Origin of particle accumulation structures in liquid bridges: Particle–boundary-interactions versus inertia

Abstract

The formation of particle-accumulation structures in the flow in a cylindrical liquid bridge driven by the thermocapillary effect is studied with the aim of determining the physical mechanism which forms the structures. The flow is modeled using the incompressible Navier–Stokes and energy equations with the assumption of constant fluid properties except for surface tension, which is assumed to depend linearly on temperature. Different models for the motion of small non-interacting spherical particles at low concentration are employed, taking into account particle inertia due to density differences between fluid and particles and the restricted particle motion near the boundaries of the flow domain. Attention is focused on differences in formation time between particle-accumulation structures arising as a result of inertial effects only, particle–boundary-interaction effects only, and a combination of the two.

Coherent Particle Structures in High-Prandtl-Number Liquid Bridges

“…= ρ p /ρ f = 1 and particle Stokes number St = (2/9) a 2 O(10 −5 ). For such particles suspended in the liquid with the flow velocity, inertia has a negligible effect on the PAS formation as was demonstrated in Muldoon and Kuhlmann (2016) and Romanò and Kuhlmann (2018). This is confirmed for the motion of density-matched particles considered.…”

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

“…ratio (Kuhlmann et al 2014;Muldoon & Kuhlmann 2016). In contrast, the inertial time scale ∼ | − 1| −1 St −1 can become very large as | − 1| → 0.…”

“…The attraction to periodic or quasi-periodic orbits due to the boundary interaction effect is typically very rapid, because the process scales with the turnover time (non-dimensional viscous time) of the respective orbit (table 3), independent of the density ratio (Kuhlmann et al. 2014; Muldoon & Kuhlmann 2016). In contrast, the inertial time scale can become very large as .…”

“…Since this type of particle clustering is solely due to the particle size, Romanò, Wu & Kuhlmann (2019b) coined the term finite-size coherent structures (FSCS) for these attractors to distinguish them from the well-known Lagrangian coherent structures (LCS) which are caused by inertia (Haller 2015). Typically, FSCS form much more rapidly than inertial LCS, because the attraction rate to FSCS scales with the Reynolds number of the flow (Kuhlmann et al 2014;Muldoon & Kuhlmann 2016;Romanò et al 2019a), while the inertial attraction rate (inverse inertial time) is very small for small and nearly neutrally buoyant particles.…”

“…Typically, FSCS form much more rapidly than inertial LCS, because the attraction rate to FSCS scales with the Reynolds number of the flow (Kuhlmann et al. 2014; Muldoon & Kuhlmann 2016; Romanò et al. 2019 a ), while the inertial attraction rate (inverse inertial time) is very small for small and nearly neutrally buoyant particles.…”