Relating dynamic contact angle to wetting front instability (original) (raw)
Related papers
Pore scale consideration in unstable gravity driven finger flow
2] To explain the dynamic behavior of the matric potential at the wetting front of gravity driven fingers, we take into account the pressure across the interface that is not continuous and depends on the radius of the meniscus, which is a function of pore size and the dynamic contact angle h d . h d depends on a number of factors including velocity of the water and can be found by the Hoffman-Jiang equation that was modified for gravity effects. By assuming that water at the wetting front imbibes one pore at a time, realistic velocities are obtained that can explain the capillary pressures observed in unstable flow experiments in wettable and water repellent sands.
Modeling finger development and persistence in initially dry porous media
Geoderma, 1996
The mechanism for the growth and persistence of gravity-driven fingered flow of water in initially dry porous media is described. A Galerkin finite element solution of the two-dimensional Richards equation with the associated parameter equations for capillary hysteresis in the water retention function is presented. A scheme for upstream weighting of internodal unsaturated hydraulic conductivities is applied to limit smearing of steep wetting fronts. The growth and persistence of a single finger in an initially dry porous media is simulated using this numerical solution scheme. To adequately simulate fingered flow, it was found that the upstream weighting factor had to be negative, meaning that the internodal unsaturated hydraulic conductivities were weighted more by the downstream node. It is shown that the growth and persistence of a finger is sensitive to the character of the porous media water retention functions. For porous media where the water-entry capillary pressure on the main wetting function is less than the air-entry capillary pressure on the main drainage function, a small perturbation will grow into a finger, and during sequential drainage and wetting the finger will persist. In contrast, for porous media where the water-entry capillary pressure on the main wetting function is greater than the air-entry capillary pressure on the main drainage function, the same small perturbation will dissipate by capillary diffusion. The finger widths derived from the numerical simulation are similar to those predicted by analytical theory. 0016-7061/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0016-7061 (95)00086-0
Experimental study of fingered flow through initially dry sand
2006
Water infiltration into coarse textured dry porous media becomes instable depending on flow conditions characterized through dimensionless quantities, i.e. the Bond number and the Capillary number. Instable infiltration fronts break into flow fingers which we investigate experimentally using Hele-Shaw cells. We further developed a light transmission method to measure the dynamics of water within flow fingers in great detail with high spatial and temporal resolution. The method was calibrated using x-ray absorption and the measured light transmission was corrected for scattering effects through deconvolution with a point spread function. Additionally we applied a dye tracer to visualize the velocity field within flow fingers. We analyzed the dynamics of water within the finger tips, along the finger core behind the tip, and within the fringe of the fingers during radial growth. Our results confirm previous findings of saturation overshoot in the finger tips and revealed a saturation minimum behind the tip as a new feature. The finger development was characterized by a gradual increase in water content within the core of the finger behind this minimum and a gradual widening of the fingers to a quasi-stable state which evolves on time scales that are orders of magnitudes longer than those of fingers' evolution. In this state, a sharp separation into a core with fast convective flow and a fringe with exceedingly slow flow was detected. All observed phenomena could by consistently explained based on the hysteretic behavior of the soil-water characteristic and on the positive pressure induced at the finger tip by the high flow velocity.
Transport in Porous Media, 1990
Three-dimensional fingers caused by gravity driven, wetting front instability in unsaturated porous media were explored through laboratory experimentation. Two sets of experiments were conducted using initially dry sand in large 30 cm diameter columns to guide analytical development for finger velocity and diameter. The first set consisted of ponding water on a two-layer sand system with a fine sand overlying a coarse sand. Here, a complicated pattern of interaction among fingers was found to occur. In the second set, water was applied directly to the coarse layer as 2 cm diameter area sources, enabling systematic study of individual finger structure. Based on dimensional analysis and the experimental results, general relationships were found for finger velocity and cross-sectional area as a function of both the flux through the finger and hydraulic properties of the coarse layer represented by the sorptivity, saturated conductivity, and initial and saturated moisture contents. Unlike the two-dimensional case, air entrapment was an important factor in explaining the experimental results.
Hydraulic contacts controlling water flow across porous grains
Physical Review E, 2007
Water flow between porous grains varies widely depending on the water distribution in contacts between grains. The hydraulic behavior of contacts varies from highly conductive when water fills the contacts to a bottleneck to flow as water pressure drops and contact asperities rapidly drain. Such changes greatly impact the hydraulic conductivity of porous grain packs such as aggregated soil. The dominant driving force of water flow across contacts is capillarity, often quantified relative to gravity and viscous forces using the capillary and Bond numbers. For fast water infiltration, viscous forces dominate. For simplicity we modeled the water distribution between spherical porous grains whose surfaces are covered by spherical bumps of much smaller radii. We provide experimental evidence obtained by neutron radiography and synchrotron-based x-ray tomographic microscopy documenting transitions in the flow behavior across contacts.
1991
As water infiltrates downward into an air-filled, water wettable porous medium, the wetting front which forms may become unstable and allow the formation of downward moving fingers within the vadose zone. In this paper we first review stability criteria and estimated finger widths determined from linear stability theory in two-dimensional systems. Two approaches reported in the literature which employ different formulations for the interfacial boundary conditions, yield different estimates of the finger width. We extend the analyses to investigate finger diameter in three-dimensional systems by considering axisymmetric disturbances. Results of the three-dimensional analyses are illustrated through comparison to previously reported experimental results in three-dimensional systems. Because either approach gives similar results for low system fluxes, in practice, it probably will not matter which formulation is used. However, one approach represents the data better and contains only traditionally measured porous media properties. 144, 107-112, 1987. van Ommen, H. C., and R. Dejksma, Analysis of transport in a coupled unsaturated-saturated system, in Proceedings of the International Conference and Workshop on Validation of Flow and Transport Models for the Unsaturated Zone, Ruidoso, N.M., May 23-26, 1988, edited by P. J. Wierenga, pp. 447-462, New Mexico State Press, Las Cruces, 1988. van Ommen, H. C., L. W. Dekker, R. Dejksma, J. Hulshof, and W. H. van der Molen, A new technique for evaluating the presence of preferential flow paths in non-structured soils, Soil Sci.
Hydrology and Earth System …, 2002
Wetting front instability creates a shallow induction zone from which fingers emerge that rapidly transport water and solutes downwards. How the induction zone affects finger location and spacing is unknown. In the moist subsoil, fingers may well dissipate because the finger tips no longer have to overcome the water entry value. Both flow regions were investigated in a two-dimensional chamber with a fine-overcoarse glass bead porous medium. A capillary fringe was created by upward wetting through capillary rise. Upon ponding with dye-coloured water, fingers emerged, propagated downward and diverged when reaching the capillary fringe. Microtensiometers were installed in the induction zone, the fingers, and in the capillary fringe. In the induction zone, a lateral sinusoidal pressure head developed within minutes. Only in one of two experiments could the observed pressure head pattern be satisfactorily reproduced by a steady-state model assuming uniform induction zone properties and uniform infiltration. Later, fingers emerged below the pressure head minima. The induction zone did not affect finger properties. The pressure head in the induction zone was determined by the depth of the finger tips. The water requirement of the fingers dictated the lateral pressure head gradients. The pressure heads in the capillary fringe supported the hypothesis that the flow stabilised and dissipated there.
Journal of Colloid and Interface Science, 2013
Understanding the role of geometry, inertia, and dynamic contact angle on wetting and dewetting of capillary tubes has theoretical and practical aspects alike. The specific and synergistic effects of these factors were studied theoretically using a mathematical model that includes inertial and dynamic contact angle terms. After validating the model for capillaries of uniform cross section, the model was extended to capillaries with sinusoidal modulations of the radius, since in practice, capillaries rarely have uniform crosssections. The height of the meniscus during wetting and dewetting was significantly affected by the relations between the local slope of the capillary surface and the Young contact angle. Non-dimensional variables were defined using viscous effects and gravity as the scaling parameters. Simulations using the dimensionless model showed that the inertial and dynamic contact angle terms can be neglected for narrow capillaries of uniform cross-section but not for uniform, wide cross-section capillaries. Moreover, nonuniformity in cross-sectional area induced hysteresis, deceleration, blocking, and metastable equilibrium locations. An increase in contact angle further amplified the effect of geometry on wetting and dewetting processes. These results enable characterization and modeling of fluid retention and flow in porous structures that inherently consist of capillaries of varying cross section.
Effective Darcy-scale contact angles in porous media imbibing solutions of various surface tensions
2009
Surface tensions of high-salinity solutions are significantly different from those of pure water. Our objective was to develop and test a methodology to determine whether these surface tension effects predictably alter imbibition into dry and moist porous media. Static and dynamic experiments were performed using four grades of quartz sand to determine the effects of solution salinity on imbibition. Results were quantified as apparent contact angles between the sand and three solutions (pure water, 5 molal NaNO 3 , and n-hexane). Contact angles determined using a static method in initially air dried sand ranged from 23°to 31°, with the same values found for both water and the NaNO 3 solution. Effective contact angles determined for the air-dried sand using a dynamic method based on a modified version of the Green and Ampt model were about twice those found using the static method, averaging 45°and 62°for water and the NaNO 3 solution, respectively. In prewetted sands, the dynamic imbibition data yielded apparent contact angles of 2°and 21°for water and the NaNO 3 solution, respectively, with the latter value comparing well to a predicted value of 25°for the NaNO 3 solution solely on the basis of surface tension contrast. The results of this study indicate that on the Darcy scale, saline solutions appear to follow the relationship of nonzero contact angles with other miscible fluids of different surface tensions used to prewet the sand grains, in agreement with the macroscale infiltration results of Weisbrod et al. (2004).