Statistical Mechanics of Electrowetting.

We derive the ab initio equilibrium statistical mechanics of the gas-liquid-solid contact angle on planar periodic, monodisperse, textured surfaces subject to electrowetting. To that end, we extend an earlier theory that predicts the advance or recession of the contact line amount to distinct first-order phase transitions of the filling state in the ensemble of nearby surface cavities. Upon calculating the individual capacitance of a cavity subject to the influence of its near neighbors, we show how hysteresis, which is manifested by different advancing and receding contact angles, is affected by electrowetting. The analysis reveals nine distinct regimes characterizing contact angle behavior, three of which arise only when a voltage is applied to the conductive liquid drop. As the square voltage is progressively increased, the theory elucidates how the drop occasionally undergoes regime transitions triggering jumps in the contact angle, possibly changing its hysteresis, or saturating it at a value weakly dependent on further voltage growth. To illustrate these phenomena and validate the theory, we confront its predictions with four data sets. A benefit of the theory is that it forsakes trial and error when designing textured surfaces with specific contact angle behavior.

Statistical mechanics of the triple contact line.

We outline a statistical mechanics of the triple gas-solid-liquid contact line on a rough plane. The analysis regards the neighborhood of the line as a solid dotted with cavities. It adopts the simplest mean-field statistical mechanics, in which each cavity is either full or empty, while being connected to near neighbors by thin necks. The theory predicts equilibrium angles for advance and recession in terms of the Young contact angle and the joint statistical distribution of two quantifiable geometrical parameters representing specific neck cross-section and specific cavity opening. It attributes contact angle hysteresis to first-order phase transitions among adjacent cavities, as they collectively imbibe or reject liquid. It also calculates the potential energy barriers that hysteresis erects against overcoming contact line pinning. By determining whether the phase transitions can release latent energy, this ab initio analysis distinguishes six regimes, including two metastable recession states. We compare predictions with data for superhydrophobia on microscopic rods; for hysteresis in the "Wenzel state"; and for variations of the advancing contact angle with surface energies of the liquid.

Microbial Characterization of Qatari Barchan Sand Dunes.

This study represents the first characterization of sand microbiota in migrating barchan sand dunes. Bacterial communities were studied through direct counts and cultivation, as well as 16S rRNA gene and metagenomic sequence analysis to gain an understanding of microbial abundance, diversity, and potential metabolic capabilities. Direct on-grain cell counts gave an average of 5.3 ± 0.4 x 105 cells g-1 of sand. Cultured isolates (N = 64) selected for 16S rRNA gene sequencing belonged to the phyla Actinobacteria (58%), Firmicutes (27%) and Proteobacteria (15%). Deep-sequencing of 16S rRNA gene amplicons from 18 dunes demonstrated a high relative abundance of Proteobacteria, particularly enteric bacteria, and a dune-specific-pattern of bacterial community composition that correlated with dune size. Shotgun metagenome sequences of two representative dunes were analyzed and found to have similar relative bacterial abundance, though the relative abundances of eukaryotic, viral and enterobacterial sequences were greater in sand from the dune closer to a camel-pen. Functional analysis revealed patterns similar to those observed in desert soils; however, the increased relative abundance of genes encoding sporulation and dormancy are consistent with the dune microbiome being well-adapted to the exceptionally hyper-arid Qatari desert.

Granular flows on a dissipative base.

We study inclined channel flows of sand over a sensor-enabled composite geotextile fabric base that dissipates granular fluctuation energy. We record strain of the fabric along the flow direction with imbedded fiber-optic Bragg gratings, flow velocity on the surface by correlating grain position in successive images, flow thickness with the streamwise shift of an oblique laser light sheet, velocity depth profile through a transparent side wall using a high-speed camera, and overall discharge rate. These independent measurements at inclinations between 33∘ and 37∘ above the angle of repose at 32.1±0.8∘ are consistent with a mass flow rate scaling as the 3/2 power of the flow depth, which is markedly different than flows on a rigid bumpy boundary. However, this power changes to 5/2 when flows are forced on the sand bed below its angle of repose. Strain measurements imply that the mean solid volume fraction in the flowing layer above the angle of repose is 0.268±0.033, independent of discharge rate or inclination.

Statistical mechanics of unsaturated porous media.

We explore a mean-field theory of fluid imbibition and drainage through permeable porous solids. In the limit of vanishing inertial and viscous forces, the theory predicts the hysteretic "retention curves" relating the capillary pressure applied across a connected domain to its degree of saturation in wetting fluid in terms of known surface energies and void space geometry. To avoid complicated calculations, we adopt the simplest statistical mechanics, in which a pore interacts with its neighbors through narrow openings called "necks," while being either full or empty of wetting fluid. We show how the main retention curves can be calculated from the statistical distribution of two dimensionless parameters λ and α measuring the specific areas of, respectively, neck cross section and wettable pore surface relative to pore volume. The theory attributes hysteresis of these curves to collective first-order phase transitions. We illustrate predictions with a porous domain consisting of a random packing of spheres, show that hysteresis strength grows with λ and weakens as the distribution of α broadens, and reproduce the behavior of Haines jumps observed in recent experiments on an ordered pore network.

Model for dense granular flows down bumpy inclines.

We consider dense flows of spherical grains down an inclined plane on which spherical bumps have been affixed. We propose a theory that models stresses as the superposition of a rate-dependent contribution arising from collisional interactions and a rate-independent part related to enduring frictional contacts among the grains. We show that dense flows consist of three regions. The first is a thin basal layer where grains progressively gain fluctuation energy with increasing distance from the bottom boundary. The second is a core region where the solid volume fraction is constant and the production and dissipation of fluctuation energy are nearly balanced. The last is a thin collisional surface layer where the volume fraction abruptly vanishes as the free surface is approached. We also distinguish basal flows with the smallest possible height, in which the core and surface layers have disappeared. We derive simple closures of the governing equations for the three regions with insight from the numerical simulations of Silbert et al. [Phys. Rev. E64, 051302 (2001)] and the physical experiments of Pouliquen [Phys. Fluids 11, 542 (1999)]. The theory captures the range of inclination angles at which steady, fully developed flows are observed, the corresponding shape of the mean and fluctuation velocity profiles, the dependence of the flow rate on inclination, flow height, interparticle friction, and normal restitution coefficient, and the dependence of the height of basal flows on inclination.

Anomalous behavior of normal kinematic restitution in the oblique impacts of a hard sphere on an elastoplastic plate.

We observe oblique impacts of a hard aluminum oxide sphere on a thick elastoplastic polycarbonate plate by recording stroboscopic photographs of the sphere trajectory and spin. The apparent kinematic coefficient of normal restitution grows monotonically with the magnitude of the tangent of the angle of incidence, and the apparent coefficient of friction decreases with increasing normal impact velocity. Although every collision dissipates the total kinetic energy of the sphere, we observe restitution coefficients exceeding unity for the most grazing impacts. We exploit this example to confirm that, although an apparent kinematic coefficient of normal restitution below one is sufficient to guarantee dissipation of kinetic energy in any collision, this condition is not necessary for oblique impacts of spheres on a plate.