  We investigate spinodal decomposition and structuring effects in binary
immiscible and ternary amphiphilic fluid mixtures under shear by means of three
dimensional lattice Boltzmann simulations. We show that the growth of
individual fluid domains can be arrested by adding surfactant to the system,
thus forming a bicontinous microemulsion. We demonstrate that the maximum
domain size and the time of arrest depend linearly on the concentration of
amphiphile molecules. In addition, we find that for a well defined threshold
value of amphiphile concentration, the maximum domain size and time of complete
arrest do not change. For systems under constant and oscillatory shear we
analyze domain growth rates in directions parallel and perpendicular to the
applied shear. We find a structural transition from a sponge to a lamellar
phase by applying a constant shear and the occurrence of tubular structures
under oscillatory shear. The size of the resulting lamellae and tubes depends
strongly on the amphiphile concentration, shear rate and shear frequency.
