A multiphase DNS (direct numerical simulation) method is used to investigate two types of particle-particle interactions relevant in dispersed liquid-solid flows: the interaction between two solid particles under non-isothermal conditions, and the interaction between a solid particle and a deforming particle (e.g. a bubble). It is shown that the drafting, kissing and tumbling sequence of two sedimenting solid particles can be significantly affected by the presence of simultaneous particle-fluid heat transfer. For small but finite internal particle heat sources, the drafting sequence is faster and the interaction is speeded up. However, for larger internal heat sources, the kissing and tumbling events may be inhibited altogether by the natural convection currents developing around the particles. In addition, isothermal interactions between a solid particle and a bubble are investigated. It is shown that the particle-bubble attachment process may be significantly altered under conditions of lowered surface tension (i.e. after addition of surfactants) due to an increased tendency for the bubble to deform.