Catenary shape evolution of spanning structures in direct-write assembly of colloidal gels

This paper proposes a catenary model to describe the shape evolution of spanning filaments created by an extrusion-based, solid freeform fabrication process. Although colloidal gels have excellent self-support properties, their transient viscoelastic dynamics inevitably leads to fast deflection of spanning filaments under gravity. This model is derived from static force analysis of finite spanning filaments by assuming mechanical behavior of colloidal gels to follow a Kelvin-Voigt analogue. This model resembles a viscoelastic catenary to track the dynamic shape of spanning filaments after deposition, and compute their equilibrium shape profiles after long resting time. The model results are compared to published experimental data of lead zirconate titanate (PZT) colloidal inks (Smay et al., 2002a), which confirm the validity of this model for understanding of shape evolution of spanning features in solid freeform fabrication.