Darcy's law–based numerical simulation for modeling 3D liquid absorption into porous wicks

Abstract

Liquid imbibition into polymer wicks, where a clear liquid front can be seen rising during the wicking process, is modeled using the concepts of flow in porous media. The flow of liquid behind the moving liquid front is modeled using the physics of single-phase flow in a porous medium where the Darcy's law is combined with the continuity equation and a capillary suction pressure is imposed at the liquid front. A novel numerical simulation PORE-FLOW V V C based on the finite element/control volume method is proposed to model such imbibitional flows in wicks of complex shapes. A validation of the simulation is obtained by achieving an excellent comparison of its predictions with an experimental result, an analytical solution, and the Washburn equation for the case of wicking against gravity in a cylindrical wick. The simulation is also used to predict a case of two-dimensional (2D) wicking in the altered cylindrical wicks with two different cross-sectional areas. Once again an excellent match is obtained with the experimental results, while analytical solutions for the single and double cross-section cases along with the Washburn equation fail to predict the 2D wicking. Later, some other types of altered wicks with sharp changes in their cross-sectional areas were analyzed numerically for their wicking behavior. It was observed that the height of liquid front in a vertical wick as a function of time, which is proportional to the history of liquid imbibed, is strongly dependent on the extent of reduction in the wick cross-sectional area as well as its location vis-a`-vis the wick entrance.

Cellulosic Substrates for Removal of Pollutants from Aqueous Systems: A Review. 3. Spilled Oil and Emulsified Organic Liquids

“…Various authors have proposed that "capillary action" is a key mechanism by which oil is taken up by sorbent materials (Choi et al 1993(Choi et al , 1994Ribeiro and Rubio 1999;Ribeiro et al 2000;Inagaki et al 2002b;Al-Marzouqi et al 2003;Haussard et al 2003;Lim and Huang 2006;Cojocaru et al 2011;Diersch et al 2010;Masoodi et al , 2011Carrillo et al 2012). In other words, contact angle phenomena govern the wicking of oils into porous substrates.…”

Highly efficient synthesis of cumene via benzene isopropylation over nano-sized beta zeolite in a submerged ceramic membrane reactor

“…The filtration rate was dependent on the temperature, and the higher temperature the better filtration performance. As the viscosity of the reaction mixture decreased with the increase in the temperature, the filtration rate would increase when the transmembrane pressure and efficient membrane surface area were kept constant according to the Darcy's law [30,31]. Considering the volatility of the organic matters, the suitable filtration temperature of 60°C was employed in the membrane filtration process.…”

Numerical simulation of liquid absorption in paper‐like swelling porous media

“…9 The Darcy's law, for the flow of a single liquid in an isotropic porous medium under isothermal conditions, is given as ‡ (Clear liquid-front assumption is a good one in the case of wicking/imbibition of liquids in thin, paper-like materials.…”

“…8,9 However, in the case of complex wick-geometries, the analytical solution of the Darcy's law based governing equations may not be possible. 8,9 However, in the case of complex wick-geometries, the analytical solution of the Darcy's law based governing equations may not be possible.…”

“…8,9 However, in the case of complex wick-geometries, the analytical solution of the Darcy's law based governing equations may not be possible. 9 Among the different numerical methods, the finite element method (FEM) has been extensively used for modeling flows in porous media. 9 Among the different numerical methods, the finite element method (FEM) has been extensively used for modeling flows in porous media.…”