Simulating the interaction between a descending super-quadric solid object and a soap film

Abstract

<jats:p>We investigate the interaction that occurs between a light solid object and a horizontal soap film of a ‘bamboo’ foam contained in a cylindrical tube. We vary the shape of the descending object from a sphere to a cube by changing a single shape parameter. We investigate in detail how the soap film deforms and determine the forces that the film exerts on the object, depending on the radius of the cylindrical tube, and the shape, orientation and position of the object. We show that a cubic particle in a particular orientation experiences the largest drag force, and that this orientation is also the most likely outcome of dropping a cube from an arbitrary orientation through a bamboo foam.</jats:p>

Effect of gravity on the orientation and detachment of cubic particles adsorbed at soap film or liquid interfaces

“…(as derived in [31]), where the gamma functions Γ (a/λ) = ∞ 0 t a/λ−1 e −t dt are computed numerically. As in previous work [29], we set the volume of the cube to that of a sphere with radius 1, that is V s = 4 3 π, so that its sides have a half length of r s ≈ 0.817. The surface area of the cube is A s ≈ 14.24.…”

“…As in previous work [29], when the object is in contact with the soap film, we assume that its motion is slow and over-damped so that inertial effects can be neglected, and a quasi-static model is appropriate. In this case, the soap film is at equilibrium between small increments in the position and orientation of the cube.…”

“…(Note that ρ should be replaced by ρ − ρ and 2γ by γ for the interaction at the interface of two liquids of the same density ρ .) We have previously showed that a cube with a Bond number of 1 is reoriented by a soap film to a flat orientation as it descends through a horizontal soap film [29]. We now ask what are the conditions for a cubic object to be trapped or to detach from a soap film in terms of the Bond number and its initial orientation?…”

The distortion of a horizontal soap film due to the impact of a falling sphere

“…Also of direct relevance is the works of Davies (Davies and Cox, 2012;Davies, 2018) where numerical simulations are presented that describe the distortion of a horizontal soap film when a spherical and 'super quadric' object falls through it. The falling object was either spherical bead or roughly a cube with rounded corners and edges.…”

“…Note that the work of Le Goff and co-workers (Le Goff et al, 2008) was entirely experimental and involved fast-moving objects, whereas that of Davies (Davies, 2018) and co-workers (Morris et al, 2012, 2010) was theoretical and quasi-static. Here we compare theory with experiment for the simplest case, that of a sphere falling vertically through a horizontal soap film.…”