We report on the stress response of gyroidal and lamellar amphiphilic
mesophases to steady shear simulated using a bottom-up lattice-Boltzmann model
for amphiphilic fluids and sliding periodic (Lees-Edwards) boundary conditions.
We study the gyroid per se (above the sponge-gyroid transition, of high
crystallinity) and the molten gyroid (within such a transition, of
shorter-range order). We find that both mesophases exhibit shear-thinning, more
pronounced and at lower strain rates for the molten gyroid. At late times after
the onset of shear, the skeleton of the crystalline gyroid becomes a structure
of interconnected irregular tubes and toroidal rings, mostly oriented along the
velocity ramp imposed by the shear, in contradistinction with free-energy
Langevin-diffusion studies which yield a much simpler structure of disentangled
tubes. We also compare the shear stress and deformation of lamellar mesophases
with and without amphiphile when subjected to the same shear flow applied
normal to the lamellae. We find that the presence of amphiphile allows (a) the
shear stress at late times to be higher than in the case without amphiphile,
and (b) the formation of rich patterns on the sheared interface, characterised
by alternating regions of high and low curvature.Comment: 15 pages, 10 figures, Physical Review E, in pres