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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. [ABSTRACT FROM AUTHOR]

We create nearly perfect centimetric spheres of water by splitting a cavity consisting of two metal hemispheres coated with a hydrophobic paint and under-filled with liquid, while releasing the apparatus in free-fall. A high-speed camera captures how water spread on hydrophobic aluminum and polycarbonate plates perforated with cylindrical capillaries. We compare observations at the ZARM drop tower in Bremen with Lattice-Boltzmann numerical simulations of Frank, Perré and Li for the inertial phase of imbibition.

A fiber-optic sensor that measures the particle volume fraction in dense suspensions is calibrated against a quantitative capacitance probe. For homogeneous, dense, random suspensions of smooth, monodisperse, transparent dielectric spheres, the calibration is simulated by using a ray-tracing Monte Carlo algorithm that predicts systematic uncertainties of the sensor's output, the extent of its measurement volume, and the effects of changing its optical properties. The simulation shows that the output and accuracy of the sensor increase with a decreasing sphere diameter and with an increasing N.A. of the fiber. The output also increases when the ratio of the indices of refraction of the sphere and the suspending medium is increased. For small particles the measurement volume scales as the average interparticle distance.

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. [ABSTRACT FROM AUTHOR]

We consider moderately dense bounded shear flows of agitated homogeneous inelastic frictionless solid spheres colliding in a gas between two parallel bumpy walls at finite particle Reynolds numbers, volume fractions between 0.1 and 0.4, and Stokes numbers large enough for collisions to determine the velocity distribution of the spheres. We adopt a continuum model in which constitutive relations and boundary conditions for the granular phase are derived from kinetic theory, and in which the gas contributes a viscous dissipation term to the fluctuation energy of the grains. We compare its predictions to recent lattice-Boltzmann (LB) simulations. The theory underscores the role played by the walls in the balances of momentum and fluctuation energy. When particle inertia is large, the solid volume fraction is nearly uniform, thus allowing us to treat the rheology using unbounded flow theory with an effective shear rate, while predicting slip velocities at the walls. When particle inertia decreases or fluid inertia increases, the solid volume fraction becomes increasingly heterogeneous. In this case, the theory captures the profiles of volume fraction, mean and fluctuation velocities between the walls. Comparisons with LB simulations allow us to delimit the range of parameters within which the theory is applicable. [ABSTRACT FROM AUTHOR]

We outline an algorithm to extract the mean and fluctuation velocities of identical spheres colliding in microgravity from a sequence of digital images. We analyze four kinds of intrinsic errors. The first two artificially reduce the apparent fluctuation velocity. They derive from the inability of the algorithm to track indistinguishable spheres moving with excessive speed, and from invisible collisions occurring between consecutive frames. The third is due to the finite pixel size. The resulting uncertainty in the position of the spheres increases the measured fluctuation velocity. The last arises from the partitioning of the flow domain in strips to calculate velocity profiles. While this last kind of error can always be reduced by increasing the number of images acquired, the first three cannot be made arbitrarily small without improving pixel resolution. Using microgravity experiments and numerical simulations of a shear flow, we illustrate insidious distortions of the mean and fluctuation velocity profiles that originate with the unavoidable errors that we have discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]