Mathematical model to predict separation of C-phycocyanin from Spirulina sp. using an expanded-bed vortex flow reactor and its subsequent scaling-up

This study presents a novel single-step method for the separation and purification of C-phycocyanin (CPC) extracted from dry Spirulina sp. using an expanded-bed vortex flow reactor (EB-VFR). The EB-VFR employed a DA405/EB polymethacrylate resin functionalized with tertiary amino groups, expanded by axial flow and stabilized by a laminar Taylor vortex generated by a central rotating cylinder. The CPC extract (2.3 g/L) was processed through the reactor (settled resin height: 20 cm) at rotation speeds of 0, 50, 100, and 150 rpm with an axial flow rate of 200 cm/h, followed by elution with a 500 mM phosphate buffer. At 100 rpm, the CPC yield reached 45%, while purity increased from 0.50 to 2.0 and the concentration to 3.3 g/L, demonstrating the reactor's ability to achieve simultaneous concentration and purification. A mathematical model was developed to correlate operating parameters with dimensionless numbers (Taylor and Reynolds), providing quantitative predictions of CPC adsorption and elution performance. Experimental results obtained using radially and axially scaled-up EB-VFRs were in good agreement with the model predictions, confirming its applicability in process design and scale-up. These findings highlight the EB-VFR as an effective and scalable platform for the recovery of bioactive proteins from cyanobacteria, enabling efficient separation under dynamic hydrodynamic conditions. The approach offers significant potential for sustainable bioprocessing by integrating adsorption, washing, and elution into a single continuous operation with controllable hydrodynamic expansion and mixing behavior.