  We describe some scaling issues that arise when using lattice Boltzmann
methods to simulate binary fluid mixtures -- both in the presence and in the
absence of colloidal particles. Two types of scaling problem arise: physical
and computational. Physical scaling concerns how to relate simulation
parameters to those of the real world. To do this effectively requires careful
physics, because (in common with other methods) lattice Boltzmann cannot fully
resolve the hierarchy of length, energy and time scales that arise in typical
flows of complex fluids. Care is needed in deciding what physics to resolve and
what to leave unresolved, particularly when colloidal particles are present in
one or both of two fluid phases. This influences steering of simulation
parameters such as fluid viscosity and interfacial tension. When the physics is
anisotropic (for example, in systems under shear) careful adaptation of the
geometry of the simulation box may be needed; an example of this, relating to
our study of the effect of colloidal particles on the Rayleigh-Plateau
instability of a fluid cylinder, is described. The second and closely related
set of scaling issues are computational in nature: how do you scale up
simulations to very large lattice sizes? The problem is acute for systems
undergoing shear flow. Here one requires a set of blockwise co-moving frames to
the fluid, each connected to the next by a Lees-Edwards like boundary
condition. These matching planes lead to small numerical errors whose
cumulative effects can become severe; strategies for minimising such effects
are discussed.
