Entrained flow gasification is a promising approach in dean and efficient utilization of coal as well as biomass. Knowledge of slag mobility is of fundamental as well as practical importance to maintain high performance in entrained flow coal or biomass gasification applications. Due to the complex behavior of slag mobility, especially in iron oxide-containing fuel slags, slag tap blockage remains a challenge. Slag mobility is directly related to the structure-dependent property viscosity. In this paper, a reliable, general viscosity model is therefore developed by taking into account the structure determined by temperature and composition and, for the first time, by oxygen partial pressure. The structure is described by means of a non-ideal associate solution used to describe the Gibbs energy of the liquid phase. This is a novel approach to bridge chemical and physical properties. In order to obtain a reasonable set of the model parameters, the viscosity behavior with respect to temperature, composition, and oxygen partial pressure is critically assessed in conjunction with the melt structure. The model calculations are further extended to evaluate systems with more than three components and the similarity in the predicted viscosity behavior in comparison to the experimental results in turn implies the validation of model parameters. The viscosities of several real coal and biomass slags are used to validate the model. The results show that the model gives a good performance in describing the viscosity over the whole range of compositions and a wide range of temperatures, as well as predicting the influence of oxygen partial pressures. This is achieved using only one set of model parameters, which have a clear physico-chemical meaning. The model is a self consistent, reliable, predictive tool for use in the regions where no experimental data are available. In combination with the phase relation this reliable model is applied to determine an optimum liquid slag system according to a target viscosity value under given conditions through a proper blending proportion of several fuel slags, which prevents a potential complex slag mobility of liquid-solid mixtures. The limitations of the current model applied to describe the slag mobility in real entrained flow gasifiers are also specified.