Microfluidic model of micro-haemodynamics in porous media

Quantifying the flow of red blood cells (RBCs) within complex biological porous tissues, such as the heterogeneous intervillous space (IVS) in the human placenta, remains an open problem. Due to comparable dimensions between RBCs and IVS structures, it is essential to model blood flow as a suspension rather than a continuum. The rheology of this soft suspension remains unexplored in disordered porous media. We design a suspension of ultra-soft, deflated polydimethylsiloxane (PDMS) microcapsules, which can mimic the large deformation of RBCs when propagated at a constant flow rate in confined capillary tubes, to serve as a valuable tool to investigate microhaemodynamics. We aim to relate the global resistance of our porous medium to the local distribution of particles and their velocity as a function of the disorder of the medium, volume fraction and capillary number Ca. In contrast to a hexagonal array, where the lateral dispersion of capsules is approximately linear with downstream distance, a uniformly random array provides preferential paths that are weakly influenced by clogs and lead to anomalous dispersion. The interaction between suspension and geometry results in a non-linear variation of the relative resistance as a function of both volume fraction and Ca.