Capillary Filling in Microchannels with Wall Corrugations: A Comparative Study of the Concus−Finn Criterion by Continuum, Kinetic, and Atomistic Approaches

Abstract

We study the impact of wall corrugations in microchannels on the process of capillary filling by means of three broadly used methods: computational fluid dynamics (CFD), lattice Boltzmann equations (LBE), and molecular dynamics (MD). The numerical results of these approaches are compared and tested against the Concus-Finn (CF) criterion, which predicts pinning of the contact line at rectangular ridges perpendicular to flow for contact angles of theta > 45 degrees . Whereas for theta = 30, 40 (no flow), and 60 degrees (flow) all methods are found to produce data consistent with the CF criterion, at theta = 50 degrees the numerical experiments provide different results. Whereas the pinning of the liquid front is observed both in the LB and CFD simulations, MD simulations show that molecular fluctuations allow front propagation even above the critical value predicted by the deterministic CF criterion, thereby introducing a sensitivity to the obstacle height.

Simulation of capillary infiltration into packing structures for the optimization of ceramic materials using the lattice Boltzmann method

“…A major obstacle to improvements resides in the over-occurrence of pinning. This situation could be improved by considering other combinations of surface tension, viscosity and, especially, contact angle (Chibbaro, Costa, et al, 2009). This could also be an extension of this work to Si alloys.…”

“…For the units of the basic quantities of mass, length, the symbols mu, lu and ts are used, respectively. The data obtained from simulations can be expressed in regular units of the International System SI after suitable transformations (Chibbaro, Biferale, Binder, et al, 2009;Chibbaro, Costa, et al, 2009;Gross, Varnik, Raabe, & Steinbach, 2010;Joshi and Sun, 2010;Komnik, Harting, & Herrmann, 2004). For comparisons with experimental data the approach is applied based on dimensionless numbers like the Reynolds or capillary numbers (Landau & Lifshitz, 2008).…”

“…In the region occupied by the porous structure the boundaries of the simulation domain are solid and subject to the common bounceback rule; elsewhere they are periodic. This is done in order to reduce the phenomenon of pinning near narrowto-wide parts (Blow, Kusumaatmaja, & Yeomans, 2009;Chibbaro, Biferale, Binder, et al, 2009;Chibbaro, Costa, et al, 2009;Kusumaatmaja, Pooley, Girardo, Pisignano, & Yeomans, 2008;Mognetti & Yeomans, 2009;Wiklund & Uesaka, 2012. The reason is that pinning can result in a significant slowdown of infiltration or even stop the flow.…”

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

“…In general, it is possible to distinguish phases of pronounced acceleration followed by phases of weaker acceleration eventually leading to plateaus. This phenomenon is usually referred to as the pinning of the interface (Blow, Kusumaatmaja, & Yeomans, 2009;Chibbaro, Biferale, Binder, et al, 2009;Chibbaro, Costa, et al, 2009;Kusumaatmaja, Pooley, Girardo, Pisignano, & Yeomans, 2008;Mognetti & Yeomans, 2009;Wiklund & Uesaka, 2012. Basically, pinning occurs in proximity to the necks, i.e., close to narrow-to-wide structures.…”

“…It is a pore-scale process arising from the adhesive forces between the liquid and solid phases. Computational fluid dynamics (CFD) relying on the finite element method (FEM) allows the problem to be addressed (Chibbaro, Costa, et al, 2009;Svihla & Xu, 2006;Xu & Guetari, 2004). Our study is based on simulations using the Lattice Boltzmann (LB) method in 2D (Benzi, Succi, & Vergassola, 1992;Chen & Doolen, 1998;Sukop & Thorne, 2010;Wolf-Gladrow, 2005).…”