Johanna Hemauer, Mingfeng Qiu, James J. Feng & Jean-Christoph Loudet

*Eur. Phys. J. E* **44**, 30 (2021)

**Abstract** - We use dynamic numerical simulations to investigate the role of particle rotation in pairwise capillary interactions of particles trapped at a fluid interface. The fluid
interface is modeled with a phase-field method which is coupled to the Navier-Stokes
equations to solve for the flow dynamics. Numerical solutions are found using
a finite element scheme in a bounded two-dimensional geometry. The interfacial
deformations are caused by the buoyant weight of the particles, which are allowed
to both translate and rotate due to the capillary and viscous forces and torques at
play. The results show that the capillary attraction is faster between freely rotating
particles than if particle rotation is inhibited, and the higher the viscosity mismatch,
the greater the effect. To explain this result, we analyze the drag force exerted on the
particles and find that the translational drag force on a rotating particle is always
less than its non-rotating counterpart due to attenuated velocity gradients in the
vicinity of the particle. We also find that the influence of interfacial deformations
on particle rotation is minute.