Capillary rise of water in hydrophilic nanopores

We report on the capillary rise of water in three-dimensional networks of hydrophilic silica pores with 3.5nm and 5nm mean radii, respectively (porous Vycor monoliths). We find classical square root of time Lucas-Washburn laws for the imbibition dynamics over the entire capillary rise times of up to 16h investigated. Provided we assume two preadsorbed strongly bound layers of water molecules resting at the silica walls, which corresponds to a negative velocity slip length of -0.5nm for water flow in silica nanopores, we can describe the filling process by a retained fluidity and capillarity of water in the pore center. This anticipated partitioning in two dynamic components reflects the structural-thermodynamic partitioning in strongly silica bound water layers and capillary condensed water in the pore center which is documented by sorption isotherm measurements.Comment: 4 pages, 3 figure

Interface Equations for Capillary Rise in Random Environment

We consider the influence of quenched noise upon interface dynamics in 2D and 3D capillary rise with rough walls by using phase-field approach, where the local conservation of mass in the bulk is explicitly included. In the 2D case the disorder is assumed to be in the effective mobility coefficient, while in the 3D case we explicitly consider the influence of locally fluctuating geometry along a solid wall using a generalized curvilinear coordinate transformation. To obtain the equations of motion for meniscus and contact lines, we develop a systematic projection formalism which allows inclusion of disorder. Using this formalism, we derive linearized equations of motion for the meniscus and contact line variables, which become local in the Fourier space representation. These dispersion relations contain effective noise that is linearly proportional to the velocity. The deterministic parts of our dispersion relations agree with results obtained from other similar studies in the proper limits. However, the forms of the noise terms derived here are quantitatively different from the other studies

On the anomalous dynamics of capillary rise in porous media

The anomalous dynamics of capillary rise in a porous medium discovered experimentally more than a decade ago (Delker et al., Phys. Rev. Lett. 76 (1996) 2902) is described. The developed theory is based on considering the principal modes of motion of the menisci that collectively form the wetting front on the Darcy scale. These modes, which include (i) dynamic wetting mode, (ii) threshold mode and (iii) interface de-pinning process, are incorporated into the boundary conditions for the bulk equations formulated in the regular framework of continuum mechanics of porous media, thus allowing one to consider a general case of three-dimensional flows. The developed theory makes it possible to describe all regimes observed in the experiment, with the time spanning more than four orders of magnitude, and highlights the dominant physical mechanisms at different stages of the process

Percolation study for the capillary ascent of a liquid through a granular soil

Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length {\lambda} of the capillary bridges among grains. Low {\lambda} generate a disconnect structure, with small clusters everywhere. On the contrary, for high {\lambda}, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of {\lambda} on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold {\lambda}_{c} = (0.049 \pm 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length {\nu} = (0.830 \pm 0.051), suggesting that the percolation transition falls into the universality class of ordinary percolation

Groundwater recharge and capillary rise in a clayey catchment: modulation by topography and the Arctic Oscillation

International audienceThe signature left by capillary rise in the water balance is investigated for a 16 km2 clayey till catchment in Denmark. Integrated modelling for 1981?99 substantiates a 30% uphill increase in average net recharge, caused by the reduction in capillary rise when the water table declines. Calibration of the groundwater module is constrained by stream flow separation and water table wells. Net recharge and a priori parameterisation has been estimated from those same data, an automatic rain gauge and electrical sounding. Evaluation of snow storage and compensation for a simplified formulation of unsaturated hydraulic conductivity contribute to a modelling of the precipitation-runoff relation that compares well with measurements in other underdrained clayey catchments. The capillary rise is assumed to be responsible for a 30% correlation between annual evapotranspiration and the North Atlantic Oscillation. The observed correlation, and the hypothesis of a hemispherical Arctic Oscillation linking atmospheric pressure with surface temperature, suggests that modelled evapotranspiration from clayey areas is better than precipitation records for identifying the region influenced by oscillation. Keywords: catchment modelling, MIKE SHE, capillary rise, degree-day model, climat

Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation

When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by Molecular Dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a $\sqrt{\textrm{time}}$-law. For the polymer melt, however, we find that the capillary flow exhibits a slip length $\delta$, comparable in size with the nanotube radius $R$. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification of the Lucas-Washburn law which takes explicitly into account the slip length $\delta$.Comment: 4 pages 4 figure