Particle clusters at fluid-fluid interfaces: equilibrium profiles, structural mechanics and stability against detachment
We investigate clustering of particles at an initially flat fluid-fluid interface of surface tension γ under external force f directed perpendicular to the interface. We employ analytical theory, numerical energy minimization (Surface Evolver) and computational fluid dynamics (Lattice-Boltzmann method) to study the equilibrium deformation of the interface and structural mechanics of the clusters, in particular at the onset of instability. In the case of incompressible clusters, we find that the equilibrium 3D interface profiles are uniquely determined by the length scale γ/(fn0), where n0 is the particle surface number density, and a non-dimensional shape parameter f^2 N n0/γ^2. The scaling remains valid in the whole regime of forces f, i.e., even close to the stability limit fcrit. In the cases with initial hexagonal arrangement of the particles, upon f approaching fcrit, our simulations additionally reveal emergence of curvature-induced defects and 2D stress anisotropy. We develop stability diagrams in terms of f, N (we study 7 ≤ N ≤ 61), and the contact angle θp at the particles and identify three unstable regimes corresponding to (i) the collective detachment of the whole cluster, (ii) ejection of individual particles from the interface, and (iii) both detachment and ejection. We also discuss possible metastable states. Altogether, our results may help in better understanding and controlling the particle interfacial instabilities with potential uses in synthesis of new materials, environmental sciences and microfluidics.