GENERALIZED FLUID-FLOW MODEL FOR CERAMIC TAPE CASTING

The fluid mechanics associated with the flow of a ceramic slurry during the tape casting process is analyzed in this paper. The rheology of the slurry is described in generalized terms using the Ostwald-de Waele power-law equation, tau = m\gamma\(n), where the yield constant, m, and the shear rate exponent, n, are empirical functions of the particle loading in the slurry, the particle shape and size distributions in the slurry, and the slurry temperature. The effects of an imposed pressure gradient due to the height of the slurry in the casting head, as well as those of the drag due to the moving substrate on the slurry flow, are accounted for by modeling the slurry discharge as a generalized planar Couette flow. The model yields an analytical expression for the tape thickness as a function of various slurry and process parameters. The influence of the physical parameters of the slurry and the geometrical dimensions of the casting head on the tape thickness are examined in the context of a commonly used BaTiO3 system. It is shown that the various parametric effects may be represented concisely in the form of a nondimensional design plot employing (a) a flow parameter, alpha, (b) a shrinkage parameter, beta, and (c) the theology exponent, n.