Microfluidic Model of Haemodynamics in Porous Media

Abstract

The flow of soft particle suspensions in complex porous media is a fundamental process in both biological and industrial applications. It is directly relevant to microcirculatory transport, where red blood cells (RBCs) navigate intricate vascular networks or porous structures to ensure efficient oxygen and nutrient delivery. Although the flow of these dense suspensions contributes significantly to regulating microvascular function and disease progression, their rheology in complex geometries remains, for the most part, unknown. In this thesis, we develop a mechanical model of RBCs based on deflated microcapsules with highly deformable, tuneable polydimethylsiloxane (PDMS) membranes to explore and connect steady-flow rheology of dense soft suspensions in planar microfluidic porous structures with pore-scale dynamics and transport processes. We begin by demonstrating that the steady flow and deformation of our microcapsules in confined circular capillaries capture the behaviour of RBCs. We then fabricate large numbers of these tuneable microcapsules (10,000s) to investigate soft suspension flows in both ordered and disordered planar porous media, as a function of the capillary number Ca - the ratio of viscous to elastic forces - and the capsule suspension volume fraction ϕ. We propose a novel scaling law for the excess resistance of soft suspension flow in porous media relative to Newtonian flow as a function of Ca, where the scaling exponent depends sensitively on ϕ due to clustering effects. We also find that the channel geometry has a limited impact on rheology but determines the pore-scale flow in terms of capsule velocity distribution and dispersion behaviour. The presence of capsules induces an intriguing banding phenomenon in the Hele-Shaw channel and ordered media, whereas it promotes preferential pathways and various clogging mechanisms in disordered media. As Ca and ϕ increase, the flow becomes more homogeneous, and clogging increasingly occurs via lingering, where the capsules get trapped through hyperelastic stretching, which wraps them around the cylindrical pillars of the porous medium. In the disordered porous medium, the presence of preferential pathways underpins both dispersion and transit through the medium. We find that particle transport exhibits ballistic motion along the flow direction, while a Brownian random walk occurs in the transverse direction, in the Hele-Shaw and ordered media. In contrast, in disordered media, the capsules initially follow a Brownian dispersion pattern before transitioning to an anomalous confined dispersion a short distance downstream of a localised inlet. Finally, we also reveal an anti-Fåhræus effect in porous media, where the local volume fraction of the suspension can transiently exceed the flow-weighted capsule fraction at the inlet, reflecting the storage capacity of porous media. These findings have the potential to enhance our understanding of blood flow dynamics in microvascular networks, and thus contribute to advancements in haematopathology research, disease modelling and the development of therapeutic strategies, as well as suspensions in other potential engineering applications, like enhanced oil recovery.

Date of Award	6 Jun 2025
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Igor Chernyavsky (Supervisor) & Anne Juel (Supervisor)