The fundamental operation in binder jet three-dimensional printing is the deposition of liquid binder into a powder layer to selectively bond particles together. Upon droplet impact, the binder spreads into the powder bed forming a bound network of wetted particles called a primitive. A computational fluid dynamics framework is proposed to directly simulate the capillary and hydrodynamic effects of the interfacial flow that is responsible for primitive formation. The computational model uses the volume-of-fluid method for capturing dynamic binder-air interfaces, and the immersed boundary method is adopted to include particle geometries on numerical Cartesian grids. Three-phase contact angles are prescribed through an interface extension algorithm. Binder droplet impact on powder beds of varying contact angle are simulated. Furthermore, the numerical model is used to simulate liquid bridges connecting binary and ternary particle systems, and the resulting capillary and hydrodynamic forces are validated by comparison with published experimental and theoretical model results.