Flows with suspended and floating particles

The evolution of the configuration of a set of particles dispersed in a flowing liquid is crucial in many applications such as sedimentation, slurry transport, rheology and structured arrays of micro- and nano-particles. Direct simulation based on what is called fictitious domain method coupled with finite element method has been used to study particulate flows and sedimentation process. Here we extend the previously proposed formulations to naturally include buoyancy force and the capillary driven attraction or repulsion of particles located at fluid interfaces. The set of differential equations is discretized using a fully implicit-fully coupled fictitious domain/finite element approach, avoiding numerical instabilities that may arise from explicit integration. The proposed formulation and implementation are validated by comparing the predictions of simple 2D flows to available numerical or analytical solutions. The method is then used to analyze the flotation of 2D particles and capillary driven aggregation at fluid interfaces.