Deep-Learning-Enhanced Modeling of Electrosprayed Particle Assembly on Non-spherical Droplet Surfaces

Monolayer assembly of charged colloidal particles at liquid interfaces opens a new avenue for advancing the additive manufacturing of thin film materials and devices with tailored properties. In this study, we investigated the dynamics of electrosprayed colloidal particles at curved droplet interfaces through a combination of physics-based computational simulations and machine learning. We employed a novel mesh-constrained Brownian dynamics (BD) algorithm coupled with Ansys® electric field simulations to model the transport and assembly of charged particles on a non-spherical droplet surface. We demonstrated that the electrostatic repulsion between particles, electrophoretic forces induced by substrate surface charge, and Brownian motion are the key factors influencing the compactness and ordering of the assembly structure. We further trained a deep neural network surrogate model using the data generated from the BD simulations to predict radial distribution functions (RDF) of particle assembly. By coupling the surrogate model with Bayesian optimization, we identified the optimal particle and substrate charge densities that yield the best match between the simulation and experimental assembly. Using the optimal charge densities, the RDF profile of the simulated assembly accurately matches the experiment with a similarity of 96.4%, and the corresponding average bond order parameter differs by less than 5% from the experimental one. This deep-learning-based approach significantly reduces computational time while maintaining high accuracy in predicting the important features of the assembly structures. The charge densities inferred from the modeling provide critical insights into the surface charge accumulation in the electrospray process.