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We present a progress report on our work on lattice Boltzmann methods forcolloidal suspensions. We focus on the treatment of colloidal particles inbinary solvents and on the inclusion of thermal noise. For a benchmark problemof colloids sedimenting and becoming trapped by capillary forces at ahorizontal interface between two fluids, we discuss the criteria for parameterselection, and address the inevitable compromise between computationalresources and simulation accuracy.Comment: 14 pages, 3 figures. Invited talk, Colloidal Dispersions in External  Fields, Bonn 2004. To appear in published proceeding

Simulating colloid hydrodynamics with lattice Boltzmann methods