Escape from the chip: flowing and clogging in confined suspensions

People leaving a room in panic, sand in an hourglass, particles in a fluid through a porous medium, blood through a narrowed vessel. These are all examples of "things" of different nature being forced through constrictions. In all these cases it is important to make sure that the system keeps continuously flowing, sometimes even lives are at risk. The case of particles in a fluid affects porous mediums, filters and membranes, which become unusable when clogged. Even though the case of silos and dry particles driven by gravity towards a funnel has been well-studied and understood for years, the case of suspensions passing through a constriction is not well understood. This case has been often explained exclusively relying on the adhesion of the particles (Wyss et al., PRE 2006). In this talk, I will show that suspensions surprisingly follow the same statistics as dry granular matter. In order to show this, we use microfluidic devices with a bottleneck of squared cross-section through which we force dilute polystyrene particle solutions with diameters comparable to the bottleneck size and down to one tenth its size. In low friction conditions, we show experimental evidence of a strong transition at a critical particle-to-neck ratio, just as it occurs in dry granular systems (Zuriguel et al., PRE 2003). We describe analytically such a transition by modelling the arch formation as a purely stochastic process, which yields a good agreement with the experimental data.

If the constriction is removed, particles flow without trouble. However, their dynamics are far from trivial even in diluted conditions. At critical interparticle distances, particles tend to interlace their trajectories, only bonded by hydrodynamic interactions. While classical studies on non-Brownian self-diffusivity report average particle displacements of fractions of the particle diameter (Drazer et al., JFM 2002), the trajectories observed in our system show displacements of several particle diameters. Furthermore, entangled particles seem to "synchronize" their motion with others located at several particle diameters. Particle trajectory statistics are obtained from the experiments for different shear rates and particle sizes showing the same results in wide range of parameters. The results are then compared with particle dynamics simulations and analysed to elucidate the nature of the hydrodynamic interactions entering into play. The reported phenomenon could be applied to promote advective mixing (Souzy et al., Phys. Fluids 2015) in micro-channels or particle/droplet self-assembly.

References

[1] Wyss, H., Blair, D., Morris, J. F., Stone, H. A. Weitz, D., Physical Review E 74, 061402 (2006).

[2] Zuriguel, I., Pugnaloni, L., Garcimartn, A. & Maza, D.,Physical Review E 68, 030301 (2003).

[3] Drazer, G., Koplik, J., Khusid, B. & Acrivos, A., J. Fluid Mech. 460, 307335 (2002).

[4] Souzy, M., Yin, X., Villermaux, E., Abid, C. & Metzger, B., Phys. Fluids 27, 0417057 (2015).

[5] Marin, A., Lhuissier, H., Rossi, M., Kaehler, C.J., "Clogging in constricted suspension flows." Physical Review E 97.2 (2018).