Khoromskaia, Diana (2017) Active liquid crystals in confined geometries. PhD thesis, University of Warwick.

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Abstract

Active liquid crystals, in which the rod-like constituents endow the fluid they are immersed in with active stresses, have proven successful as a paradigm for biologically inspired complex fluids with orientational alignment. These include suspensions of swimming bacteria or cell extracts comprising cytoskeletal filaments and molecular motors, whose natural environment is characterised by spatial confinement.

In this thesis we study active liquid crystals in three confined geometries – a planar thin film, a droplet on a flat surface, and a spherical shell. For alignment fields with topological defects, which are known to be energy minima for passive liquid crystals in these geometries, we investigate with analytical and numerical methods the effect of activity. Novel results include defect-driven motility of active drops and shells as well as the formation of stable flow vortices in spherical confinement.

In the first part we calculate analytically the active flows in a thin film, which are driven by a generic defective alignment field, and identify the type of flow singularity that a defect with arbitrary topological strength generates. The sliding velocity of an active drop, which moves due to an asymmetrically placed defect within, is calculated analytically. In general, asymmetry in the alignment generates motion of the drop due to directed flows in the bulk, although slip at the substrate and active flows resulting from gradients in the drop shape counteract this motion. Steady state shapes of a drop with a central defect reveal the formation of a hole or a cusp in its free surface.

The thin film model is adapted to a spherical shell in the second part, where locally the defect-driven flows are analogous to a flat film. Globally, the active flow is restrained by the Poincaré -Hopf theorem, which prescribes a total winding of +2. We find that the flow typically forms two counterrotating vortices, which is shown to have crucial implications for the defect motion and for the swimming behaviour of the shell. The dynamics of different defect configurations are simulated numerically with a particle-based model, where the defects move due to elastic forces and active advection, which is extracted from an exact expression for the active flow in the shell. We recover the oscillatory motion of four half-integer defects known from experiments and interpret it in view of the two counterrotating vortices, which advect the defects. The onset of oscillations is captured analytically in a linear stability analysis. Further, new predictions are provided for the scaling of measurable quantities, like oscillation frequency and defect speed, for the dynamics of additional defect-pairs and for polar shells, in which unit strength defects are found to attract or repel due to active flows. Finally, the swimming speeds of active nematic shells through a passive medium are calculated analytically, or numerically if half-integer defects are present. Remarkably, shells with triangular defect arrangements are found to be swimming and rotating.

In summary, this work furthers the understanding of geometrically confined active liquid crystals, highlighting the role of topological defects and the active flows they produce. The results presented here could also find application in microfluidics, for instance aiding in the design of artificial crawlers and swimmers.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QC Physics
Library of Congress Subject Headings (LCSH):	Liquid crystals, Topological defects (Physics), Hydrodynamics, Liquid crystals -- Elastic properties
Official Date:	April 2017
Dates:	Date Event April 2017 Submitted
Institution:	University of Warwick
Theses Department:	Centre for Complexity Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Alexander, Gareth P.
Format of File:	pdf
Extent:	ix, 169 leaves : illustrations, charts
Language:	eng

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