Effect of matrix solidification on the structure formation in electromagnetic suspensions

For suspensions with electromagnetic particles exposed to an external field, we examine the effect of the solidification of the suspending medium on the formation of particle structures, representative of the curing of a photo-reactive resin during stereolithography. To that end, Brownian Dynamics (BD) simulations are examined in which the solidification of the suspending medium can be incorporated by increasing its viscosity in the course of time. For illustrative purposes, it is assumed that the viscosity function is known apriori in explicit and parametrized form, however, experimental data can be used as well. It is demonstrated that one can study the effects of the viscosity increase by a transformation of time, akin to the time–temperature superposition principle, but here also in the presence of thermal noise on the suspended particles. Therefore, instead of performing BD simulations with a continuously increasing viscosity (computationally inefficient), we advocate performing simulations at a constant (low) viscosity and subsequently transform time (nonlinearly) for re-interpretation of the simulation results. So doing, one can predict the formation of particle structures during on-going solidification of the suspending medium. In practice, the viscosity increase is so drastic that further evolution of the particle structure can be considered as arrested after the characteristic transition-time of the viscosity is reached. Semi-quantitative rules of thumb are formulated for the 3D-printing practitioner. Graphical Abstract