Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles

Recent work on single bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can already be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. In this work we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is enlarged, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles against surface oscillations, we conclude that the ideal liquid for violently collapsing, surface stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (>40 times the viscosity of water) will again preclude collapses.Comment: 41 pages, 21 eps and ps figures; LaTeX stylefiles replaced because the PostScript file produced at the archive had misplaced and misscaled figure

The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently rotating cylinders

A new turbulent Taylor-Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 x 10^6 with water as working fluid. With this Taylor-Couette system, the parameter space (Re_i, Re_o, {\eta}) extends to (2.0 x 10^6, {\pm}1.4 x 10^6, 0.716-0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor-Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness.Comment: 13 pages, 14 figure

Bubbly Turbulent Drag Reduction Is a Boundary Layer Effect

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to 4×105), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in the rough-wall case no smooth boundary layers can develop, the results demonstrate that bubbly drag reduction is a pure boundary layer effec

Geostrophic convective turbulence: The effect of boundary layers

Rayleigh--B\'enard (RB) convection, the flow in a fluid layer heated from below and cooled from above, is used to analyze the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotated while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier--Stokes equations for two values of the thermal forcing, i.e. $Ra=10^{10}$ and $Ra=5\cdot10^{10}$, a constant Prandtl number~$Pr=1$, and vary the Ekman number in the range $Ek=1.3\cdot10^{-7}$ to $Ek=2\cdot10^{-6}$ which satisfies both requirements of super-criticality and strong rotation. We focus on the differences between the application of no-slip vs. stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at~$Ek\approx 9\times 10^{-7}$ for~$Ra=1\times 10^{10}$ and at~$Ek\approx 3\times 10^{-7}$ for~$Ra=5\times 10^{10}$. However, the transition is gradual and it does not exactly coincide in~$Ek$ for different flow indicators. In particular, we report the characteristics of the transitions in the heat transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes.Comment: Submitted to JF

Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow

Direct numerical simulations of turbulent Taylor-Couette flow are performed up to inner cylinder Reynolds numbers of {Re_i=10^5} for a radius ratio of {\eta=r_i/r_o=0.714} between the inner and outer cylinder. With increasing {Re_i}, the flow undergoes transitions between three different regimes: (i) a flow dominated by large coherent structures, (ii) an intermediate transitional regime, and (iii) a flow with developed turbulence. In the first regime the large--scale rolls completely drive the meridional flow while in the second one the coherent structures recover only on average. The presence of a mean flow allows for the coexistence of laminar and turbulent boundary layer dynamics. In the third regime the mean flow effects fade away and the flow becomes dominated by plumes. The effect of the local driving on the azimuthal and angular velocity profiles is quantified, in particular we show when and where those profiles develop.Comment: 22 pages, submitted to Po

Logarithmic mean temperature profiles and their connection to plume emissions in turbulent Rayleigh-B\'enard convection

Two-dimensional simulations of Rayleigh-B\'enard convection at $Ra = 5\times10^{10}$ show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is logarithmic only in these regions and not in the rest of the boundary layer where it is sheared by the large scale wind and impacted by plumes. In addition, the logarithmic behavior is not visible in the horizontal average. The findings reveal that the temperature profiles are strongly connected to thermal plume emission and support a perception that parts of the boundary layer can be turbulent, while others are not. The transition to the ultimate regime, in which the boundary layers are considered to be fully turbulent, can therefore be understood as a gradual increases in fraction of the plume-emitting ('turbulent') regions of the boundary layer.Comment: 6 page

Mixed insulating and conducting thermal boundary conditions in Rayleigh-B\'enard convection

A series of direct numerical simulations of Rayleigh-B\'enard convection, the flow in a fluid layer heated from below and cooled from above, were conducted to investigate the effect of mixed insulating and conducting boundary conditions on convective flows. Rayleigh numbers between $\text{Ra}=10^7$ and $\text{Ra}=10^9$ were considered, for Prandtl numbers $\text{Pr}=1$ and $\text{Pr}=10$. The bottom plate was divided into patterns of conducting and insulating stripes. The size ratio between these stripes was fixed to unity and the total number of stripes was varied. Global quantities such as the heat transport and average bulk temperature and local quantities such as the temperature just below the insulating boundary wall were investigated. For the case with the top boundary divided into two halves, one conducting and one insulating, the heat transfer was found to be approximately two thirds of the fully conducting case. Increasing the pattern frequency increased the heat transfer which asymptotically approached the fully conducting case, even if only half of the surface is conducting. Fourier analysis of the temperature field revealed that the imprinted pattern of the plates is diffused in the thermal boundary layers, and cannot be detected in the bulk. With conducting-insulating patterns on both plates, the trends previously described were similar, however, the half-and-half division led to a heat transfer of about a half of the fully conducting case instead of two-thirds. The effect of the ratio of conducting and insulating areas was also analyzed, and it was found that even for systems with a top plate with only $25\%$ conducting surface, heat-transport of $60\%$ of the fully conducting case can be seen. Changing the 1D stripe pattern to 2D checkerboard tessellations does not result in a significantly different response of the system.Comment: Submitted to JF

Dynamic equilibrium Mechanism for Surface Nanobubble Stabilization

Recent experiments have convincingly demonstrated the existence of surface nanobubbles on submerged hydrophobic surfaces. However, classical theory dictates that small gaseous bubbles quickly dissolve because their large Laplace pressure causes a diffusive outflux of gas. Here we suggest that the bubbles are stabilized by a continuous influx of gas near the contact line, due to the gas attraction towards hydrophobic walls (Dammer & Lohse, PRL96, 206101 (2006); Zhang {\it et al.}, PRL98, 136101 (2007); Mezger {\it et al.}, J.\ Chem. Phys. 128, 244705 (2008)). This influx balances the outflux and allows for a meta-stable equilibrium, which however vanishes in thermodynamic equilibrium. Our theory predicts the equilibrium radius of the surface nanobubbles, as well as the threshold for surface nanobubble formation as a function of hydrophobicity and gas concentration.Comment: 4 pages, 3 figures. Phys. Rev. Lett. 101, in press (2008

3+2 + X: what is the most useful depolarization input for retrieving microphysical properties of non-spherical particles from lidar measurements using the spheroid model of Dubovik et al. (2006)?

The typical multiwavelength aerosol lidar data set for inversion of optical to microphysical parameters is composed of three backscatter coefficients (β) at 355, 532, and 1064 nm and two extinction coefficients (α) at 355 and 532 nm. This data combination is referred to as a 3β+2α or 3+2 data set. This set of data is sufficient for retrieving some important microphysical particle parameters if the particles have spherical shape. Here, we investigate the effect of including the particle linear depolarization ratio (δ) as a third input parameter for the inversion of lidar data. The inversion algorithm is generally not used if measurements show values of δ that exceed 0.10 at 532 nm, i.e. in the presence of non-spherical particles such as desert dust, volcanic ash, and, under special circumstances, biomass-burning smoke. We use experimental data collected with instruments that are capable of measuring δ at all three lidar wavelengths with an inversion routine that applies the spheroidal light-scattering model of Dubovik et al. (2006) with a fixed axis-ratio distribution to replicate scattering properties of non-spherical particles. The inversion gives the fraction of spheroids required to replicate the optical data as an additional output parameter. This is the first systematic test of the effect of using all theoretically possible combinations of δ taken at 355, 532, and 1064 nm as input in the lidar data inversion. We find that depolarization information of at least one wavelength already provides useful information for the inversion of optical data that have been collected in the presence of non-spherical mineral dust particles. However, any choice of δλ will give lower values of the single-scattering albedo than the traditional 3+2 data set. We find that input data sets that include δ355 give a spheroid fraction that closely resembles the dust ratio we obtain from using β532 and δ532 in a methodology applied in aerosol-type separation. The use of δ355 in data sets of two or three δλ reduces the spheroid fraction that is retrieved when using δ532 and δ1064. Use of the latter two parameters without accounting for δ355 generally leads to high spheroid fractions that we consider not trustworthy. The use of three δλ instead of two δλ, including the constraint that one of these is measured at 355 nm does not provide any advantage over using 3+2+δ355 for the observations with varying contributions of mineral dust considered here. However, additional measurements at wavelengths different from 355 nm would be desirable for application to a wider range of aerosol scenarios that may include non-spherical smoke particles, which can have values of δ355 that are indistinguishable from those found for mineral dust. We therefore conclude that – depending on measurement capability – the future standard input for inversion of lidar data taken in the presence of mineral dust particles and using the spheroid model of Dubovik et al. (2006) might be 3+2+δ355 or 3+2+δ355+δ532.Peer reviewe