Monopole and quadrupole capillary interaction in turbulent interfacial suspensions

Particle suspensions at the interface of turbulent liquids are governed by the balance of capillary attraction, strain-induced drag and lubrication. Here, we extend previous findings, obtained for small particles whose capillary interactions are dominated by quadrupolar-mode deformation of the interface, to larger spherical and disc-shaped particles experiencing monopole-dominant capillarity. By combining pair-approach experiments, two-dimensional turbulent flow realizations and particle imaging, we demonstrate that particles experiencing monopole-dominant attraction exhibit enhanced clustering compared with their quadrupole-dominant counterparts. We introduce an interaction scale defined by balancing viscous drag and capillary attraction, which is compared with the particle size and interparticle distance. This allows us to map the clustering behaviour onto a parameter space solely defined by those characteristic length scales. This yields a unified framework able to predict the tendency to cluster (and the concentration threshold for those clusters to percolate) in a vast array of fluid–particle systems.