Simulative Minimization of Mass Transfer Limitations Within Hydrogel-Based 3D-Printed Enzyme Carriers

In biotechnology, immobilization of functional reactants is often done as a surface immobilization on small particles. Examples are chromatography columns and fixed-bed reactors. However, the available surface for immobilization is directly linked to particle diameter and bed porosity for these systems, leading to high backpressure for small particle sizes. When larger molecules, such as enzymes are immobilized, physical entrapment within porous materials like hydrogels is an alternative. An emerging technique for the production of geometrically structured, three-dimensional and scalable hollow bodies is 3D-printing. Different bioprinting methods are available to produce structures of the desired size, resolution and solids content. However, in case of entrapped enzymes mass transfer limitations often determine the achievable reactivities. With increasing complexity of the system, for example a fixed-bed reactor, 3D-simulation is indispensable to understand the local reaction conditions to be able to highlight the optimization potential. Based on experimental data, this manuscript shows the application of the dimensionless numbers effectiveness factor and Thiele modulus for the design of a 3D-printed flow-through reactor. Within the reactor, enzymes are physically entrapped in 3D-printed hydrogel lattices. The local reaction rate of the enzymes is directly dependent on the provided substrate amount at the site of reaction which is limited by the diffusion properties of the hydrogel matrix and the diffusion distance. All three parameters can be summed up by one key figure, the Thiele modulus, which, in short, quantifies mass transfer limitations of a catalytic system. Depending on the rate of the enzymatic reaction in correlation to the diffusional transport, mass transfer limitations will shift the optimum of the system, favoring slow enzyme kinetics and small diffusion distances. Comparison with the enzymatic reaction rate in solution yields the effectiveness factor of the system. As a result, the optimization potential of varying the 3D-printed geometries or the reaction rate within the experimentally available design space can be estimated.