“…After passing through the submerged part, the liquid rises mainly by capillary action. Based on the balance between gravity and capillary suction force, the equation for calculating the maximum capillary rise height is as follows 37 : where h c is the capillary rising height (m), is the surface tension between water and air (N/m), is the wetting angle (°), d is the capillary diameter (m), and is the water bulk density (KN·m -3 ). Figure 3 Evolution of capillary rise parameters with time: H in : height of the internal wetting surface, H out : height of the external wetting line, and W—water content.…”
Capillary penetration is widely existed in stope leaching, both the rate of liquid wetting ore and flow out of ore are affected by it. Stope leaching is carried out in a high-temperature environment when mining minerals with large burial depth. The mechanism of intra-particle liquid capillary penetration mechanisms at high-temperature have not been revealed. In this paper, samples with a size of Φ50 mm × 100 mm were selected for quantitative analysis. The capillary rise behaviour inside samples with different porosity were detected at 30 °C, 40 °C and 50 °C by using magnetic resonance imaging (MRI). In most cases, capillary rise height is underestimated when the outside wetting line is used as an indicator, because the rise height inside the sample is greater. The liquid capillary rise height increased slightly with the temperature, whereas the wetting surface profile remained unchanged. The capillary rise rate increased significantly with porosity, mainly due to the increase of internal effective porosity. The results help to understand the liquid penetration behaviour under high-temperature stope leaching condition, and lay a theoretical foundation for improving the liquid permeability.
“…After passing through the submerged part, the liquid rises mainly by capillary action. Based on the balance between gravity and capillary suction force, the equation for calculating the maximum capillary rise height is as follows 37 : where h c is the capillary rising height (m), is the surface tension between water and air (N/m), is the wetting angle (°), d is the capillary diameter (m), and is the water bulk density (KN·m -3 ). Figure 3 Evolution of capillary rise parameters with time: H in : height of the internal wetting surface, H out : height of the external wetting line, and W—water content.…”
Capillary penetration is widely existed in stope leaching, both the rate of liquid wetting ore and flow out of ore are affected by it. Stope leaching is carried out in a high-temperature environment when mining minerals with large burial depth. The mechanism of intra-particle liquid capillary penetration mechanisms at high-temperature have not been revealed. In this paper, samples with a size of Φ50 mm × 100 mm were selected for quantitative analysis. The capillary rise behaviour inside samples with different porosity were detected at 30 °C, 40 °C and 50 °C by using magnetic resonance imaging (MRI). In most cases, capillary rise height is underestimated when the outside wetting line is used as an indicator, because the rise height inside the sample is greater. The liquid capillary rise height increased slightly with the temperature, whereas the wetting surface profile remained unchanged. The capillary rise rate increased significantly with porosity, mainly due to the increase of internal effective porosity. The results help to understand the liquid penetration behaviour under high-temperature stope leaching condition, and lay a theoretical foundation for improving the liquid permeability.
“…Avramenko, Tyrinov, and Shevchuk [2,3] successful compared to Lattice-Boltzman-simulations for the start-up flow with slip. We note that the analytic solutions can also be used as a basis to investigate the interaction between slip and heat conduction in start-up flows [7] or can be combined into phenomenological models to describe more complex phenomena such as the rise of liquid in capillaries [11].…”
The transient Couette and Poiseuille channel flow solutions with different Navier slip conditions on the wall boundaries require the solution of a non-linear root-finding problem. A novel algorithm is developed that automates the computation of these roots with arbitrary precision and for general input parameters. The obtained results show a significant improvement to available coefficient values for this analytic solution. A parameter variation for the slip lengths reveals a new power law for the first series coefficient that governs the stability of the solution and is essential for slip length computations from molecular dynamics simulations. Based on the new algorithm, the time scales for the asymptotic approach to the stationary solution are quantified. A double-precision implementation and an arbitrary precision implementation provide a fast, verified, and highly accurate method to obtain benchmark quality reference solutions or a module for more general applications.
“…The rise of liquid in capillary due to surface tension and against gravitational forces is a prototypical case for wetting phenomena and a suitable benchmark for continuum mechanical simulations [1]. A standard description for this problem is a model family of ordinary differential equations originating from [2] and considered in [3].…”
Section: Introductionmentioning
confidence: 99%
“…A standard description for this problem is a model family of ordinary differential equations originating from [2] and considered in [3]. This model family is based on the assumption that the interface has the form of a spherical cap [1,4].…”
When liquid rises in a capillary, the interface has a shape close to a spherical cap when the Eotvos number is sufficiently small. This assumption is typically used when computing the stationary rise height of the liquid. Considering a continuum mechanical approach it can be shown that the exact shape of a spherical cap is not a solution to the rise problem yet a good approximation. Consequently, the assumption of a spherical cap used in Washburn-type rise models is justified only for small Eotvos numbers. In this limit, Jurin's height has the largest error.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
