  We simulate by lattice Boltzmann the steady shearing of a binary fluid
mixture with full hydrodynamics in three dimensions. Contrary to some
theoretical scenarios, a dynamical steady state is attained with finite
correlation lengths in all three spatial directions. Using large simulations we
obtain at moderately high Reynolds numbers apparent scaling expon ents
comparable to those found by us previously in 2D. However, in 3D there may be a
crossover to different behavior at low Reynolds number: accessing this regime
requires even larger computational resource than used here.
