Abstract
In porous media, pore geometry and wettability are determinant factors for capillary flow in drainage or imbibition. Pores are often considered as cylindrical tubes in analytical or computational studies. Such simplification prevents the capture of phenomena occurring in pore corners. Considering the corners of pores is crucial to realistically study capillary flow and to accurately estimate liquid distribution, degree of saturation and dynamic liquid behavior in pores and in porous media. In this study, capillary flow in polygonal tubes is studied with the Shan-Chen pseudopotential multiphase lattice Boltzmann model (LBM). The LB model is first validated through a contact angle test and a capillary intrusion test. Then capillary rise in square and triangular tubes is simulated and the pore meniscus height is investigated as a function of contact angle θ. Also, the occurrence of fluid in the tube corners, referred to as corner arc menisci, is studied in terms of curvature versus degree of saturation. In polygonal capillary tubes, the number of sides leads to a critical contact angle θc which is known as a key parameter for the existence of the two configurations. LBM succeeds in simulating the formation of a pore meniscus at θ > θc or the occurrence of corner arc menisci at θ < θc. The curvature of corner arc menisci is known to decrease with increasing saturation and decreasing contact angle as described by the Mayer and Stoewe-Princen (MS-P) theory. We obtain simulation results that are in good qualitative and quantitative agreement with the analytical solutions in terms of height of pore meniscus versus contact angle and curvature of corner arc menisci versus saturation degree. LBM is a suitable and promising tool for a better understanding of the complicated phenomena of multiphase flow in porous media.
Highlights
H acceleration, h is the height of the liquid column where is the fluid density, g is the gravitational under the pore meniscus, L is the size of the side of the rectangular polygon, z is the coordinate along the height and rarc is the radius of curvature of the corner arc meniscus
Where ρ is the fluid density, g is the gravitational acceleration, h is the height of the liquid column under the pore meniscus, L is the size of the side of the rectangular polygon, z is the coordinate along the height and rarc is the radius of curvature of the corner arc meniscus
Capillary rise in polygonal tubes is investigated, taking into account the appearance of a pore meniscus and corner arc menisci, the presence of which depends on the contact angle
Summary
2016, 4,flow is a common phenomenon of multiphase flow in porous media with various applications, such as in the built environment, textile dyeing industry, oil recovery and ink printing. Capillary capillary flow flow is is ubiquitous ubiquitousand andhas hasbeen beenstudied studiedtheoretically theoreticallyand andexperimentally experimentallyforfor a a longtime, time,the thedetermination determinationofof vapor/liquid vapor/liquidinterface interfaceconfigurations configurationsin in complex complex porous porous media long remains a achallenging problem. Those configurations dependdepend on the pore connectivity, challenging problem. Simplifications prevent capturing significant pore geometry, modeling pores asor cylindrical tubesSuch or parallel plates Such simplifications prevent unsaturated phenomena such as corner flow. A common method to experimentally study capillary flow of in n-sided regular resulting in different cross-section geometries, as triangle, square, complex pores polygonal is the usetubes of n-sided regular polygonal tubes resulting in such different cross-section hexagon, etc.such.
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