Hydrodynamics of the Renn-Lubensky twist grain boundary phase, and the decoupled lamellar phase

Abstract

The long-wavelength hydrodynamics of the Renn-Lubensky twist grain boundary phase with grain boundary angle 2πα, a irrational, is studied. We find three propagating sound modes, with two of the three sound speeds vanishing for propagation orthogonal to the grains, and one vanishing for propagation parallel to the grains as well. In addition, we find that the viscosities η₁, η₂, η₄, and η₅ diverge like 1/‖ω‖ as frequency ω→0, with the divergent parts Δη₁ satisfying Δη₁Δη₄=(Δη₅)², exactly. Our results should also apply to the predicted decoupled lamellar phase.