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Interplay of inertia and deformability on rheological properties of a suspension of capsules

Published online by Cambridge University Press:  27 June 2014

Timm Krüger*
School of Engineering, University of Edinburgh, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, UK Centre for Computational Science, University College London, 20 Gordon Street, London WC1H 0AJ, UK
Badr Kaoui
Theoretische Physik I, Physikalisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Jens Harting
Department of Applied Physics, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Faculty of Science and Technology, Mesa+ Institute, University of Twente, 7500 AE Enschede, The Netherlands
Email address for correspondence:


The interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing, and only a limited number of experimental and theoretical studies are available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that the Segré–Silberberg effect is suppressed with respect to the particle deformability. Depending on the deformability and strength of inertial effects, inward or outward lateral migration of the particles takes place. In particular, for increasing Reynolds numbers and strongly deformable particles, a hitherto unreported distinct flow focusing effect emerges, which is accompanied by a non-monotonic behaviour of the apparent suspension viscosity and thickness of the particle-free layer close to the channel walls. This effect can be explained by the behaviour of a single particle and the change of the particle collision mechanism when both deformability and inertia effects are relevant.

© 2014 Cambridge University Press 

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Krüger et al. supplementary movie

Visualisation of two exemplary simulations (Re = 50, Ca = 0.003 and Re = 333, Ca = 0.3) in quasi-steady state. The movie shows the 3D capsule configurations and a 2D slice of the lateral (in direction of the walls) velocity component in colour coding as function of time. The scaling of the velocity is identical for both simulations. In particular one can see that the lateral velocity activity for Re = 333 is much smaller than for Re = 50.

Download Krüger et al. supplementary movie(Video)
Video 9 MB