By means of numerical simulations, using a computational fluid dynamics software together with an optical ray tracing analysis platform, we show that we can tune various optical aberrations by electrically manipulating the shape of liquid lenses using one hundred individually addressable electrodes. To demonstrate the flexibility of our design, we define electrode patterns based on specific Zernike modes and show that aspherical, cylindrical and decentered shapes of liquid lenses can be produced. Using different voltages, we evaluate the tuning range of spherical aberration (Z11), astigmatism (Z5 and Z6) and coma (Z7), while a hydrostatic pressure is applied to control the average curvature of a microlens with a diameter of 1mm. Upon activating all electrodes simultaneously spherical aberrations of 0.15 waves at a pressure of 30Pa can be suppressed almost completely for the highest voltages applied. For astigmatic and comatic patterns, the values of Z5, Z6 and Z7 increase monotonically with the voltage reaching values up to 0.06, 0.06 and 0.2 waves, respectively. Spot diagrams, wavefront maps and modulation transfer function are reported to quantify the optical performance of each lens. Crosstalk and independence of tunability are discussed in the context of possible applications of the approach for general wavefront shaping.

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This paper presents an experimental and numerical investigation of solid–liquid fluidized beds consisting of bonded spheres in very narrow tubes, i.e., when the ratio between the tube and grain diameters is small. In narrow beds, high confinement effects have proved to induce crystallization, jamming, and different patterns, which can be intensified or modified if some grains are bonded together. In order to investigate that, we produced duos and trios of bonded aluminum spheres with a diameter of 4.8 mm and formed beds consisting either of 150–300 duos or 100–200 trios in a 25.4 mm-ID pipe, which were submitted to water velocities above those necessary for fluidization. For the experiments, we filmed the bed with high-speed and conventional cameras and processed the images, obtaining measurements at both the bed and grain scales. For the numerical part, we computed the bed evolution for the same conditions with a computational fluid dynamics–discrete element method code. Our results show distinct motions for individual duos and trios and different structures within the bed. We also found that jamming may occur suddenly for trios, where even the microscopic motion (fluctuation at the grain scale) stops, calling into question the fluidization conditions for those cases.

We propose a new design for tuning the astigmatism of liquid micro-lenses using electric field and hydrostatic pressure as control parameters. We explore the feasibility and operating range of the lens with a self-consistent numerical calculation of the electric field distribution and the shape of the two-phase interface. Equilibrium shapes, including surface profiles parallel and perpendicular to a stripe electrode, are extracted to determine the astigmatism. The wavefronts are decomposed into Zernike polynomials under zero defocus conditions using a commercial ray-tracing software. We observe that the global curvature of the lens is primarily controlled by the hydrostatic pressure, while asphericity and astigmatism are controlled by the electric field. For optimized electrode geometries and simultaneous control of pressure and electric fields the astigmatism can be tuned from Z6 = 0…0.38 μm with minor changes in the focal length.

From small seeds falling from trees to asteroids colliding with planets and moons, the impact of projectiles onto granular targets occurs in nature at different scales. In this paper, we investigate open questions in the mechanics of granular cratering, in particular the forces acting on the projectile, and the roles of granular packing, grain-grain friction and projectile spin. For that, we carried out DEM (discrete element method) computations of the impact of solid projectiles on a cohesionless granular medium, where we varied the projectile and grain properties (diameter, density, friction and packing fraction) for different available energies (within relatively small values). We found that a denser region forms below the projectile, pushing it back and causing its rebound by the end of its motion, and that solid friction affects considerably the crater morphology.Besides, we show that the penetration length increases with the initial spin of the projectile, and that differences in initial packing fractions can engender the diversity of scaling laws found in the literature. Finally, we propose an ad hoc scaling that collapsed our data for the penetration length and can perhaps unify existing correlations. Our results provide new insights into the formation of craters in granular matter.