Intermembrane spacing and velocity profiling of a lamellar lyotropic complex fluid under flow using x-ray diffraction.

Abstract

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.