Numerical Simulation of Droplet Impacting and Sliding on Hydrophobic Granular Surfaces

Droplet sliding naturally happens with practical significance in developing artificial self-cleaning surfaces or impermeable barriers. On water-repellent soil surfaces, such processes evolve at very small scales, typically at the particle level. To address this, this paper presents a two-dimensional Lattice Boltzmann (LB) study on the droplet sliding dynamics on a layer of regularly arranged particles with varying size and contact angle (CA) aimed at mimicking conditions comparable to those of real soils. The numerical droplet is initialized above the inclined granular surface with different lifting distances and deposited by gravity. The droplet hits the surface with different impacting velocities and subsequently slides down the slope. Four droplet-sliding behaviors were observed: a droplet sticks to the granular surface, a droplet moves by pinning and depinning of its interface (“stick-slip”), a droplet undergoes periodic elongation and shortening during sliding, and a droplet lifts off the granular surface and may be ruptured. For a droplet that displays the “stick-slip” behavior, the sliding velocity reaches a converged terminal velocity, which increases with a higher CA, a more inclined slope, and a smaller particle size. However, nonunique terminal velocities were identified to be affected by the impacting velocities, but their correlation is not continuous and may not be positive. Finally, we propose to quantify the rotational or translational movement by effective kinematic ratio (EKR), which is defined as the translational kinematic energy divided by the total kinematic energy. The unique relation between the EKR and the terminal velocity is suggested to be one practical indicator to intrinsically characterize the water repellency at the particle level.

A two-layer shallow flow model with two axes of integration with application to submarine avalanches and generated tsunamis

<p>There exits in the literature many approaches that has been used to model submarine avalanches (See [5]). These models are mainly based on the pioneer work of Savage and Hutter (SH) [4] that is a shallow water type model for aerial avalanches, which is written in local coordinates, in order to simulate the tangential velocity to the bottom. A depth-averaged SH model over a general bottom with curvature was introduced in [1]. An extension to submarine avalanches is developed in [2]. In this paper the same local coordinate system is used for the two layers. Nevertheless, using a local coordinates the model would prescribe the perturbation at the surface at a wrong placement. In [3] a bilayer depth-averaged model for submarine avalanches is presented with cartesian coordinates for the water layer and local coordinates for the avalanche. The drawback is that the seabed deformation is considered as an input data for the water layer equations, then no interaction between the two fluids are taken into account and it is necessary to do an interpolation of the granular surface at each time step of the numerical simulation. In this work we present firstly the details of the proposed model, a coupled two-layer shallow water system where we consider local coordinates for the granular layer and cartesian coordinates for the fluid one. The main difference with other models that adopt the same stragie is that any interpolation of the granular surface is required. Moreover, the velocity of the granular layer has an explicit influence on the mass and momentum conservation laws of the fluid layer. Secondly, several numerical tests will be presented.</p><p>References</p><p>[1] F. Bouchut, E.D. Fernández-Nieto, A. Mangeney, and P.Y. Lagrée. On new erosion models of Savage-Hutter type for avalanches. Acta Mechanica, 199(1):181--208, 2008.<br>[2] E.D. Fernández-Nieto, F. Bouchut, D. Bresch, M.J. Castro Díaz, and A. Mangeney. A new Savage-Hutter type model for submarine avalanches and generated tsunami. Journal of Computational Physics, 227(16):7720--7754, 2008.<br>[3] P.H. Heinrich, A. Piatanesi, and H. Hébert. Numerical modelling of tsunami generation and propagation from submarine slumps: the 1998 papua new guinea event. Geophysical Journal International, 145(1):97--111, 2001.<br>[4] S. B. Savage and K. Hutter. The dynamics of avalanches of granular materials from initiation to runout. part I: Analysis. Acta Mechanica, 86(1):201–223, 1991.<br>[5] S. Yavari-Ramshe and B. Ataie-Ashtiani. Numerical modeling of subaerial and submarine landslide-generated tsunami waves-recent advances and future challenges. Landslides, 13(6):1325–1368, 2016.</p>

On tylosis ultrastructure in Quercus cerris L.

A study of tylosis in European Turkey oak (Quercus cerris L.) shows correspondences in the formation of tyloses and of regular cell walls. The outer tylosis wall has a smooth, granular surface with simple perforations analogous to that of the primary wall of ordinary cells. The underlying wall stratum shows parallel oriented macro-fibrils, normally found in the secondary walls of regular cells. At the contact areas of tyloses, stabilizing seams can be observed. Various types of wall openings such as simple pits, blind pits and vestured pits were present. Also tylosis division was detected. The characteristics of parenchyma cell walls can be re-discovered in tyloses.

Granular surface flow on an asymmetric conical heap

We carry out an experimental study of the granular surface flow of nearly monodisperse glass beads on a conical heap formed on a rough circular disc by a narrow stream of the particles from a hopper, with the pouring point displaced from the centre of the disc. During the growth phase, an axisymmetric heap is formed, which grows either by periodic avalanches or by non-periodic avalanches that occur randomly over the azimuthal location of the heap, depending on the operating conditions and system properties. The dynamics of heap growth is characterized by the variation of the heap height, angle of repose and the angular velocity of the periodic avalanche with time, for different mass flow rates from the hopper. When the base of the heap reaches the edge of the disc closest to the pouring point, the heap stops growing and a steady surface flow of particles is developed on the heap surface, with particles flowing over the edge of the disc into a collection tray. The geometry is a unique example of a granular flow on an erodible bed without any bounding side walls. The corresponding steady state geometry of the asymmetric heap is characterized by means of surface contours and angles of repose. The streamwise and transverse surface velocities are measured using high-speed video photography and image analysis for different mass flow rates. The flowing layer thickness is measured by immersing a coated needle in the flow at different positions on the mid-line of the flow. The surface angle of the flowing layer is found to be significantly smaller than the angle of repose and to be independent of the mass flow rate. The velocity profiles at different streamwise positions for different mass flow rates are found to be geometrically similar and are well described by Gaussian functions. The flowing layer thickness is calculated from a model using the measured surface velocities. The predicted values match the measured values quite well.

Granular surface avalanching induced by drainage from a narrow silo

Using theory and experiments, we investigate granular surface avalanching due to material outflow from a narrow silo. The assumed silo geometry is a deep rectangular box, of moderate spanwise width and small gap thickness between smooth front and back walls. A small orifice deep below the free surface lets grains drain out at a constant rate. The resulting granular flows can therefore be assumed quasi-two-dimensional and quasi-steady over most of the surface descent history. To model these flows, we couple a kinematic model of deep granular flow with a dynamic model of shallow surface avalanching. We then compare the calculated flow fields with detailed particle tracking measurements, letting the silo ascend relative to the high-speed camera to increase spatial resolution. The results show that the avalanching surface shape and near-surface flow are controlled by the spanwise gradient in subsidence velocity, and how this gradient is in turn controlled by the height above orifice and the gap thickness. Whereas the deep flow pattern is rate independent, shallow avalanching is paced by the granular rheology.