Cross-streamline migration of soft particles in suspensions is essential for cell and DNA sorting, blood flow, polymer processing and so on. Pioneering work by Poiseuille on blood flow in vivo revealed an erythrocyte-free layer close to blood vessel walls. The formation of this layer is related to a viscous lift force caused by cell deformation that pushes cells towards the centre of blood capillaries. This lift force has in this case a strong impact on blood flow. In contrast, rigid spherical particles migrate from the centre towards the periphery, owing to inertia (the Segré–Silberberg effect). An important open issue is to elucidate the interplay between particle deformation and inertia. By using a capsule suspension model, Krueger, Kaoui & Harting (J. Fluid Mech., 2014, vol. 751, pp. 725–745) discovered that capsule flexibility can suppress the Segré–Silberberg effect and inertia promotes overall flow efficiency thanks to a strong inertial flow focusing effect.
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