media is defined and illustrated in detail by the derivation of the governing equations for a permeameter. Based on a systematic analysis involving: 1) our current understanding about binder behavior as a function of temperature, 2) the physics of the gas permeameter apparatus, 3) the concept of liquid drainage by gas, and 4) the experimental record of four permeameter experiments with cooked PBX‐9501, we conclude that samples heated up to 186 °C were not permeable in the Darcy‐flow sense.     

Fabrication and characterization of silica ceramic compact prepared using Aloe-Vera mucilage as a binder

In this study, silica compacts were fabricated through a powder processing route at different compaction pressure, using Aloe-Vera (AV) mucilage as a binder. The silica compacts were prepared at 90, 100, and 110 MPa compaction pressure using 0%–16 wt% of AV binder. The optimum amount of AV binder was 14 wt% for both 90 and 100 MPa and 12 wt% for 110 MPa. The maximum achieved green density and green strength of silica compacts at the optimum binder amount were 62.3% and 4 MPa, respectively at 110 MPa compaction pressure. The green silica compacts prepared at 110 MPa compaction pressure exhibited a minimum porosity of 21% and maximum flexural strength of 15 MPa after sintering at 1400°C. The green silica compacts with the optimum amount of binder were strong enough for machining. The Fourier transform infrared spectroscopy analysis revealed the functional groups present in AV mucilage. The binder burnout characteristic of AV mucilage in the silica compact was determined by thermogravimetric analysis and differential thermal analysis. Additionally, AV gel acted as a binder and solvent simultaneously for ceramic compaction.     

Permeability of Green Ceramic Tapes as a Function of Binder Loading

The permeability of green ceramic tapes was determined as a function of binder content for binder removed by air oxidation. The tapes were comprised of barium titanate as the dielectric, and polyvinyl butyral and dioctyl phthalate were the main components of the binder mixture. The flow in porous media through the tapes was analyzed in terms of models for describing Knudsen, slip, and Poiseuille flow mechanisms. The characteristic pore size was determined to be 1–2 μm, and thus Poiseuille flow was the dominant transport mechanism contributing to the flux. The permeability was then determined from Darcy's law for flow in porous media. The permeability was also determined from microstructural attributes in terms of the specific surface, the pore fraction, and a term to account for tortuosity and constrictions.     

Alumina dissolution process to fabricate bimodal pore architecture alumina with superior green and sintered properties

Herein, a straightforward, adaptable, and cost-effective approach has been proposed to realize the concept of dissolution of alumina in acidic aqueous media to fabricate porous alumina showing exceptional green machining properties and exhibiting good thermomechanical properties through in situ generated blowing agents and thermo-foaming process. The process involves dissolving alumina in concentrated sulfuric acid to generate aluminum hydroxide and aluminum sulfate, which act as blowing agents to produce pores in the final structure through a decomposition process at elevated temperatures. By varying the concentration of deionized water and acidification using sulfuric acid, different alumina slurries are prepared. Sintering shrinkage is well countered through simultaneous consolidation and decomposition process during the heat treatment, and a minimum shrinkage of 0.88% is achieved. In addition to its pore-forming properties, aluminum sulfate also provides strong binding effects to green bodies, contributing to their exceptional green machining properties. The resulting porous alumina exhibits a green flexural strength of up to 17 MPa, making it capable of bearing loads and forces during green machining. The sintered porous alumina fabricated in the study has a porosity range of 34.43%–59.24% and a flexural strength of 27.84–53.21 MPa. The prepared porous alumina also exhibits satisfactory thermal resistivity, with a minimum thermal conductivity of 1.23 W/m K, and has intra/intergranular space in the nano range. The coexistence of a combination of bimodal pores in a single monolithic matrix makes it exceptionally porous and suitable for an extensive spectrum of applications.     

Modeling of mass transfers in a porous green compact with two-component binder during thermal debinding

Mass transfers and phase changes of two-component binder in a porous green compact during thermal debinding process are modeled. The evaporation of low molecular weight (LMW) component and volatile fragments, the thermal degradation of high molecular weight (HMW) component, the capillary driven and pressure driven liquid phase transports, the binary diffusion in solutions, the convection and diffusion of gas phases, and the heat transfer in a porous medium are captured in the model. The model is validated with experimental data. The simulated results show that mass transfers during the early stage of thermal debinding are mainly due to capillary driven and pressure driven liquid transports. During the final stage of thermal debinding, both convective liquid and gas transports are important in binder removal. The developed model provides physical understanding of binder removal mechanisms that are essential for process optimization.     

Analytic Model for the Diffusant Concentration in Ceramic Green Bodies During Diffusion‐Controlled Thermal Binder Removal

The diffusion of the decomposition product of binder degradation has been modeled using the diffusion equation when a source term is present. An analytic solution to the governing nonlinear, unsteady‐state partial differential equations has been obtained for a planar body with two simplifications. The first approximation utilizes the pseudo‐steady‐state approximation whereas the second approximates the diffusivity, as given by the free volume theory, in terms of a single temperature‐dependent parameter. The analytic solution, which was compared to numerical solutions to establish the range of model validity, accurately describes the temporal and spatial distribution of the binder decomposition product during most of the heating cycle, especially when the concentration in the green body is the highest. The functional dependence of concentration within the body is established in terms of model parameters including the body size, degree of nonlinearity of the diffusivity, and the ratio of reaction rate to diffusivity.     

Fabrication of porous titania sheet via tape casting: Microstructure and water permeability study

In this article, we report the effects of slurry formulation and sintering conditions on the microstructure and permeability of porous titania sheets prepared by tape casting. It was found that solid concentration and binder content in the titania slurry play a vital role in the porosity and microstructure of the sintered titania sheets. Solid concentration and binder content were optimized based on the green tape quality and open porosity of the sintered titania sheets. The optimum solid concentration with the lowest surface roughness was obtained at 0.61 g/cm³. The effects of temperature and sintering time on the open porosity and crystal structure of the final product were also investigated. Increasing the sintering temperature from 1000 to 1100 °C resulted in increasing the pore size from 170 to 264 nm and decreasing the open porosity. Finally, water permeability of the porous titania sheets was studied to evaluate the permeation flux and maximum operating pressure. The results revealed that the permeability of the porous titania sheet is increased not only by increasing the open porosity but also by increasing the pore size.     

Pressure Distribution and Defect Formation in Green Ceramic Bodies During Supercritical Extraction of Binder

Supercritical extraction (SCE) with carbon dioxide at 10–40 MPa and 55°–90°C has been used to remove binder from multilayer green ceramic bodies. Defects such as cracking and delamination were occasionally observed in the green bodies following the extraction process, and these defects were attributed to pressure gradients that arise during isothermal depressurization from conditions of SCE. A model based on flow in porous media was developed to describe the temporal and spatial distribution of pressure within the green body during depressurization. The model incorporates both nonideal pressure–volume–temperature behavior and nonconstant viscosity of the supercritical fluid. The effects of the body size and gas-phase permeability on the pressure within the green body were examined.     

Study of the effect of aluminosilicate binder chemical composition on physicotechnical properties of porous permeable ceramic

Results are provided for a study of the effect of processing binder chemical composition on physicotechnical and corrosion properties of porous permeable ceramic based on electrocorundum. It is shown that physicotechnical properties of porous permeable ceramic depend both on chemical composition, and on specimen firing temperature. Use of a processing binder of aluminosilicate composition makes it possible to prepare objects from porous permeable ceramic with high strength properties with low firing temperatures.     

Numerical and experimental investigations on thermal debinding of polymeric binder of powder injection molding compact

A mathematical model is established to describe the thermal debinding process of polymeric binder from a powder injection molding compact. The model takes into account of the thermal degradation of liquid polymer into liquid volatile fragment, the evaporation of liquid volatile fragment, the capillary driven liquid phase transport, the binary diffusion in solution, the convection and diffusion of gas phases, and the heat transfer in a porous medium. The proposed model is solved numerically based on a finite volume method and validated with experimental data. Based on the numerical results, the binder removal, the pressure buildup, the binder distribution, the mass transfers, and the removal mechanisms during thermal debinding are studied.     

NMR RESPONSE OF POROUS MEDIA BY RANDOM WALK ALGORITHM: A PARALLEL IMPLEMENTATION

NMR well logging is a popular tool in the petroleum industry to estimate porosity, specific surface area, and permeability of porous media. In this study, a random walk algorithm is used to simulate the NMR response of porous, water-saturated media, which, in turn, probes the relation between microstructure and transport. The serial implementation of the random walk algorithm is computationally very intensive for large porous samples. A parallel random walk code is developed using Message Passing Interface (MPI) in Fortran. Various domain decomposition techniques are implemented. The walker distribution across processors without domain decomposition gives the best speedup. The domain decomposition with overlapped layers requires smaller processor memory. Increasing the overlap between adjacent domains lowers the interprocessor communication and leads to improved speedup. For the given parameters, an overlap of two layers was found to be optimal. Domain decomposition along the z direction was found to be more effective than decomposition along either the x or y direction. By using the parallel random walk code, we are able to solve a 256 ×256 ×256 voxel system in less than 8 h using 32 processors on an IBM SP2 machine.