The static profile for a floating particle

Abstract

The equilibrium profile of a single floating particle is numerically investigated using transformed equations depending on the inclination angle of the deformed surface, which is governed by the Young–Laplace equation. The relationship between the depth far from the flat interface and the filling angle is derived from the force balance acting upon the particle. The Chebyshev nodes are employed as a discretization for the inclination angle and yield satisfactory results for computation. The computational results show that this is an efficient way to analyze the deformed surface around floating particles with an infinity boundary condition. The static profile of the free surface around the spherical particle is largely dependent on the density ratio and the contact angle.