Phase-field-based modelling of the gelation process of biopolymer droplets in 3D bioprinting

Naturally derived hydrogels are the most common bioink material for droplet-based bioprinting. The mechanical stability of the printed construct and the cell viability are closely related to the gelation process of natural hydrogels, which is initiated by the coil-to-helix transition in a single polymer chain and followed by association of helices. In this study, a phase-field-based modelling approach is employed to simulate the gelation process of microdroplets. A thermo-viscoelastic model incorporating a phase-field variable is used to describe the deformation behaviour of hydrogels in the thermal-induced gelation process. In connection with the gelation kinetics, a new form of the bulk free energy density is proposed to include the free energies related to the mixture of macromolecules in the solution and the coil-to-helix transition. Using the proposed phase-field model, numerical simulations are performed to study the effects of the droplet size and the printing medium on the gelation process of microdroplets.