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.