Liquid crystal microflows play a fundamental role in materials, modern display technologies, and biological systems. However, a quantitative and spatially resolved measurement of the director field and surface anchoring remain a significant challenge. In this talk, I will present our recent efforts to use small angle X-ray scattering to characterize stationary flows of 4-Cyano-4-pentylbiphenyl (5CB) in circular capillaries under homeotropic and random planar anchoring, at temperatures between 280 K and 310 K. The flow rates vary from 0 to 128 nl/s, resulting in Ericksen numbers between 0 and 200, spanning both the elastic and viscous flow regimes. The X-ray scans are performed perpendicular to the axis with a spatial resolution of 1/100 of the capillary dimension (500 and 800 μm in diameter). We imaged simultaneously the scattering peaks from both periodic length scales (0.45 nm, 2.5 nm), of which the smaller one caused 25 times more counts. Their angular dependency is separately approximated by a double Gaussian fit with four parameters: amplitude, angle, width and background amplitude. The peak angles were found to be in quantitative agreement with director field simulations based on the Leslie-Ericksen theory assuming cylindrical symmetry. Raising the temperatures increased the angular widths of the peaks and reduced the amplitudes, indicating a decrease of the order parameter. For the larger length scales, this effect is less pronounced than for the smaller one. At Ericksen numbers below 1 and above 30, the simulations suggest bistable regimes: For lower numbers, the director escapes along the axis, with relative orientation either parallel or antiparallel to the flow direction. In the higher regime, one solution corresponds to a non-trivial director flow profile analogous to those reported by Sengupta et al (Phys. Rev. Lett. 110, 2013).
Dr. Paul Steffen received his doctoral degree in Physics in 2002 from the University of Potsdam, Germany. Subsequently he went to Hamburg, and joined Landwehr Electronics GmbH (later acquired by Gooch & Housego Ltd.), and headed the RF development efforts. From 2008 to 2013, he was a postdoc at the Max Planck Institute for Dynamics and Self-Organization in Göttingen. Thereafter Dr. Steffen served as Project Manager at the CFD development firm, LaVision GmbH in Göttingen (Germany). Dr. Steffen spends time as an independent writer and research consultant. His interests include optical techniques (microscopy, interference, acousto-optics), optical tweezers, and fluid mechanics (turbulence and microflows). He enjoys interdisciplinary opportunities resulting from the combination of these fields.