We report on studies using a new X-ray extensional flow cell to examine, for the first time, the structure of undulating lamellar lyotropic liquid crystal systems under extensional flow. The extensional component of the flow profile produced within this cell causes the lamellae to orient. We find that, although the intermembrane spacing does not change at low flow rates, it suddenly decreases after a critical flow rate has been attained due to the stretching and straightening of the lamellae. The effects of the shear component of flow on this oriented system have been examined in the context of a theoretical model developed by Ramaswamy.PACS. 61.30.St Lyotropic phases -83.85.Rx Extensional flow measurement -61.10.Eq X-ray scattering (including small-angle scattering)

We report on the use of x-ray diffraction as a means of extracting velocity profiles from a non-Newtonian complex fluid under laminar flow. In particular, we applied this technique to a concentrated undulating membrane system flowing through a cylindrical capillary tube. The intermembrane separation d was measured as a function of simple shear using a Couette flow cell. A logarithmic dependence of d as a function of the shear rate was observed, while there was a linear relationship between the fractional intermembrane spacing and the shear stress. Subsequent measurement of the system's intermembrane spacing as a function of position within the cylindrical flow pipe allowed for the calculation of a shear-rate profile within the capillary. Simple numerical integration then yielded an accurate velocity profile of the fluid flowing through the pipe. Both shear thickening and plug flow shear thinning profiles were observed.