Jet breakup is strongly affected by fluid rheology. In particular, small amounts of polymer can cause substantially different breakup dynamics compared to a Newtonian jet, influencing in-flight fragmentation and detachment from the nozzle. Significant concentrations may also impede jettability. Furthermore, most commercial and industrial inks are inherently colloidal due to the presence of pigment and other additives. Fluids containing a particulate phase are normally shear-thinning and so may have a different characteristic viscosity within the nozzle compared to the ejected ligament. We have developed numerical simulations using a Lagrangian finite element method that captures the free surface automatically, and admits a variety of viscosity dependences, e.g. on the local shear rate (generalized Newtonian fluid) or on the particle concentration (Krieger-Dougherty type models), in addition to several viscoelastic models for polymeric fluids. This method has been benchmarked against experimental data for Newtonian jets. Appropriate rheological models are discussed, and results are presented alongside comparisons with experimental work.