A dimensionless framework for hold-up mass prediction and scale transfer in continuous linear blending

In this work, a dimensionless model is proposed to describe the influence of operating conditions on the hold-up mass (HUM) of a continuous linear blender. The model relates the fill level (normalized hold‑up mass per blender volume) to three key dimensionless groups: a flow-related parameter (χ), the Froude number (Fr), and the number of mixing elements (H). A physically interpretable analytical expression is introduced and calibrated using experimental data across multiple materials and operating conditions. The model demonstrates strong predictive performance, with root mean square errors typically below 5%. Predictions obtained with the intermediate shaft configuration, which was excluded from parameter calibration, demonstrated the model's interpolation capability and calibration robustness. Furthermore, scale transfer was evaluated by calibrating the model using a smaller scale CDC-10 blender and applying it to predict fill level in a larger CDC-50 blender. Comparable prediction errors between calibration and external validation demonstrate the ability of the model to capture the dominant trends governing hold-up behavior across the process conditions studied. In addition, a simplified set of scale transfer rules is derived from the dimensionless framework, showing that maintaining Froude number and χ enables consistent performance across scales. These rules are experimentally validated across a range of formulations and operating conditions, including a real industrial case study. Overall, this work provides a predictive framework to quantify and transfer blending conditions in continuous tableting, supporting more efficient process development and more robust scale transfer.