Surface Growth Effects On Reactive Capillary-Driven Flow: Lattice Boltzmann Investigation

Abstract

ABSTRACT:The Washburn law has always played a critical role for ceramics. In the microscale, surface forces take over volume forces and the phenomenon of spontaneous infiltration in narrow interstices becomes of particular relevance. The Lattice Boltzmann method is applied in order to ascertain the role of surface reaction and subsequent deformation of a single capillary in 2D for the linear Washburn behavior. The proposed investigation is motivated by the problem of reactive infiltration of molten silicon into carbon preforms. This is a complex phenomenon arising from the interplay between fluid flow, the transition to wetting, surface growth and heat transfer. Furthermore, it is characterized by slow infiltration velocities in narrow interstices resulting in small Reynolds numbers that are difficult to reproduce with a single capillary. In our simulations, several geometric characteristics for the capillaries are considered, as well as different infiltration and reaction conditions. The main result of our work is that the phenomenon of pore closure can be regarded as independent of the infiltration velocity, and in turn a number of other parameters. The instrumental conclusion drawn from our simulations is that short pores with wide openings and a round-shaped morphology near the throats represent the optimal configuration for the underlying structure of the porous preform in order to achieve faster infiltration. The role of the approximations is discussed in detail and the robustness of our findings is assessed.

Lattice Boltzmann simulations on the role of channel structure for reactive capillary infiltration

“…More precisely, the velocity space is discretized and distribution functions account for the particles moving along a given direction (Benzi et al, 1992;Chen & Doolen, 1998;Sukop & Thorne, 2010;Wolf-Gladrow;2005). In the present work we employ the same models as in Sergi et al (2014) with the same notation and terminology. More details can be found in the related literature.…”

“…In general, the analysis of more complex geometries is based on the theoretical results for these types of system. In a previous work (Sergi et al, 2014), we investigated the retardation effects induced by surface growth for the linear Washburn law for interstices of uniform radii. The linear time dependence for the infiltration depth is characteristic of reactive Si infiltration (Israel et al, 2010;Voytovych et al, 2008).…”

“…The density values are chosen so that ρ 0 = ρ 1 + ρ 2 = 2 mu/lu 2 and ρ 1 /ρ 2 = 2.5%, where the first fluid is the main component; elsewhere the ratio between the densities of the two components is inversed. Unless stated otherwise, the parameter for fluid-fluid interactions (cohesive forces) is G c = 0.9 lu/mu/ts 2 , for which the surface tension turns out to be γ = 0.16403 lu·mu/ts 2 (Sergi et al, 2014). Solidfluid interactions are instead determined by the parameters G ads,1 = − G ads,2 = − 0.35 lu/ts 2 .…”

“…These settings (Sergi et al, 2014) reproduce an equilibrium contact angle around 30°, typical for droplets of molten Si on SiC substrates (Bougiouri et al, 2006;Voytovych et al, 2008). Regarding solute transport, we proceed as Sergi et al (2014). In the initial configuration, in the region filled with the first fluid component, the wetting one, the solute concentration is C 1 = 10 −2 mu/lu 2 ; elsewhere the solute concentration is C 2 = 2·10 −3 mu/lu 2 .…”

“…In so doing, the first component wets the solid phase while the second is a non-wetting fluid. These settings (Sergi et al, 2014) reproduce an equilibrium contact angle around 30°, typical for droplets of molten Si on SiC substrates (Bougiouri et al, 2006;Voytovych et al, 2008). Regarding solute transport, we proceed as Sergi et al (2014).…”