Self-concentration and large-scale coherence in bacterial dynamics

Suspensions of aerobic bacteria often develop flows from the interplay of chemotaxis and buoyancy. We find in sessile drops that flows related to those in the Boycott effect of sedimentation carry bioconvective plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom. On scales much larger than a cell, concentrated regions in both geometries exhibit transient, reconstituting, high-speed jets straddled by vortex streets. A mechanism for large-scale coherence is proposed based on hydrodynamic interactions between swimming cells.     

Ultrasonic Vibration Suspends Large Pendant Drops

A stationary substrate can suspend only small pendant drops even with excellent wetting ability because of gravity. We report the suspension of large pendant water drops by a copper substrate that vibrates ultrasonically with a frequency of 22 kHz. The mass of the largest pendant drop suspended by the vibrating substrate reaches 1.1 g, which is 9 times that by the same stationary substrate. The pendant drop deforms drasticaJly and quickly at both the beginning and the end of the vibration procedure. As the vibration power increases, the contact area between the drop and substrate expands and the drop height shrinks accordingly. Theoretical analysis indicates that the Bernoulli pressure induced by ultrasonic vibration may contribute strongly to enhancing the suspensibility of pendant drops.     

Star-drops formed by periodic excitation and on an air cushion – A short review

When simply put on a solid, a liquid drop usually adopts the shape of a spherical cap or a puddle depending on its volume and on the wetting conditions. However, when the drop is subjected to a periodic field, a parametric excitation can induce a transition of shape and can break the drop’s initial axial symmetry, provided that the pinning forces at the contact-line are weak enough. Therefore, a standing wave appears at the drop interface and induces a periodic motion, with a frequency that equals half the excitation frequency. In the first part, we review the different situations where star drops can be generated from various types of periodic excitations. In the second part, we show that similar star drops can occur in a much less intuitive fashion when the drop is put on an air cushion, where no periodic motion is imposed a priori. Preliminary experiments as well as theoretical clues for a hydrodynamic interpretation, suggest that the periodic vibration is due to an inertial instability in the air layer below the drop.     

Vibration-induced climbing of drops

We report an experimental study of liquid drops moving against gravity, when placed on a vertically vibrating inclined plate, which is partially wetted by the drop. The 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 or 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.     

Rain induced depolarization from 1 GHz to 300 GHz in a tropical environment

The rain induced depolarization in a tropical environment has been studied using a tropical raindrop size distribution developed by Ajayi and Olsen (A-O). The differential attenuation, differential phase shift and cross polarization discrimination, XPD, were computed over a frequency range of 1GHz to 300GHz for spheroidal drops and up to 33GHz for Pruppacher-Pitter drops. The variations of XPD with frequency, rainfall rate and copolar attenuation, CPA, were investigated. A mathematical relationship was established between the XPD and the CPA, canting angle and frequency of propagation from 5GHz to 300 GHz for spheroidal drops and up to 33 GHz for Pruppacher-Pitter drops. The results obtained using the A-O drop size distribution have been compared with those assuming the Laws and Parsons (L-P) distribution. The Pruppacher-Pitter drop shape has been found to give rise to higher XPD, especially at low CPA and high frequencies.     

Parametric resonance in acoustically levitated water drops

Liquid drops can be suspended in air with acoustic levitation method. When the sound pressure is periodically modulated, the levitated drop is usually forced into an axisymmetric oscillation. However, a transition from axisymmetric oscillation into sectorial oscillation occurs when the modulation frequency approaches some specific values. The frequency of the sectorial oscillation is almost exactly half of the modulation frequency. It is demonstrated that this transition is induced by the parametric resonance of levitated drop. The natural frequency of sectorial oscillation is found to decrease with the increase of drop distortion extent.     

Coalescence of spreading droplets on a wettable substrate

We investigate experimentally and theoretically the coalescence dynamics of two spreading droplets on a highly wettable substrate. Upon contact, surface tension drives a rapid motion perpendicular to the line of centers that joins the drops and lowers the total surface area. We find that the width of the growing meniscus bridge between the two droplets exhibits power-law behavior, growing at early times as t1/2. Moreover, the growth rate is highly sensitive to both the radii and heights of the droplets at contact, scaling as ho3/2/Ro. This size dependence differs significantly from the behavior of freely suspended droplets, in which the coalescence growth rate depends only weakly on the droplet size. We demonstrate that the scaling behavior is consistent with a model in which the growth of the meniscus bridge is governed by the viscously hindered flux from the droplets.     

Chaotic dynamics of driven flux drops: a superconducting "dripping faucet"

When a current is applied to a type-I superconducting strip containing a narrow channel across its width, magnetic flux spots nucleate at the edge and are then driven along the channel by the current. These flux "drops" are reminiscent of water drops dripping from a faucet, a model system for studying low-dimensional chaos. We use a novel high-bandwidth Hall probe to detect in real time the motion of individual flux spots moving along the channel. Analyzing the time series consisting of the intervals between successive flux drops, we find distinct regions of chaotic behavior characterized by positive Lyapunov exponents, indicating that there is a close analogy between the dynamics of the superconducting and water drop systems.     

声悬浮液滴的表面毛细波及八阶扇谐振荡

采用声悬浮方法研究了自由液滴表面的毛细波形成机理,并利用主动调制声场技术激发了液滴的八阶扇谐振荡.实验结果表明,当声场调制频率接近液滴本征频率的两倍时,液滴将由轴对称受迫振荡向非轴对称扇谐振荡模态转变.实验与理论分析证实,参数共振是毛细波与扇谐振荡的形成原因.扇谐振荡的本征频率随液滴赤道半径的增大而减小,可通过修正的Rayleigh方程来描述. 关键词： 声悬浮 液滴 毛细波 扇谐振荡     

Bound states of 3He at the edge of a 4He drop on a cesium surface

We show that small amounts of 3He atoms, added to a 4He drop deposited on a flat cesium surface at zero temperature, populate bound states localized at the contact line. These edge states show up for drops large enough to develop well defined surface and bulk regions together with a contact line, and they are structurally different from the well-known Andreev states that appear at the free surface and at the liquid-solid interface of films. We illustrate the one-body density of 3He in a drop with 1000 4He atoms, and show that for a sufficiently large number of impurities the density profiles spread beyond the edge, coating both the curved drop surface and its flat base and eventually isolating it from the substrate.     

倾斜均质表面上等径水滴聚合过程的可视化实验

对倾斜均匀表面上等直径水滴的聚合过程及特性进行了可视化实验研究,获得了水滴直径和表面倾角等参数对液滴聚合过程中液滴液桥半径、接触角和接触线变化特性的影响,分析了水滴聚合对其运动的影响.实验结果表明:表面倾角越大,下滑的临界半径越小;液滴的直径越大,液滴聚合后越容易下滑;液滴聚合可以加快液滴的运动,使下滑临界半径减小.     

倾斜均质表面上非等径液滴的聚合特性

对倾斜均匀表面上非等径液滴的聚合过程及特性进行了可视化实验研究,获得了液滴半径和表面倾角等参数对液滴聚合过程中液滴液桥半径、接触角和接触线变化特性的影响规律,进一步说明了倾斜表面上液滴聚合可以加快液滴的运动.     

Evaporation of Charged Drops

A model of evaporation of a multiply charged liquid drop is developed. The model self-consistently takes into account the main factors influencing the charged drop evaporation, including effects of the drop surface curvature and charge on the saturated vapor pressure, repeated fragmentation of drops during evaporation, and the capability of drops having a unit charge and a certain stabilization radius not to evaporate even in an unsaturated vapor medium. Analytical dependences are derived that can be used to calculate an integral lifetime of a charged drop with allowance for its fragmentation into smaller drops. Our estimates demonstrate that the evaporation time of charged drops is much smaller than that of uncharged drops.     

Spreading of liquid drops on Agar gels

We study the spreading of pure water drops or water drops with surfactine (surfactant produced by bacteria Bacillus Subtilis) on gels (Agar/Water gel). We find that, surprisingly, the drops do not spread indefinitely, but remain in a state of partial wetting. Eventually the liquid diffuses into the gel on a time scale short with respect to evaporation times. The drops containing surfactant show a complex dynamics: at first the spreading velocity decreases, until the front stops and starts receding at about constant velocity. Concurrently, a second front detaches from the rim of the drop if the agar concentration is sufficiently low, and continues to move outwards.     

Motion of a drop driven by substrate vibrations

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.     

水平均质表面上液滴聚合过程的可视化实验研究

对水平均匀表面上液滴的聚合过程及特性进行了可视化实验研究,获得了液滴半径和液滴物性等参数对液滴聚合过程中液滴液桥半径和接触角变化特性的影响规律。实验结果表明:液滴聚合中液桥半径和接触角都呈衰减振荡变化; 聚合前液滴半径越小,液桥半径振荡频率越大,振幅越小,振荡时间越短;液滴的粘度越大,液桥半径的振荡频率越小, 振幅越小,振荡时间越短;液滴聚合前的接触角明显大于聚合液滴静止后的接触角,其差值与固体界面状况和气、固、液物性相关。     

The wetting angle of very small and large drops

On the basis of Born-Green-Yvon integral equations for the density distribution functions, an approximate integral equation is established for the profile of the surface of the drop. Numerical solutions and analytical solutions for limiting cases are obtained for this profile. Equations relating the angle at the leading edge and in its vicinity to parameters characterizing the interaction forces between the molecules of the liquid and between those of the liquid and solid are derived for large and for very small drops on a horizontal solid surface. One concludes that there is a rapid spatial variation of shape near the leading edge, that for large drops the measured macroscopic wetting angle is reached at a distance of about 20 to 40 Å from the leading edge, and that for very small drops the wetting angle is weakly size dependent. A condition for drop stability is established, which if not satisfied, the liquid will spread over the surface of the solid.     

Effect of CO2 shielding gas on metal droplet formationin arc welding

We have developed a unified arc electrode model that enables us to make predictions of the time development of molten drops from the welding wire in gas metal arc welding. The wire is taken as the positive electrode, and the effects of surface tension, magnetic pinch forces, and convection within the drop are taken into account to predict drop detachment for any given arc current. For pure argon, we have previously predicted the sharp transition that is observed experimentally at about 300 A between globular transfer at low current, when drop diameters are larger than the wire diameter, and spray transfer, for currents above 300 A, when drop diameters are smaller than the wire diameter. In this paper, we predict that addition of 25% of CO₂ to the argon leads to an increase in the transition current to more than 325 A, also in agreement with published experimental results. For pure CO₂, we find a significantly different drop behavior due to the more constricted arc. Both small and large drops are produced, with many very small drops being produced successively between each large drop     

Debye's relaxation frequency: A poor man's approach

We present a simple approach to introduce Debye's relaxation frequency. Our model is based on a kinetic equation at the electrodes, describing the time variation of the ionic charge pushed at the limiting surfaces by the effective electric field. In a first approximation the surface region where the ions are confined is assumed of negligible thickness. We show that this approximation allows to define a frequency at which the effective resistance of the sample begins to decrease. This frequency coincides with Debye's relaxation frequency. An equivalent electric circuit describing the frequency dependence of the effective impedance of the cell, valid in this approximation, is presented. In a second approximation we discuss the influence of a perfectly dielectric surface layer on the relaxation frequency, where the electrolytic cell is described by means of a Maxwell-Wagner system. The equivalent electrical circuit is discussed.     

Lateral vibration of a water drop and its motion on a vibrating surface

The resonant modes of sessile water drops on a hydrophobic substrate subjected to a small-amplitude lateral vibration are investigated using computational fluid dynamic (CFD) modeling. As the substrate is vibrated laterally, its momentum diffuses within the Stokes layer of the drop. Above the Stokes layer, the competition between the inertial and Laplace forces causes the formation of capillary waves on the surface of the drop. In the first part of this paper, the resonant states of water drops are illustrated by investigating the velocity profile and the hydrostatic force using a 3d simulation of the Navier-Stokes equation. The simulation also allows an estimation of the contact angle variation on both sides of the drop. In the second part of the paper, we investigate the effect of vibration on a water drop in contact with a vertical plate. Here, as the plate vibrates parallel to gravity, the contact line oscillates. Each oscillation is, however, rectified by hysteresis, thus inducing a ratcheting motion to the water droplet vertically downward. Maximum rectification occurs at the resonant states of the drop. A comparison between the frequency-dependent motion of these drops and the variation of contact angles on their both sides is made. The paper ends with a discussion on the movements of the drops on a horizontal hydrophobic surface subjected to an asymmetric vibration.