Mathematical modelling of active fluids in a channel

Joseph, Ijuptil Kwajighu (2025) Mathematical modelling of active fluids in a channel. PhD thesis, University of Glasgow.

Abstract

Active fluids, such as active nematics, consist of self-driven units that convert energy into directed motion. Examples include suspensions of cytoskeletal filaments, motor proteins, bacteria, schools of fish, cellular layers, and cell tissues. This thesis presents a theoretical and computational study of active nematics using an adapted Ericksen-Leslie dynamical theory, with a focus on understanding how activity, external fields, and geometry influence flow and director patterns in confined systems. In one dimension, we investigate the effects of an orienting field on extensile and contractile nematics under planar and homeotropic anchoring. Extensile systems with planar anchoring exhibit minimal director distortion, whereas contractile systems display significant distortion when the orienting field exceeds a threshold from the initial homeotropic alignment. A kickback effect is observed in contractile nematics, which diminishes in extensile systems as activity increases. Nonlinear analyses reveal uniform, symmetric, and antisymmetric states, with activity enhancing flow and inducing bistability in contractile systems. In two-dimensional channels, we analyse the influence of activity and non-constant boundary conditions. Under inlet/outlet normal flow conditions, low activities produce localised flows, while higher activities generate spatial fluctuations in contractile systems. Extensile nematics at high activity exhibit transitions from unidirectional to bidirectional flow. For inlet/outlet periodic conditions, the system behaviour is similar to that under normal flow conditions. Variation in the splay-to-bend elastic constant ratio leads to transitions from positive to negative flux, demonstrating that active stresses can dominate elastic forces and produce unidirectional flow with positive flux for extensile systems. We also explore time-dependent boundary conditions as a conceptual demonstration of object sensing, showing that the speed of anchoring transitions affects flow patterns: slower transitions delay system activation, while faster transitions reduce bidirectional flows. These results indicate that small local disturbances can produce large-scale flows. In a biological context, such as wound healing, the tissue edge acts as a dynamic boundary where cells actively migrate and reorganise. Our findings on time-dependent boundary anchoring and activity-driven flows suggest that localised changes at wound margins can trigger large-scale tissue flows, mimicking the collective migration observed during wound closure. Overall, this work provides a theoretical framework for understanding how activity and confinement can be harnessed in systems that respond sensitively to local perturbations, highlighting potential applications for active-nematic-based sensing.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics
• Supervisor's Name: Mottram, Professor Nigel and Kowal, Dr Katarzyna
• Date of Award: 2025
• Depositing User: Theses Team
• Unique ID: glathesis:2025-85589
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 13 Nov 2025 14:49
• Last Modified: 14 Nov 2025 10:10
• Thesis DOI: 10.5525/gla.thesis.85589
• URI: https://theses.gla.ac.uk/id/eprint/85589