  By means of a three-dimensional amphiphilic lattice-Boltzmann model with
short-range interactions for the description of ternary amphiphilic fluids, we
study how the phase separation kinetics of a symmetric binary immiscible fluid
is altered by the presence of the amphiphilic species. We find that a gradual
increase in amphiphile concentration slows down domain growth, initially from
algebraic, to logarithmic temporal dependence, and, at higher concentrations,
from logarithmic to stretched-exponential form. In growth-arrested
stretched-exponential regimes, at late times we observe the self-assembly of
sponge mesophases and gyroid liquid crystalline cubic mesophases, hence
confirming that (a) amphiphile-amphiphile interactions need not be long-ranged
in order for periodically modulated structures to arise in a dynamics of
competing interactions, and (b) a chemically-specific model of the amphiphile
is not required for the self-assembly of cubic mesophases, contradicting claims
in the literature. We also observe a structural order-disorder transition
between sponge and gyroid phases driven by amphiphile concentration alone or,
independently, by the amphiphile-amphiphile and the amphiphile-binary fluid
coupling parameters. For the growth-arrested mesophases, we also observe
temporal oscillations in the structure function at all length scales; most of
the wavenumbers show slow decay, and long-term stationarity or growth for the
others. We ascribe this behaviour to a combination of complex amphiphile
dynamics leading to Marangoni flows.
