The mean acoustic intensity, m, in the quiet Sun seems to increase with depth, as shown in Fig. 3. The depth dependence of m may be related to the variation of acoustic absorption with depth and the fraction of the acoustic spatiotemporal spectrum that is detected in viewing different depths. (5) The spatial resolution of constructed images decreases with depth. The time-distance relations flatten with increasing depth, so the phase gradient over the observing annulus decreases. The difference in phases used to image adjacent spatial points becomes small, and a point in space is imaged with a broad point-spread function. Another cause is that shorter-wavelength modes cannot be detected in viewing a deeper region.Finally, we mention some important questions that call for further study. What is the degree of cancellation of signals from points other than the target point in this phased detection? What are the horizontal and vertical spatial resolutions corresponding to this 'computational acoustic lens'? What is the correct interpretation of the mean intensity, m, and its apparent variation with depth? Can this method reconstruct the complex index of refraction of acoustic waves at each target point, using the phase information in addition to the intensity? Finally, could one use this method to detect active regions before they emerge, or active regions at the other side of the Sun?Ⅺ

Solids dispersed in a drying drop will migrate to the edge of the drop and form a solid ring. This phenomenon produces ringlike stains and occurs for a wide range of surfaces, solvents, and solutes. Here we show that the migration is caused by an outward flow within the drop that is driven by the loss of solvent by evaporation and geometrical constraint that the drop maintain an equilibrium droplet shape with a fixed boundary. We describe a theory that predicts the flow velocity, the rate of growth of the ring, and the distribution of solute within the drop. These predictions are compared with our experimental results.

Ring formation in an evaporating sessile drop is a hydrodynamic process in which solids dispersed in the drop are advected to the contact line. After all the liquid evaporates, a ring-shaped deposit is left on the substrate that contains almost all the solute. Here I show that the drop itself can generate one of the essential conditions for ring formation to occur: contact line pinning. Furthermore, I show that when self-induced pinning is the only source of pinning an array of patterns-that include cellular and lamellar structures, sawtooth patterns, and Sierpinski gaskets-arises from the competition between dewetting and contact line pinning.

We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wet by the drop. Frequency of vibrations ranges from 30 to 200 Hz, and above a threshold in vibration acceleration, drops experience an upward motion. We attribute this surprising motion to the deformations of the drop, as a consequence of an up/down symmetry-breaking induced by the presence of the substrate. We relate the direction of motion to contact angle measurements. This phenomenon can be used to move a drop along an arbitrary path in a plane, without special surface treatments or localized forcing. PACS numbers:A drop of liquid on an inclined substrate will slide downward due to gravity, unless the drop is pinned by contact angle hysteresis [1,2]. Since the contact angle hysteresis is reduced by vertical vibrations [3,4], one might expect that sufficiently strong shaking will always make the drop come loose and provoke it to slide. Here we report for the first time that on the contrary, sufficiently strong harmonic shaking in the vertical direction will always cause the drop to climb up the slope, regardless of system parameters.We attribute the upward force to a combination of the broken symmetry caused by the inclination of the substrate with respect to the applied acceleration and the nonlinear frictional force between the drop and the substrate. During the downward acceleration phase, the drop becomes taller and thus more compliant to lateral forcing. Hence, the maximum value of the contact angle attained on the upper side ( Fig. 1(d)) is greater than the maximum value attained on the lower side ( Fig. 1(b)), and the drop thus experiences a net upward force [5]. However, for a purely linear frictional force the net force on the drop would average to zero over one period; hence some nonlinearity in the interaction between the drop and the substrate is needed. This key issue is illustrated by a model calculation below.In our experiments a drop of a glycerol-water mixture, of volume V between 0.5 and 20 µl was deposited on a plexiglass substrate inclined to the horizontal with an angle α up to 85 o . The resulting sessile drop was between 1 and 3 mm in diameter, and pinned in the absence of shaking. The substrate was oscillated vertically using an electromagnetic shaker with acceleration up to 50g where g is the acceleration due to gravity, and frequencies between 30 Hz and 200 Hz. The acceleration was monitored with a single-axis accelerometer; the acceleration due to unwanted lateral motion did not exceed 3% of the vertical acceleration.The kinematic viscosity ν of the various mixtures * Electronic address: p.brunet@bristol.ac.uk ranged between 31 and 55 mm 2 /s. For lower viscosities the drop can break up before the onset of climbing; for higher viscosities, drops move slower and thus their dynamics is more difficult to access. The surface tension γ was equal to 0.066 N/m, the density ρ at 20• C ranged from 1190 kg/m 3 for ν= 31 mm 2 /s to 1210 kg/m 3 for ν=...

We study the impact of a drop of liquid onto a thin layer of the same liquid. We give an overview of the sequence of events that occur as the two most important dimensionless control parameters are varied. In particular, multiple cohorts of droplets can be ejected at different stages after impact due to different mechanisms. Edgerton's famous Milkdrop Coronet is only observed for a narrow range of parameters. Outside this range, the splash is either qualitatively different, or suffers from a much lower level of regularity.

No abstract

The impact of a drop onto a liquid layer produces a splash that results from the ejection and dissolution of one or more liquid sheets, which expand radially from the point of impact. In the crown splash parameter regime, secondary droplets appear at fairly regularly spaced intervals along the rim of the sheet. By performing many experiments for the same parameter values, we measure the spectrum of small-amplitude perturbations growing on the rim. We show that for a range of parameters in the crown splash regime, the generation of secondary droplets results from a Rayleigh-Plateau instability of the rim, whose shape is almost cylindrical. In our theoretical calculation, we include the time dependence of the base state. The remaining irregularity of the pattern is explained by the finite width of the Rayleigh-Plateau dispersion relation. Alternative mechanisms, such as the Rayleigh-Taylor instability, can be excluded for the experimental parameters of our study.

We observe stable holes in a vertically oscillated 0.5 cm deep aqueous suspension of cornstarch for accelerations a above 10g. Holes appear only if a finite perturbation is applied to the layer. Holes are circular and approximately 0.5 cm wide, and can persist for more than 10 5 cycles. Above a ≃ 17g the rim of the hole becomes unstable producing finger-like protrusions or hole division. At higher acceleration, the hole delocalizes, growing to cover the entire surface with erratic undulations. We find similar behavior in an aqueous suspension of glass microspheres.