A scaling law of particle transport in inkjet-printed particle-laden polymeric drops

Hydrogels with embedded functional particulates are widely used to create soft materials with innovative functionalities. In order to advance these soft materials to functional devices and machines, critical technical challenges are the precise positioning of particulates within the hydrogels and the construction of the hydrogels into a complex geometry. Inkjet printing is a promising method for addressing these challenges and ultimately achieving hydrogels with voxelized functionalities, so-called digital hydrogels. However, the development of the inkjet printing process primarily relies on empirical optimization of its printing and curing protocol. In this study, a general scaling law is proposed to predict the transport of particulates within the hydrogel during inkjet printing. This scaling law is based on a hypothesis that water-matrix interaction during the curing of inkjet-printed particle-laden polymeric drops determines the intra-drop particle distribution. Based on the hypothesis, a dimensionless similarity parameter of the water-matrix interaction is proposed, determined by the hydrogel's water evaporation coefficient, particle size, and mechanical properties. The hypothesis was tested by correlating the intra-drop particle distribution to the similarity parameter. The results confirmed the scaling law capable of guiding ink formulation and printing and curing protocol.