Orientation selection in lamellar phases by oscillatory shears.

Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear

We introduce a model constitutive law for the dissipative stress tensor of lamellar phases to account for low frequency and long wavelength flows. Given the uniaxial symmetry of these phases, we argue that the stress tensor must be the same as that of a nematic but with the local order parameter being the slowly varying lamellar wavevector. This assumption leads to a dependence of the effective...

The role of viscoelastic contrast in orientation selection of block copolymer lamellar phases under oscillatory shear

The mesoscale rheology of a lamellar phase of a block copolymer is modeled as a structured fluid of uniaxial symmetry. The model predicts a viscoelastic response that depends on the angle between the the local lamellar planes and velocity gradients. We focus on the stability under oscillatory shear of a two layer configuration comprising a parallel and a perpendicularly oriented domain, so that...

Orientation of the Inverse Bicontinuous Cubic Phase Induced by Combination of Oscillatory Shears with Different Strain Amplitudes

Effects of Oscillatory Shear on the Orientation of the Inverse Bicontinuous Cubic Phase in a Nonionic Surfactant/Water System.

The bicontinuous inverse cubic phase (V2 phase) formed in amphiphilic systems consists of bilayer networks with a long-range order. We have investigated effects of oscillatory shear on the orientation of the V2 phase with space group Ia3d formed in a nonionic surfactant (C12E2)/water system by using simultaneous measurements of rheology/small-angle X-ray scattering. It is shown that grain refin...

A Resolution of the Sommerfeld Paradox

Sommerfeld paradox roughly says that mathematically Couette linear shear is linearly stable for all Reynolds number, but experimentally arbitrarily small perturbations can induce the transition from the linear shear to turbulence when the Reynolds number is large enough. The main idea of our resolution of this paradox is to show that there is a sequence of linearly unstable shears which approac...