ALBERT

Description: The collisional dynamics of equal-sized water and normal-alkane droplets, in the 150 μm radius range, have been experimentally studied for situations involving 0(1) droplet Weber numbers and head-on to grazing impact parameters. Results show that in the parametric range investigated the behaviour of hydrocarbon droplets is significantly more complex than that of water droplets. For head-on collisions, while permanent coalescence always results for water droplets, the outcome is quite nonmonotonic for the hydrocarbon droplets in that, with increasing droplet Weber number, the collision can result in permanent coalescence, bouncing, permanent coalescence again, and coalescence followed by separation with or without production of satellite droplets. Similar complexities exist for off-centre collisions. Phenomenological explanations are offered for these observations based on the material properties of the fluids, the relative influences of the normal and shearing aspects of the collision, and the nature and extent of energy dissipation due to droplet deformation during collision. © 1992, Cambridge University Press. All rights reserved.

Description: A vertically vibrating liquid layer produces liquid ligaments that disintegrate to form a spray with drops of a controllable size. Previous experimental investigations of ultrasonic atomisation have shown that when such a spray forms, there exists a predominant surface-wave mode from which drops are generated with a mean diameter that follows Lang's equation. In this paper, we determined this predominant surface-wave mode physically and, by utilising the coupled level-set and volume-of-fluid method, we numerically studied the threshold condition for spray formation based on a cell model of the predominant surface wavelength that excludes the effects of the container walls. We defined a condition whereby the broken drop holds a zero area-averaged vertical velocity in the laboratory reference frame as the criterion for the formation of a spray. The results of our calculations indicated that the onset of a spray occurs in the subharmonic unstable region for a threshold dimensionless forcing strength βc = (ρlΔ03Ω2)/σ ∼ O(1), where ρl and σ denote the liquid density and surface tension coefficient, respectively, Δ0 is the forcing displacement amplitude and Ω is the forcing angular frequency. Spray formation due to the Faraday instability can be considered as a process whereby the liquid layer absorbs energy from the inertial force, and releases it by producing drops that leave the surface of the liquid layer. We demonstrated that for a deep liquid layer, the threshold condition for the formation of a spray is determined only by the forcing strength, and is independent of the initial conditions of the liquid surface. © Cambridge University Press 2014.

Description: A laminar water jet issuing at high speed from a short circular nozzle into air exhibits various instability features at different distances from the nozzle exit. Near the exit, the effects of gaseous friction and pressure are relatively weak. Deformation of the jet surface in this region is mainly due to the instability of a thin liquid shear layer flow, which relaxes from the velocity profile produced by the nozzle wall. In this paper, a model for this type of instability based on linear stability analysis is investigated to describe the process initiating the formation of liquid ligaments disintegrating into fine droplets near the nozzle exit. The modelling comprises identifying unstable waves excitable in the liquid shear layer and exploring a self-destabilizing mechanism by which unstable waves responsible for the formation of liquid ligaments are naturally reproduced from the upstream-propagating capillary waves produced by the growth of the unstable waves themselves. An expression for the location of ligament formation onset is derived that can be compared with experiments. The model also explains changes in jet instability features away from the nozzle exit and for very short nozzles.

Description: It is well known that water slowly issued vertically downward exhibits a hysteresis phenomenon. A jetting-to-dripping transition appearing upon a stepwise decrease in jet issue speed was used to identify the origin of the Plateau-Rayleigh unstable wave elements which disintegrate the jetting liquid. In the present laboratory experiment using a stainless steel nozzle of inner radius 1 mm and length 30 mm, the transition occurred at a dimensionless jet issue speed of 0.8, where and respectively denote the density and surface tension coefficient of the liquid issued at the speed U from the nozzle of radius a-0. The jet length gradually shortened with an oscillation of considerably large amplitude and period. High-speed camera images show that this oscillation is caused by tip contraction capillary wave (TCCW) elements which are elongated by the gravitationally accelerating jet flow and become Plateau-Rayleigh unstable wave elements. The jet length increases while the jet tip experiences end-pinching and radiates TCCW elements upstream. Only those TCCW elements destabilized at appropriate locations can grow sufficiently to shorten the jet. Since the unstable wave elements produced nearer the nozzle exit have much smaller amplitude at the jet tip, the end-pinching becomes effective. Thus, these processes are repeatable and constitute a self-destabilizing loop. The observed jetting-to-dripping transition has nothing to do with the random nozzle disturbances which were believed to be the origin of the Plateau-Rayleigh unstable wave in conventional instability theories. It is also different from the feature conjectured from current absolute/convective instability analysis. The underling physics of the self-destabilizing loop are explored in detail by numerical simulations based on a one-dimensional model. © 2014 Cambridge University Press.

Description: A one-dimensional global mode analysis is conducted for low-speed water jets emanating from a circular orifice in microgravity, in which the observed spontaneous convective instability causes almost periodic jet disintegrations at a fixed location for each jet-issue speed that exceeds a certain threshold. The inviscid spatial linear stability analysis identifies four wave modes excitable at the frequency: the Plateau-Rayleigh (PR) unstable wave, its complex conjugate and two neutral waves which may transfer energy upstream. Their linear combination satisfying the orifice exit condition may describe the synchronised reproduction of a PR unstable wave from each neutral wave at the orifice exit. On the other hand, a weakly nonlinear analysis shows that the growth of the nonlinear PR unstable wave produces the two neutral waves near the orifice. Thus, the same PR unstable wave can be reproduced on a newly issued liquid surface owing to the neutral waves produced by its own nonlinear growth. This self-destabilising loop, dominantly operating for the most unstable PR wave, determines the initial PR unstable wave amplitude and, consequently, the breakup length as a function of jet-issue speed. The predicted initial amplitude of the PR unstable wave is in reasonably good agreement with the value calculated from the average breakup length measured in our microgravity experiments. It is found that that the loop consists mainly of the downstream-and upstream-moving neutral waves at relatively high and low jet speeds, respectively. The stability of the self-destabilising loop is also discussed. © 2016 Cambridge University Press.

Description: Jeffery’s solution in bi-polar co-ordinates of the two-dimensional Stokes equations cannot be applied to the low-Reynolds-number flow past two parallel circular cylinders because of severe mathematical difficulties. These difficulties can be overcome by considering the flow field far from the cylinders and then modifying the solution near the cylinders so that it becomes the inner expansion for an application of the method of matched asymptotic expansions. After the calculation of the drag, lift and moment coefficients of two adjacent equal circular cylinders to 0(1) in the Reynolds number R, the analysis is extended to incorporate partially the effects of fluid inertia of order R. The results show fairly good agreement with Taneda’s experimental data. © 1982, Cambridge University Press. All rights reserved.

Description: A matched-asymptotic analysis has been carried out for an axisymmetric convection cell in the case of stress-free boundaries. This problem differs from that of two-dimensional convection rolls mainly through the special role played by the central plume. The radius, of order e, of the latter depends on the Rayleigh number R through the relationship ε4(— In ε) = R-23, The plume velocity is independent of height at lowest order and its magnitude exceeds by a factor (— In ε)12the strength, of order R23of the core flow. As a result of these properties the central plume is governed by advection, in contrast to the perimeter plume which is affected by conduction as well. This asymmetry is reflected in the different thickness of the horizontal thermal boundary layers and gives rise to the deviation of the core temperature from the mean value of the top and bottom temperatures. This deviation is positive (negative) for the case of a falling (rising) central plume. While the core flow is driven mainly by the perimeter plume the fraction of the heat flux carried by the central plume is always above three-quarters and increases as the radius-to-height-ratio A decreases. © 1989, Cambridge University Press. All rights reserved.

Description: The natural-convection boundary-layer flow over a semi-infinite heated plate of arbitrary inclination is studied by first identifying a set of combined boundary-layer variables and then casting the governing equations into a universal form. The generalized problem yields the existing similarity solutions for the limiting cases of horizontal and vertical plates, and describes the gradual transition of the flow pattern between these two limits at distances from the leading edge which depend on the inclination angle. Near the leading edge the buoyancy force acting normal to the plate causes an ‘impulsive5 driving force to the fluid motion along the plate, while the ‘regular’ driving force exerted by the tangential buoyancy force becomes dominating downstream. Both the exact and the locally-similar solutions are obtained and are found to agree well with each other. © 1990, Cambridge University Press. All rights reserved.

Description: For detecting life from reflection spectra on extrasolar planets, trace of photosynthesis is one of the indicators. However, it is not yet clear what kind of radiation environments is acceptable for photosynthesis. Light absorption in photosystems on the Earth occurs using limited photosynthetic pigments such as chlorophylls (Chls) and bacteriochlorophylls (BChls). Efficiencies of light absorption for the pigments were evaluated by calculating the specific molecular absorption spectra at the high accuracy-quantum mechanical level. We used realistic stellar radiation spectra such as F, G, K and M-type stars to investigate the efficiencies. We found that the efficiencies are increased with the temperature of stars, from M to F star. Photosynthetic pigments have two types of absorption bands, the Qy and Soret. In higher temperature stars like F star, contributions from the Soret region of the pigments are dominant for the efficiency. On the other hand, in lower temperature stars like M stars, the Qy band is crucial. Therefore, differences on the absorption intensity and the wavelength between the Qy and Soret band are the most important to characterize the photosynthetic pigments. Among photosynthetic pigments, Chls tend to be efficient in higher temperature stars, while BChls are efficient for M stars. Blueward of the 4000 Å break, the efficiencies of BChls are smaller than Chls in the higher temperature stars.