Particle accumulation structures in noncylindrical liquid bridges under microgravity conditions

Abstract

The emergence of Particle Accumulation Structures (PAS) in non-cylindrical liquid bridges (LB) is studied numerically for a high Prandtl number liquid considering microgravity conditions. Simulations are conducted in the framework of a finite-volume (Eulerian) approach with non-isodense particles being tracked using a Lagrangian, one-way coupling scheme. First, the threshold of the Marangoni-flow instability is determined as a function of the aspect ratio and the volume of liquid held between the supporting disks, thereafter, PAS formation is investigated for supercritical conditions. The overall approach is specifically conceived to provide details about the morphological evolution of these structures as the main control parameters are varied. For this reason a set of new notions and definitions (such as the linear extension of the PAS, its inner core radius and the area of the "petals" or "blades") are introduced to allow a precise quantification of a series of purely geometrical effects. Though the analysis is deliberately limited to illustrating the macroscopic patterning behavior and its relationship with the overarching factors, a new model is proposed to interpret the increased ability of slender (concave) liquid bridges to support the formation of PAS over extended ranges of values of the particle Stokes number. This model yet relies on essentially geometrical arguments, that is, the triadic relationship among the curvature of the free surface, the topology of fluid streamlines and particle mass effects.

Particle Accumulation Structures in a 5 cSt Silicone Oil Liquid Bridge: New Data for the Preparation of the JEREMI Experiment

“…All the simulations reported in the present work have been carried out by means of the transient incompressible "buoy-antBoussinesqPimpleFoam" solver available in the Open-FOAM package, while the thermocapillary stress condition was implemented anew and thoroughly tested by our group (see e.g., Capobianchi and Lappa (2020)). Moreover, the boundary/interface-particle interaction schemes available in the native OpenFOAM releases have been modified to take into account the actual dimension of the particles (see further below for a more detailed discussion of this model).…”

“…Closure of the mathematical problem also requires the introduction of the tangential stress boundary condition needed to account for the thermocapillary force arising as a consequence of thermally induced surface tension imbalance. Assuming an inviscid surrounding gaseous phase this condition simply reads (see, e.g., (Capobianchi and Lappa 2020)) where is the dynamic viscosity, is the unit normal vector at the liquid-gas interface, and the operator s represents the surface gradient, i.e., the projection of the vector gradient on the interface of the liquid bridge.…”

On the influence of gravity on particle accumulation structures in high aspect-ratio liquid bridges

“…The dimensionless numbers appearing in the above set of equations are the Grashof number, Gr = gβΔTL 3 /ν 2 , the Prandtl number, Pr = ν/α, and the Reynolds number, Re = σ T ΔTL/ρ 0 ν 2 , where α and β are the thermal diffusivity and thermal expansion coefficient of the fluid, respectively, ν is its kinematic viscosity and σ T = −∂σ/∂T| T=T 0 . For consistency with a companion work (Capobianchi & Lappa 2020), in the following we shall refer to the Marangoni number, Ma = RePr, rather than Re.…”

“…As illustrated, e.g. by Capobianchi & Lappa (2020), experiments dealing with a variety of fluids and particle types (see the literature cited in the introduction) have shown that once particles are inside the attractor (the KAM torus), even if φ increases locally to a significant extent, inter-particle forces or other 'back influence' effects are not intense enough to force particles to leave the attractor. This may be regarded as the sought justification about the effective possibility to neglect two-and four-way effects even when all the particles are concentrated in a thin region (the PAS itself).…”

“…Yet in line with the existing literature, we neglect the Saffman lift force and the Faxén corrections (Kuhlmann et al 2014). The influence of the Basset force is also disregarded on the basis of the earlier analysis by Lappa (2013c) (where it was clarified that this force can play a non-negligible role only for non-dimensional angular frequencies of the flow exceeding 10 3 ; the reader being also referred to the more recent study by Capobianchi & Lappa (2020)). Accordingly, the motion of each individual particle can be described by the abovementioned Maxey-Riley equation cast in the following condensed form (see, e.g.…”