Modeling filtration flow rate in peristaltic pump systems for high-viscosity bovine serum albumin: A multivariate nonlinear approach.

Filtration of highly viscous pharmaceutical solutions exhibits a non-linear relationship between pump speed and flow rate. To systematically investigate this phenomenon, experiments were conducted across a wide range of solution viscosities (1.0-25.7 cP) and pump speeds (10-120 rpm). In 1.0 and 2.5 cP solutions, flow rate increases linearly with pump speed. However, for solutions with viscosity ≥ 5 cP, the relationship exhibits a linear region followed by a nonlinear decline beyond a critical inflection point. Notably, this inflection point shifts to lower pump speeds as viscosity increases. Four different models were fitted and compared, a segmented kinetic model was developed to describe the relationship between flow rate, pump speed, and viscosity, capturing both linear and nonlinear regimes. By identifying a consistent inflection point at approximately 19 psi and applying a power-law function to characterize viscosity-dependent pump speed, Darcy's law and theoretical flow limits were integrated to enable direct calculation of key process parameters. This model achieved an excellent fit (R²: 0.998), reduced prediction error (MAPE: 3.2 %, MAE: 0.229, RMSE: 0.303), and revealed consistent kinetic behavior. These findings provide a predictive method for optimizing filtration performance, improving technology transfer, and enhancing scale-up reliability in biopharmaceutical manufacturing.