Statistics of turbulent fluctuations in counter-rotating Taylor-Couette flows

The statistics of velocity fluctuations of turbulent Taylor-Couette flow are examined. The rotation rate of the inner and outer cylinder are varied while keeping the Taylor number fixed to $1.49 \times 10^{12}$ ($\mathcal{O}(\text{Re})=10^6$). The azimuthal velocity component of the flow is measured using laser Doppler anemometry (LDA). For each experiment $5\times10^6$ datapoints are acquired and carefully analysed. Using extended self-similarity (ESS) \cite{ben93b} the longitudinal structure function exponents are extracted, and are found to weakly depend on the ratio of the rotation rates. For the case where only the inner cylinder rotates the results are in good agreement with results measured by Lewis and Swinney \cite{lew99} using hot-film anemometry. The power spectra shows clear -5/3 scaling for the intermediate angular velocity ratios $-\omega_o/\omega_i \in \{0.6, 0.8, 1.0\}$, roughly -5/3 scaling for $-\omega_o/\omega_i \in \{0.2, 0.3, 0.4, 2.0\}$, and no clear scaling law can be found for $-\omega_0/\omega_i = 0$ (inner cylinder rotation only); the local scaling exponent of the spectra has a strong frequency dependence. We relate these observations to the shape of the probability density function of the azimuthal velocity and the presence of a neutral line

Turbulence strength in ultimate Taylor-Couette turbulence

We provide experimental measurements for the effective scaling of the Taylor-Reynolds number within the bulk $\text{Re}_{\lambda,\text{bulk}}$, based on local flow quantities as a function of the driving strength (expressed as the Taylor number Ta), in the ultimate regime of Taylor-Couette flow. The data are obtained through flow velocity field measurements using Particle Image Velocimetry (PIV). We estimate the value of the local dissipation rate $\epsilon(r)$ using the scaling of the second order velocity structure functions in the longitudinal and transverse direction within the inertial range---without invoking Taylor's hypothesis. We find an effective scaling of $\epsilon_{\text{bulk}} /(\nu^{3}d^{-4})\sim \text{Ta}^{1.40}$, (corresponding to $\text{Nu}_{\omega,\text{bulk}} \sim \text{Ta}^{0.40}$ for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements ($\text{Nu}_{\omega} \sim \text{Ta}^{0.40}$) and Direct Numerical Simulations ($\text{Nu}_{\omega} \sim \text{Ta}^{0.38}$). The resulting Kolmogorov length scale is then found to scale as $\eta_{\text{bulk}}/d \sim \text{Ta}^{-0.35}$ and the turbulence intensity as $I_{\theta,\text{bulk}} \sim \text{Ta}^{-0.061}$. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor-Reynolds number effectively scales as Re$_{\lambda,\text{bulk}}\sim \text{Ta}^{0.18}$ in the present parameter regime of $4.0 \times 10^8 < \text{Ta} < 9.0 \times 10^{10}$.Comment: 15 pages, 8 figures, J. Fluid Mech. (In press

Different intermittency for longitudinal and transversal turbulent fluctuations

Scaling exponents of the longitudinal and transversal velocity structure functions in numerical Navier-Stokes turbulence simulations with Taylor-Reynolds numbers up to \rel = 110 are determined by the extended self similarity method. We find significant differences in the degree of intermittency: For the sixth moments the scaling corrections to the classical Kolmogorov expectations are $\delta\xi_6^L= -0.21 \pm 0.01$ and \dx_6^T= -0.43 \pm 0.01, respectively, independent of \rel. Also the generalized extended self similarity exponents \rho_{p,q} = \dx_p/\dx_q differ significantly for the longitudinal and transversal structure functions. Within the She-Leveque model this means that longitudinal and transversal fluctuations obey different types of hierarchies of the moments. Moreover, the She-Leveque model hierarchy parameters $\beta^L$ and $\beta^T$ show small but significant dependences on the order of the moment.Comment: 20 pages, 10 eps-figures, to appear in Physics of Fluids, December 199

Avalanche of particles in evaporating coffee drops

The pioneering work of Deegan et al. [Nature 389, (1997)] showed how a drying sessile droplet suspension of particles presents a maximum evaporating flux at its contact line which drags liquid and particles creating the well known coffee stain ring. In this Fluid Dynamics Video, measurements using micro Particle Image Velocimetry and Particle Tracking clearly show an avalanche of particles being dragged in the last moments, for vanishing contact angles and droplet height. This explains the different characteristic packing of the particles in the layers of the ring: the outer one resembles a crystalline array, while the inner one looks more like a jammed granular fluid. Using the basic hydrodynamic model used by Deegan et al. [Phys. Rev. E 62, (2000)] it will be shown how the liquid radial velocity diverges as the droplet life comes to an end, yielding a good comparison with the experimental data.Comment: This entry contains a Fluid Dynamics Video candidate for the Gallery of Fluid Motion 2011 and a brief article with informatio

Order-to-disorder transition in ring-shaped colloidal stains

A colloidal dispersion droplet evaporating from a surface, such as a drying coffee drop, leaves a distinct ring-shaped stain. Although this mechanism is frequently used for particle self-assembly, the conditions for crystallization have remained unclear. Our experiments with monodisperse colloidal particles reveal a structural transition in the stain, from ordered crystals to disordered packings. We show that this sharp transition originates from a temporal singularity of the flow velocity inside the evaporating droplet at the end of its life. When the deposition speed is low, particles have time to arrange by Brownian motion, while at the end, high-speed particles are jammed into a disordered phase.Comment: accepted for PR

R116C mutation of cationic trypsinogen in a Turkish family with recurrent pancreatitis illustrates genetic microheterogeneity of hereditary pancreatitis

Hereditary pancreatitis is due to heterozygosity for gain-of-function mutations in the cationic trypsinogen gene which result in increased levels of active trypsin within pancreatic acinar cells and autodigestion of the pancreas. The number of disease-causing defects is generally considered to be low. To gain further insight into the molecular basis of this disorder, DNA sequence analysis of all five exons was performed in 109 unrelated patients with idiopathic chronic pancreatitis in order to determine the variability of the underlying mutations. Two German females and one German male were carriers of the most common N291 and R122H mutations (trypsinogen numbering system). In a Turkish proband, an arginine (CGT) to cysteine (TGT) substitution at amino acid position 116 was identified. Family screening demonstrated that the patient had inherited the mutation from his asymptomatic father and that he had transmitted it to both of his children, his daughter being symptomatic since the age of 3 years. In addition, a German male was found to be a heterozygote for a D100H (GAC-->CAC) amino acid replacement. Our data provide evidence for genetic heterogeneity of hereditary pancreatitis. The growing number of cationic trypsinogen mutations is expected to change current mutation screening practices for this disease

Superstability of Surface Nanobubbles

Shock wave induced cavitation experiments and atomic force microscopy measurements of flat polyamide and hydrophobized silicon surfaces immersed in water are performed. It is shown that surface nanobubbles, present on these surfaces, do not act as nucleation sites for cavitation bubbles, in contrast to the expectation. This implies that surface nanobubbles are not just stable under ambient conditions but also under enormous reduction of the liquid pressure down to &#8722;6MPa. We denote this feature as superstability.Comment: 5 pages, 2 figure

Periodically driven Taylor-Couette turbulence

We study periodically driven Taylor-Couette turbulence, i.e. the flow confined between two concentric, independently rotating cylinders. Here, the inner cylinder is driven sinusoidally while the outer cylinder is kept at rest (time-averaged Reynolds number is $Re_i = 5 \times 10^5$). Using particle image velocimetry (PIV), we measure the velocity over a wide range of modulation periods, corresponding to a change in Womersley number in the range $15 \leq Wo \leq 114$. To understand how the flow responds to a given modulation, we calculate the phase delay and amplitude response of the azimuthal velocity. In agreement with earlier theoretical and numerical work, we find that for large modulation periods the system follows the given modulation of the driving, i.e. the system behaves quasi-stationary. For smaller modulation periods, the flow cannot follow the modulation, and the flow velocity responds with a phase delay and a smaller amplitude response to the given modulation. If we compare our results with numerical and theoretical results for the laminar case, we find that the scalings of the phase delay and the amplitude response are similar. However, the local response in the bulk of the flow is independent of the distance to the modulated boundary. Apparently, the turbulent mixing is strong enough to prevent the flow from having radius-dependent responses to the given modulation.Comment: 12 pages, 6 figure