The Ericksen number and Deborah number cascades in sheared polymeric nematics

Abstract

Abstract Samples of liquid crystalline poly(γ-benzyl-glutamate) solutions are sheared between glass surfaces with gaps, d = 10–500 μ, and shearing velocities, V = 0·05–10 000 μs−1 so that the Ericksen number E [tbnd] Vdγ 1/K is varied over a large range, E ≈ 1–107. Here γ1 is the rotational viscosity and K 1 is the Frank splay constant, with γ1/K 1 estimated to be approximately 1 s μ−2 for our samples. We observe by polarizing microscopy a sequence of transitions with increasing Ericksen number analogous to that observed in small molecule tumbling nematics: namely rotation of the director out of the shearing plane and into the vorticity direction at Vd ≈ 25 μ2 s−1, and formation of roll cells at Vd ≈ 50 μ2 s−1. The roll cells become finer with increased Vd in accord with predictions of linear stability theory using the Leslie-Ericksen equations, and at Vd ≳ 500 μ2 s−1, the cells become very irregular, producing director turbulence. The turbulence becomes finer in scale as Vd increases, reaching sub-micron, and possibly molecular scales when Vd ≧ 105 μ2 s−1. At the highest velocities, transitions in orientation and texture are controlled by the Deborah number De[tbnd]λV/d, where λ is the molecular relaxation time, and uniform texture-free samples are obtained when De ≳ 5.