New empirical rheological model for ceramics suspensions based on a hyperbolic sine formulation

Abstract

Understanding the rheological behavior of ceramic suspensions is crucial for optimizing shaping technologies, including slip casting, injection molding, and additive manufacturing. Classical models often fail to account for temperature effects, interfacial phenomena, and nonlinear concentration effects, thereby limiting their applicability to real processing conditions. This study introduces a new empirical rheological model based on a hyperbolic sine formulation, incorporating three physically interpretable parameters: the effective Einstein limit offset (A), the mixing viscosity factor (beta), and the interaction viscosity factor (C), verified in the concentration range 0-40 vol.%. Unlike conventional viscosity-concentration relationships, the proposed model captures the first measurable deviation from the dilute Einstein regime and describes the progressive nonlinear rise of relative viscosity using a compact analytical expression. The parameter beta captures the effects of interfacial tension, liquid viscosity, and effective particle number density under isothermal conditions, as confirmed by its temperature and shear-dependent decrease and by its reduction in dispersant-stabilized suspensions, where steric layers diminish particle interactions. Therefore, parameter beta provides a physically grounded link between the suspension structure and its rheological response. The model demonstrates excellent agreement with experimental data, outperforming five established rheological models across multiple systems and measurement conditions. These findings highlight the novelty of the proposed formulation as both a flexible fitting tool and a physically meaningful descriptor of early-stage viscosity evolution.