Year: 2025
Type: article
Abstract: Macroscopically, a Darcian unsaturated moisture flow in the top soil is usually represented by an one-dimensional volume scale of evaporation from a static water table. On the microscale, simple pore-level models posit bundles of small-radius capillary tubes of a constant circular cross-section, fully occupied by mobile water moving in the Hagen–Poiseuille (HP) regime, while large-diameter pores are occupied by stagnant air. In our paper, cross-sections of cylindrical pores are polygonal. Steady, laminar, fully developed two-dimensional flows of Newtonian water in prismatic conduits, driven by a constant pressure gradient along a pore gradient, are more complex than the HP formula; this is based on the fact that the pores are only partially occupied by water and immobile air. The Poisson equation in a circular tetragon, with no-slip or mixed (no-shear-stress) boundary conditions on the two adjacent pore walls and two menisci, is solved by the methods of complex analysis. The velocity distribution is obtained via the Keldysh–Sedov type of singular integrals, and the flow rate is evaluated for several sets of meniscus radii by integrating the velocity over the corresponding tetragons.
Source: The ANZIAM Journal
Authors: ANVAR KACIMOV, YURII OBNOSOV
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Awards: G2466075652, G2560423651
OpenAlex ID: W4409208352