Transient flows in poroelastic media arise in a broad range of applications, from geophysical flows to biological processes and industrial applications. The interplay of medium heterogeneity, poroelasticity, and transient forcing lead to complex flow and transport behaviors that manifest as a diverse set of Lagrangian coherent structures (LCSs). Previous studies have focused on how these structures govern dispersion of diffusive solutes, but the impact on solute mixing and transport has not been previously considered. We address this problem by examining how regular regions, Kolmogorov-Arnold-Moser (KAM) islands, stochastic layers, and other LCS types impact solute transport and mixing across a broad range of Péclet numbers. 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 to transport that govern transport of diffusive solutes at all Péclet numbers. These results show that mixing and transport are profoundly impacted by the complex advective dynamics inherent to transient poroelastic flows, and they can only be fully understood by resolving the governing LCS.

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• Compressible flows
• Flows in porous media
• Lagrangian dynamics