A mathematical model describing the densification process during viscous sintering process of a material contains solid inclusions is developed (modified) from a Scherer model which describes the rate of densification during sintering for a free solid inclusions material. The modified model is used to simulate the rate of densification during sintering process for ceramic heterogeneous materials consist from mixtures of some Iraqi clays that had been prepared in a previous work. In addition the modified model is used to study the effect of several factors on densification during sintering process and used in predicting the effective viscosity of the viscous phase that formed during sintering. The factors are the sintering temperature, sintering time, and the ratio of solid inclusions volume to viscous phase volume.Another two heterogeneous models which are the composite sphere and the self consistent models are also applied and used to study the effect of sintering temperature and sintering time on densification during sintering for comparison with the present developed model.The modified model is also used to study the effect of pore size distribution on densification process by assuming a Gaussian distribution for the pore sizes and reformulating the equations of the modified model to make them depend on the standard deviation of pore size distribution.The physical parameters like viscosity are computed from the fitting process of the practical data of the samples.Computer programs in FORTRAN 90 language are designed to study the effect of sintering temperature on densification process using the developed model, the composite sphere and the self consistent models. These programs are modified to simulate the densification process versus time duration of the sintering process. Another program is designed to study the effect of pore size distribution on sintering process using the developed model.The results from the developed (modified) Scherer model are better fit the practical data, then the composite sphere model.The results from the program of the effect of sintering temperature indicates in general that the rate of densification is increased with increasing sintering temperature, this is due to the decrease in the viscosity with temperature increasing. However, when the ratio of the solid inclusions is high the viscosity is increased at relatively high sintering temperatures (about 1400oC) this increase in viscosity may be due to induced crystallization processes, accordingly the rate of densification is decreased at these circumstances. The results from the program of the effect of sintering time indicate that the modified model predicts that the increase in density is semi logarithmic with time, while the other two models predict an exponential increase with time. The results from the program of the effect of pore size distribution indicate that this parameter has a strong effect if the distribution is broad only in the last stages of densification because the largest pores are relatively slow to close.
