Cure-induced viscoelastic effects in in-air photopolymerized droplets for microfluidic droplet-based 3D printing

Motivated by droplet-based additive manufacturing processes, this work presents a multiphysics numerical framework for in-air photopolymerization of resin droplets and their subsequent impact, spreading, and recoil on a solid substrate. The model couples two-phase incompressible flow with energy and species transport, incorporating radiative transport through the Beer–Lambert law to describe free-radical photopolymerization. This formulation enables prediction of core–shell droplet morphologies, in which a partially or fully cured outer shell encapsulates an uncured liquid core prior to impact. The key novelty of the proposed framework lies in the introduction of a cure-induced viscoelastic shell model, described using an Oldroyd-B-type constitutive formulation. The evolving stress response during photocuring is decomposed into equilibrium (elastic, spring-like) and non-equilibrium (viscous, Maxwell-type) contributions. The viscoelastic properties of the shell – including relaxation time as well as equilibrium and non-equilibrium moduli – are explicitly linked to the local degree of cure, allowing the progressive evolution of material stiffness and elasticity to be captured. Using this approach, we systematically quantify how cure-dependent viscoelasticity governs droplet-substrate interaction for micro-scale droplets across various UV intensity exposures with a specific impact velocity. Particular emphasis is placed on the role of viscoelasticity in post-impact recoil and rebound suppression. The proposed model provides a predictive tool for understanding and controlling droplet dynamics in UV-curable, droplet-based additive manufacturing processes.