The structure-rheology relationship in three-dimensional sheared lamellar phase : Effect of viscosity contrast

The structure-rheology relation in a sheared lamellar mesophase is studied by varying Ericksen number Er (viscous/elastic stress), Schmidt number Sc (momentum/mass diffusivity) and difference in viscosity between hydrophilic and hydrophobic phase using a mesoscale model. It is observed that the coarsening process is not altered by viscosity contrast for any Er or Sc before segregation , because the dominant mechanism is diffusion at early times, but the scaled effective viscosity (scaled by well aligned span wise configuration viscosity) is affected After layer formation, the scaled effective viscosity decreases slowly for systems with high viscosity contrast, because the process is affected by momentum transfer. The effect of viscosity contrast is prominent at a moderately high value of Er=0.03, where the stiffness of the layers leads to a steady state defect density in layers aligned in the span-wise direction at low Sc(0.33) which is perfectly aligned for no contrast. At higher Er =0.3 with contrast , dominant contribution of shear stress from viscous effects for lesser stiff layers and presence of partially spanned layers aligned in wall normal direction brings the scaled effective viscosity below 1 though the steady state defect density is hardly changed. When Er is decreased further (Er=0.003) at low Sc and finite contrast , the steady state alignment direction changes from span-wise to wall normal direction with tilted layers because of very high stiff layers flowing through low viscosity regions.