Fluid Dynamics of Microscopic Defects in Layered Liquids

The presence of microscopic defects is important in determining the flow behavior of complex fluids, especially those that exhibit layered or lamellar structures, which are observed in small molecule liquid crystals, concentrated surfactant solutions, block copolymers, and liquid crystalline polymers. The fluid dynamics of defects impacts every process in which these molecules are used to modify the rheology of a product, improve its stability or mechanical strength, or enhance its transport properties. However, there is a lack of data and theory characterizing the role of defects on flow of layered liquids, and this impedes the formulation and efficient processing of these materials.

Our work on this project made an initial step toward addressing the lack of understanding of the flow behavior of layered liquids. The objective of the project was to generate well-defined arrays of microscopic defects in layered liquids, and then to use those prepared defect arrays to characterize the fluid dynamics of the defects. Some of our key findings include:

– We showed that static focal conic textures formed in microchannels depend on the antagonistic surface anchoring conditions at each surface of the microchannel, and the size and polydispersity of the defects depend on both the depth and width of the microchannel.

– We designed and built a microscale shear cell allowing the formation of parabolic or toric focal conic defects in a controlled manner between parallel plates separated by approximately 50 to 100 micrometers, and then the subsequent application of a linear couette flow while simultaneously observing the polarization intensity patterns as a function of time.

– In the shear cell, we found that simultaneous dilatation and shear leads to the formation of a highly ordered square lattice of parabolic focal conic defects, when the parallel plates impose the same anchoring conditions on both surfaces. The parabolic focal conic defects in the ordered array are centered below the midplane of the sample and move as a rigid body with a velocity just over half that of the moving plate.

– When the surfaces impose antagonistic anchoring conditions, toric focal conic defects form sparsely in the sample and are anchored to one of the plates.  The anchored toric focal conic defects stretch and deform in a shear flow leading to the development of a stream of satellite parabolic focal conic defects. The size of the streaming defects is controlled by the size of the anchored defect.

– Simultaneous dilatation and shear flow leads to the most ordered parabolic focal conic defect arrays compared with other methods. Although the ordering is nearly perfectly square, there is additional ordering in the direction of flow due to the presence of dislocations in the defect array itself. The ordering and size of the arrays was quantified using the pair distribution function, a technique that is standard in other areas of complex fluids but had not previously been used to examine liquid crystal defects.

– The asymmetric rigidification and magnitude of the velocity profile of square arrays of parabolic focal conic defects is explained by a minimization of free energy of the interacting layer structure during shear flow.

– In a defect array, shear at long timescales reveals a complex interplay between both annihilation and production of defects in different regions of the sample.  The annihilation occurs as a result of layer and dislocation relaxation processes, and the production occurs over longer timescales in the annealed regions of the sample.

– Anchored toroidal focal conic defects stream satellite defects whose sizes are controlled by the sizes of the original anchored defects. The evolution of the defects reveals timescales for the process that is consistent with those governed by permeative flow in layered materials.

Funding: NSF CAREER 0547432, NSF CBET 0527909, Pennsylvania Infrastructure Technology Alliance

Former Students: Shahab Shojaei-Zadeh, Sourav Chatterjee

Related Publications

S. Chatterjee and S.L. Anna, “Interaction of Toroidal Focal Conic Defects with Shear Flow,” Soft Matter, 8 (2012) 2698 – 2705.

S. Chatterjee and S.L. Anna, “Formation and Ordering of Topological Defect Arrays Produced by Dilatational Strain and Shear Flow in Smectic-A Liquid Crystals,” Physical Review E, 85 (2012) 011701.

S. Shojaei-Zadeh and S.L. Anna, “Role of Surface Anchoring and Geometric Confinement on Focal Conic Textures in Smectic-A Liquid Crystals,” Langmuir 22 (2006) 9986-93.