Pressure distribution during binder burnout in three-dimensional porous ceramic bodies with anisotropic permeability
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Z.C. Feng Department of Mechanical and Aerospace Engineering, University of Missouri—Columbia, Columbia, Missouri 65211 (Received 22 October 2001; accepted 20 March 2002)
The flow of gas-phase products in three-dimensional porous bodies was modeled for the case when a source term is present. Analytical solutions to the governing partial differential equations were obtained for bodies of parallelepiped and cylindrical geometry. An important feature of the model is that it treats the case where the permeability in the body may be anisotropic. The evolution of pressure within the body depends on a number of parameters, including the rate of production of gas-phase species, and on the dimensions of the body. The model is thus able to describe the pressure within a porous ceramic body arising from flow during a number of elevated-temperature processing operations such as drying, binder burnout, and sintering.
I. INTRODUCTION
In the fabrication of ceramic components, many elevated-temperature processing operations lead to the flow of gaseous products through a porous continuum particle network. Binder burnout, drying, and sintering are examples of such processes; of these, binder burnout1 is often the longest for which the yield losses can be substantial. The low yield arises because during binder burnout, gas-phase decomposition products are formed, which result in a distribution of pressure in the pore space of the body. This, in turn, causes stress within the skeletal network. Product loss then occurs when the local stress either causes mechanical failure of the body or leads to defects within the body. The former failure mechanism refers to cracks, delamination, or complete fracture of the body whereas the latter refers to bubbles. For the removal of poly(vinyl butyral) binder from barium titanate multilayer ceramic capacitors, Liau et al. demonstrated that the modes of failure observed were cracks, delamination, and fracture.2 They further showed that the process yield depends on the volume of the capacitor and on the aspect ratio of the body. In addition, these authors observed that the flow of the decomposition products exiting the body was faster in the directions parallel to the layers of the ceramic tapes, which suggests that the permeability is anisotropic within the body. One objective of this work is to provide a model that, in a very 1434
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J. Mater. Res., Vol. 17, No. 6, Jun 2002 Downloaded: 18 Mar 2015
general sense, can take into account anisotropic permeability along with the relevant length scales of the body. This model can then be used to guide the development of binder removal cycles to prevent the occurrence of the aforementioned defects. A number of models have been developed to describe aspects of the binder burnout process,2–22 and these models can be divided into two types. For bodies highly loaded with binder and thus having low initial values of porosity, diffusion of the decomposition products through the binder in the nearly filled pore space has been identif
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