Armoring has important environmental consequences.

1. 0.10 0.08 100 80 0.06 104 60 103 102 40 0.04 10 20 1 0 103 60 60 0.02 102 40 40 10 20 20 1 0 0 0 103 102 0 10 20 30 40 50 60 10 1 1 0.1 0.01 very fine sand fine sand coarse sand medium sand silt range of severe hydrophobicity Coast Sand WDPT (sec) % Mass Quincy soil Golf Course 10-1 Particle size fractions (mm) y=0.0015x+0.018 Mass eroded per droplet (g) Quincy y=0.0008x+0.015 Coast Golf y=0.0003x+0.011 Distance traveled (mm) 312-5 Armored Water Droplets: How They Form and Their Role in Water Redistribution and Soil Erosion María Inés Dragila Department of Crop and Soil Science, Oregon State University, Oregon, USA Overview Impact of Droplet Armoring What Causes Droplet Armoring? Detrimental effects of soil hydrophobicity are well documented, such as poor infiltration and enhanced erosion that many times result in crop drought stress and soil degradation. This work focuses on a group of soils that traditionally would not be categorized as hydrophobic (i.e., by laboratory WDPT tests) where a droplet is seen to infiltrate within ~ 2 sec. Nevertheless, these soils exhibit a peculiar behavior that causes them to behave as if they were severely hydrophobic. This form of hydrophobic behavior is caused by a mechanism called herein “droplet armoring.” The process of droplet armoring proceeds as follows: directly upon contact (< 0.1 sec) a droplet is coated with a monolayer of loose, dry, soil particles (Fig. 1); soil particles do not penetrate the droplet but rather “ride” on the air-water interface (Fig. 1, 6); and particles engender the droplet to behave as a ball bearing, preventing further infiltration and rolling down slope and eroding the soil surface. (Fig 2, top banner figure). Heretofore, these soils have not responded to traditional amelioration techniques for hydrophobic soils. Project goal is to delineate the mechanism that controls this peculiar behavior in order to develop a quantitative guide towards successful amelioration techniques. Figure 6. Schematic showing deformation of the meniscus that generates a force of attraction between the water droplet and a soil particle. Photograph of soil particles climbing onto the outer surface of a water droplet that is suspended from a plastic pipette. Droplet rests on the soil surface. Because the contact angle (~78) is greater than the critical value (~60), the droplet remains suspended, allowing particles to climb, and does not spread onto the surface. Armoring has important environmental consequences. • Particle coatings facilitate droplets to roll down slope, eroding the soil surface until it comes to rest at a topographic low. • In hill planting, redistribution of moisture not only results in hill erosion, but leads to plant drought stress. Armoring will only occur when the water droplet is inhibited from spreading onto the soil surface. Spreading is a function of the soil surface roughness and contact angle. Air-water interface is deformed when the water droplet wets a particle with a non-zero contact angle. Deformation of the meniscus results in an attractive force that lifts the particle onto the air water interface. • Because droplets imbibe within ~2 sec, traditional WDPT classification would not identify these soils as hydrophobic. • Droplets armor within 0.3 sec, much faster than the imbibition time. • Only the fine soil fraction (<5% of total mass) exhibits severe hydrophobicity. • Because of their generally coarse texture, these soils dry rapidly, exacerbating the hydrophobic condition. Theoretical Details Mechanism characteristics: • “Droplet armoring” requires contact angle to be above a critical value. • Critical contact angle value is between 45º and 90º, with the exact value dependent upon particle size distribution. For soil, the critical contact angle is ~60º. • When contact angle is greater than the critical value, the droplet will not spread onto the surface, rather the meniscus at the edge of the droplet deforms as it touches the particles. The meniscus deformation creates an attractive type force that is sufficient to draw the particle to the water droplet surface. • Rather than the water droplet spreading onto the soil surface, it becomes a collector for soil. Lifting Force Critical Contact Angle Energy to lift the particles is calculated by using the Kralchevsky et al. (1992) approach, where the force of attraction is given by the sum of capillary and hydrostatic energies. The capillary force is related to the energy in bringing a particle from infinity to the location of interest. Water spreads onto a “rough” surface in response to interfacial energy and capillarity caused by geometry of the surface roughness. Mathematical model by Hay and Dragila (2008) predicts the rate of spreading as a function of roughness geometry (d, l, dh), contact angle (q) and fluid properties (g, Po, m). (Eq. 1) predicts the existence of a critical value for the contact angle, above which water will not spread onto a rough surface, even though the contact angle is less than 90º, and theoretically wettable. where Symbols: Z is the z-coordinate of the center of mass of either the particle (ZK) or the liquid phase (ZY), ri is position vector of each particle, m is mass of each phase, g is gravitational acceleration, AKY is interfacial area between the particle and each fluid phase, wKY is solid-liquid interfacial, g is gas-liquid interfacial energy and DA is the difference in the air-water interfacial area because of the presence of the particles. Definition: Critical Contact Angle The elegance of the formulation derived by Kralchevsky’s is that the system energy depends only upon the geometry of the contact lines and the particle volumes. It does not explicitly depend on the shape of the interface. The derivation assumes the slope of the interface is low. Figure 5. Schematic of mechanisms involved in water droplet spreading: (a) main water body at atmospheric pressure; (b) film spreading driven by capillarity of the surface roughness; and, (c) thin precursor film driven by molecular diffusion. Equation 1. Mathematical model predicting the rate of spreading for a film on a rough surface (Hay and Dragila, 2008). The term in parenthesis acts as a diffusion or sorptivity term. g the surface tension, dh the hydraulic diameter, Po the Poiseuille number, m the fluid viscosity, d and l the mean roughness amplitude and wavelength, respectively, and q the contact angle. Figure 2. Soil erosion following irrigation of potato crop on Quincy soil, Hermiston, Oregon Figure 4. Particle size (beige) and Water Drop Penetration Time test (green) for three soils that exhibit armoring. Red arrows show the “whole soil” WDPT. Black line (green fill) shows the WDPT for each particle size fraction. The equation above predicts cessation of motion for the precursor film for values of the contact angle above a critical value that is controlled by roughness geometry. Thus for contact angles greater than this critical value, the droplet will not spread. General characteristics of the numerical solution: • Numerical solution shows that the interaction energy between two spheres on a liquid interface is very long range (x > 103Rparticle). • Particles floating on the surface will self-arrange as compactly as possible. • Strength of the attractive force is inversely related to the liquid-particle contact angle. • Net force is attractive regardless of contact angle for pairs of either hydrophilic or hydrophobic particles, and repulsive between mixed media where a hydrophilic particle is in the vicinity of a hydrophobic particle. • Energy to lift particles is sufficient for coating of a water droplet. Regime of droplet armoring Super hydrophobicity. Water beads on surface. no armoring behavior. General characteristics of the critical contact angle equation: • Critical contact angle lies between 45º-90º. • Analysis for a range of particle size distributions indicates that for soil surfaces there is a specific range of possible values for qcrit that lies between 60 and 87, but possibly more strongly centered around ~70. • Soils with contact angles less than 45º should not exhibit wettability problems because it’s within the contact angle criteria for liquid spreading on flat surfaces (with textures being even more permissive). Hydrophilic. Water drops imbibe q < qcrit q > 90 References Dragila, M. I., submitted. Spontaneous coating of water droplets by dry soil particles: I. Mechanism, Soil Science Society of America. Hay and Dragila. 2008. Theoretical model for the wetting of a rough surface, Journal of Colloid and Interface Science, 325, 472-477. Kralchevsky , P. A., V. N. Paunov, I. B. Ivanov, and K. Nagayama. 1992. Capillary meniscus interaction between colloidal particle attached to a liquid-fluid interface, Journal of Colloid and Interface Science, 151(1), 79-94. Kralchevsky, P. A., and K. Nagayama. 1994. Capillary Forces Between Colloidal Particles, Langmuir, 10, 23-36. contact angle Figure 3. Laboratory investigation of erosion rate caused by a continuous thin stream of water poured onto the surface from a height of only 2 cm (data shown on graph at right). Erosion channels left by previous replicates, and coated streamlet on far left of photograph are evidence of armoring behavior and it’s role on soil erosion. Figure 1. Schematic showing the full range of possible liquid-solid contact angles divided into three regions: hydrophilic (0 < q < qcrit), intermediate wettability where droplet armoring occurs (qcrit < q < 90º), and hydrophobic regime for q > 90º.