Quantitative Prediction of Incomplete Mixing in Transient Poroelastic Flows

<p dir="ltr">Transient flows in poroelastic media emerge in a wide array of contexts, spanning geophysical, biophysical, and industrial applications. Recent investigations reveal that even relatively simple poroelastic systems can exhibit Lagrangian chaos at the Darcy scale. The interplay of medium heterogeneity, poroelasticity and transient forcing leads to complex flow and transport behaviours that manifest as a diverse set of Lagrangian coherent structures (LCSs). The primary objective of this research is to elucidate how these diverse LCSs shape the transport and mixing of diffusive solutes.</p><p dir="ltr">A minimal two-dimensional, sinusoidally forced poroelastic computational model was employed, accompanied by the development of several numerical methods to simulate diffusive particles and construct continuous concentration fields. LCSs were categorised into regular regions, KAM islands, stochastic layers, and other distinct types, and their impacts on solute transport and mixing were systematically examined across a broad range of Péclet numbers. Additionally, specialised metrics were introduced to quantify the interactions between diffusing solute blobs and the LCSs, both from local and global perspectives.</p><p dir="ltr">It was found that LCS interactions impact the dispersion of solute plumes via the establishment of minimum flux manifolds, leading to strongly anomalous plume moments and solute residence time distributions. We interpret these results with fluid element stretching distributions and local Lyapunov exponents. Anomalous features persist even at low Péclet numbers. On the other hand, LCSs impart distinctly different mixing dynamics, with mixing metrics such as the dilution index ranging from algebraic to exponential growth with time. Transport structures such as KAM boundaries and hyperbolic manifolds form strong barriers that govern transport of diffusive solutes at all Péclet numbers.</p><p dir="ltr">The results in this thesis show that diffusive solute mixing and transport are profoundly impacted by the complex advective dynamics inherent to transient poroelastic flows and can only be fully understood by resolving the governing LCSs.</p>