Undulation instability under shear in smectic A liquid crystals

Abstract

Abstract. 2014 We study the undulation instability in a smectic A in the presence of shear flow parallel to the layers. We look for the dilation at the threshold where an undulation appears with a wave vector inclined at an angle 03B8 to the direction of flow. We find an integral relation showing that the dilation is necessarily positive. We develop a perturbation method to calculate the dilation explicitly as a function of the angle 03B8 and the shear rate. We show that an undulation with wave vector perpendicular to the shear direction is not affected by the flow and has a minimum threshold dilation equal to the static value. We conclude that a rectangular texture develops at higher dilations in agreement with the rectangular focal domain pattern observed experimentally.

Shear-induced instabilities in layered liquids

“…These undulation are a compromise between the effective dilatation (which is not favorable for the system) and the curvature of the layers due to the undulations (which costs energy). In the static case of dilated smectic A liquid crystals no direction is preferred, but Oswald and Ben-Abraham [23] have shown that this symmetry is broken if an additional shear is applied to the system. In this case the standard formulation of smectic A hydrodynamics predicts that the wave vector of the undulations will point along the neutral direction of the shear.…”

“…In this ansatz we made use of the results by Oswald and Ben-Abraham [23], who have shown that in standard dilated smectic A under shear the first instability will set in with a wave vector along the neutral direction of the flow ( q ·ê x = 0). After inserting the above ansatz in the linearized set of (partial differential) equations, a set of coupled linear equations is obtained to determine 1/τ and ω.…”

“…Due to Eq. (16) the z-component of v 1 is suppressed by a factor of λ p (which is typically extremely small [19,23]). Making use of the results of [23] we can assume that v 1 depends only on y and z and thus conclude [with Eq.…”

Structure and rheology of the defect-gel states of pure and particle-dispersed lyotropic lamellar phases

“…A similar type of shear induced defect structure has been seen by Larson et al [5] in a thermotropic liquid crystal. This is due to disruption of the monodomains in the form of undulation instabilities [13]. Lastly, we do not see, over the range of shear rate examined, the multilamellar vesicles ("onions" [4]) found in shear studies of more dilute lamellar phases.…”

Undulation instability under shear: A model to explain the different orientations of a lamellar phase under shear?

“…10 −5 m) because of mechanical construction, or the roughness of the walls, or the movement of defects will produce a dilation much larger than the threshold of the undulation instability. P. Oswald and co-workers [11][12][13] have shown experimentally and analytically that this instability persists under low shear flow on smectic A phases.…”