A Numerically Stable Sequential Model for Estimating Shear Rheological Parameters of Food Fluids

ABSTRACT This study aims to improve the numerical stability of rheological parameter estimation for non‐Newtonian food fluids by proposing a Sequential Herschel–Bulkley (SHB) model, which sequentially estimates yield stress ( τ 0 ), consistency index ( K ), and flow behavior index ( n ) using pressure drop and flow rate data obtained from tube flow. In contrast to the conventional Herschel–Bulkley (HB) model, which fits all three parameters simultaneously and is susceptible to numerical instability, the SHB model first determines τ 0 using the Casson equation and then fits K and n with τ 0 fixed. The method was validated using tamarind seed gum (TG) solution, xanthan gum (XG) solution, and ketchup. Flow curves derived from SHB‐based tube‐flow measurements showed improved agreement with rotational viscometer data, particularly for ketchup, where the mean absolute percentage error (MAPE) decreased from 4.49% for the HB model to 2.10% for the SHB model. In addition, repeated nonlinear fitting demonstrated that the SHB model consistently reduced the coefficients of variation and parameter variances relative to the HB model, indicating enhanced robustness. These findings demonstrate that the SHB model provides a concise, reliable, and numerically stable approach for estimating shear rheological parameters of yield‐stress food fluids using practical in‐line measurement signals.