Flows on the edge : Boundary interactions and local heterogeneities in complex fluid flows

From toothpaste to face creams, complex fluids are ubiquitous. Their flow behaviour depends not only on intrinsic material properties but also on interactions with confining boundaries and local flow heterogeneities. Understanding these effects is critical for linking microscopic interactions to macroscopic rheology in fundamental and applied contexts. This thesis addresses the influence of boundary roughness, multi-directional flows, and local heterogeneities on the flow behaviour of Newtonian and non-Newtonian fluids. Through a combination of rheological and imaging studies, it highlights how local flow dynamics connect to global rheological responses.Chapter 2 investigates laminar Newtonian flow near rough boundaries using custom-designed Couette geometries, patterned with horizontal, vertical, and angled ridges. Fluid penetration into surface asperities is quantified as penetration depth delta, which captures the spatially averaged behaviour of the decaying fluid velocity profile between the roughness patterns. Experiments and numerical simulations demonstrate that delta depends on ridge depth, spacing, and orientation. For horizontal ridges, delta collapses onto a simple exponential master curve, while vertical ridges show reduced penetration, and angled ridges exhibit intermediate penetration. This coarse-graining approach enables wall roughness to be modelled as a modified no-slip boundary condition, providing a generalised length scale for rough surfaces.Chapter 3 builds on this analysis by directly measuring penetration depth from local flow fields using rheo-MRI in angled ridged Couette geometries. Such wall patterning induces an axial flow, in addition to primary azimuthal flow, even in the laminar regime. The effect of roughness directionality on the flow behaviour of Newtonian and yield stress fluids is quantified through spatially resolved velocity profiles. A clear correlation is found between penetration depth and axial flow, both increasing with ridge angle and rotation rate. A critical rotation rate is identified for yield stress fluids, below which axial flow is suppressed. This finding demonstrates that yielding behaviour influences both primary and secondary flows, thereby controlling flow penetration.Chapter 4 introduces rheo-LSI, a technique combining rheology with laser speckle imaging, to resolve local flow heterogeneities in complex fluids. This technique maps heterogeneities at wall boundaries, with high sensitivity across a large field of view, by incorporating a deformable elastomer slab, whose deformation relates to local wall stress. The technique is validated with Newtonian fluids of different viscosities, and subsequently applied to a shear thickening cornstarch suspension. Spatially resolved stress maps reveal regions of flow heterogeneity that correspond directly to the macroscopic rheological response. Rheo‑LSI thus offers a tool to relate local spatio‑temporal stresses with bulk flow.Chapter 5 applies rheo-LSI to visualise the spatio-temporal evolution of local heterogeneities in dense cornstarch suspensions under oscillatory shear. These suspensions exhibit discontinuous shear thickening (DST) at high concentrations. Three regimes of local dynamics are identified, featuring a jamming front propagating radially inwards with increasing strain. At intermediate and high strain amplitudes, dynamic localised regions emerge, correlating with macroscopic DST. These observations elucidate the pivotal role of heterogeneous microstructural dynamics in governing bulk rheology.Overall, this thesis establishes the importance of boundary interactions and local heterogeneities in linking microscopic flow dynamics to macroscopic rheology.