  Mixed surfactant systems with strongly bound counterions show many
interesting phases such as the random mesh phase consisting of a disordered
array of defects (water-filled nano-pores in the bilayers). The present study
addresses the non-equilibrium phase transition of the random mesh phase under
shear to an ordered mesh phase with a high degree of coherence between
nano-pores in three-dimension. In-situ small-angle synchrotron X-ray study
under different shear stress conditions shows sharp Bragg peaks in the X-ray
diffraction, successfully indexed to the rhombohedral lattice with R$\bar{3}$m
space group symmetry. The ordered mesh phase shows isomorphic twinning and
buckling at higher shear stress. Our experimental studies bring out rich
non-equilibrium phase transitions in concentrated cationic surfactant systems
with strongly bound counterions hitherto not well-explored and provide
motivation for a quantitative understanding.
