The influence of particles on the dynamics and eventual rupture of stretching liquid bridges is demonstrated experimentally in a drop-forming case. To analyze the particle-scale basis for the influence of particles in this flow, a lattice Boltzmann algorithm for a three-phase system of liquid, gas, and solid particles, has been developed. This provides full coupling between particles and fluids, fluid interfacial forces, and possible entry of particles into the interface (i.e. full and partial wetting by the liquid are considered). This work details the numerical method and its validation, and presents results of the simulations and related experiments. Fully-wetting particles up to a solid volume fraction of phi = 0.3 monotonically increased the rupture length of liquid bridges, as seen in experiments; experimental results show that the increase continues to a maximum at phi approximate to 0.4, a condition beyond the present numerical capability. Depending on the wettability and volume fraction of the particles in the liquid bridge, particles can alter the structure of the bridge at pinch-off, suppress satellite drops, or produce asymmetrical pendant/sessile suspension drops as a result of their discrete nature. Particles with a neutrally wetting contact angle (theta = 90) can reside in the bulk or be immersed in the interface if fluid deformation brings them into contact with it, and capillary forces are found to bring the interfacial particles near the narrow region (or "throat") of the bridge prior to rupture. Fully wetting particles (theta approximate to 0 degrees) remained interior to the liquid bridge, leaving less space to escape the throat region. Neutrally wetting particles increased the rupture length and altered the pinch-off structure relative to the particle-free case, but less so than fully wetting particles. (C) 2015 Elsevier Ltd. All rights reserved.