  We study the behaviour of cubic blue phases under shear flow via lattice
Boltzmann simulations. We focus on the two experimentally observed phases, Blue
Phase I (BPI) and Blue Phase II (BPII). The disclination network of Blue Phase
II continuously breaks and reforms under steady shear, leading to an
oscillatory stress response in time. For larger shear rates, the structure
breaks up into a Grandjean texture with a cholesteric helix lying along the
flow gradient direction. Blue Phase I leads to a very different response. Here,
oscillations are only possible for intermediate shear rates -- very slow flow
causes a transition of the initially ordered structure into an amorphous
network with an apparent yield stress. Larger shear rates lead to another
amorphous state with different structure of the defect network. For even larger
flow rates the same break-up into a Grandjean texture as for Blue Phase II is
observed. At the highest imposed flow rates both cubic blue phases adopt a
flow-aligned nematic state. Our results provide the first theoretical
investigation of sheared blue phases in large systems, and are relevant to
understanding the bulk rheology of these materials.
