Breakthrough Curve Modeling for Protein Adsorption in Fibrous Depth Filters Using Colloid Filtration Theory

Depth filters are increasingly used in downstream bioprocess operations to separate colloidal impurities from suspensions. In this article, we present a model for the breakthrough behavior of fibrous depth filters applicable to protein suspensions and study the impact of colloidal and hydrodynamic interactions due to the flow around the adsorptive fiber surfaces. The single fiber efficiency (SFE) is used with the Thomas model to predict the breakthrough curves. The impact of protein size, flow geometry, and colloidal interactions are analyzed to show their impact on protein adsorption in fibrous filter media. Our breakthrough studies showed that depth filter performance depends upon protein size and flow details that conventional kinetic models treat empirically through rate constants. Faster breakthrough times were observed for larger proteins due to lower diffusivities leading to less effective filter bed utilization. The SFE-breakthrough model provides a basis for relating dynamic deposition rates to the hydrodynamic flow through fibrous beds. Enhanced predictive power can be obtained by applying the SFE to more comprehensive mass transfer or deposition rate models. Relating depth filter breakthrough to critical process conditions provides insight into impurity clearance and filter sizing during downstream process development.