Stokesian motion of a spherical particle near a right corner made by tangentially moving walls

Abstract

The slow motion of a small buoyant sphere near a right dihedral corner made by tangentially sliding walls is investigated. Under creeping-flow conditions the force and torque on the sphere can be decomposed into eleven elementary types of motion involving simple particle translations, particle rotations and wall movements. Force and torque balances are employed to find the velocity and rotation of the particle as functions of its location. Depending on the ratio of the wall velocities and the gravitational settling velocity of the sphere, different dynamical regimes are identified. In particular, a non-trivial line attractor/repeller for the particle motion exists at a location detached from both the walls. The existence, location and stability of the corresponding two-dimensional fixed point are studied depending on the wall velocities and the buoyancy force. The impact of the line attractors/repellers on the motion of small particles in cavities and its relevance for corner cleaning applications are discussed.

Attractors for the motion of a finite-size particle in a cuboidal lid-driven cavity

“…Different from the boundary effect, however, the particle limit cycles caused by particle inertia in a flow that is steady in the absence of the particle can be either stable or unstable. While buoyancy forces alone cannot lead to attractors, because they derive from a potential (see also Sapsis & Haller 2010), they can determine the stability of the inertia-induced limit cycles (Wu et al 2021) and boundary-induced attractors (Romanò, des Boscs & Kuhlmann 2021).…”

“…While buoyancy forces alone cannot lead to attractors, because they derive from a potential (see also Sapsis & Haller 2010), they can determine the stability of the inertia-induced limit cycles (Wu et al. 2021) and boundary-induced attractors (Romanò, des Boscs & Kuhlmann 2021).…”

Reconstructing the neutrally-buoyant particle flow near a singular corner

“…Following Ref. [45], we can write the translational and rotational equilibria for the particle centroid formulating the equations in terms of force and torque coefficients F = (F x , F y , F z ) and T = (T x , T y , T z ), where the forces and torques have been scaled by the Stokes drag 6πρ f νa p U and the couple 8πρ f νa 2 p U. Owing to the symmetries of the problem, U = (U, 0, W) and Ω = (0, Ω y , 0) and the linear system governing the particle dynamics reads:…”

“…( 8) can be derived explicitly computing the translational and rotational velocity of the particle as done by Ref. [45], i.e., assuming that the fit functions of Ref. [48] hold:…”

“…This is the case, for instance, of the non-trivial attactors reported for inertial particles in steady [37,38] or oscillatory [39][40][41] cavity flows. The prediction of the particle dynamics becomes even more challenging when the particles are immersed in a complex chaotic fluid flow [42,43], where non-dissipative forces, such as buoyancy, actively contribute to a symmetry breaking [44] or to the creation of attractors [45].…”