Measurement accuracy of a mono-fiber optical probe in a bubbly flow

The measurement accuracy of a mono-fiber optical probe is studied experimentally using isolated bubbles rising freely in a still liquid. The dwell time of the probe tip within the gas phase, which is obtained from both the optical probe signal and high-speed visualization, is compared with the value expected for a non-perturbed bubble. The difference originates mainly from the intrusive nature of the optical probe, which modifies the bubble behavior when it comes into contact with the probe tip. This interaction increases the dwell time if the bubble is pierced by the probe near its pole, and shortens it for piercing near the equator. The mean dwell time, obtained by averaging for various piercing locations, is shortened and the local void fraction indicated by the probe is thus underestimated. It is shown that the void fraction error can be correlated with a modified Weber number, and this correlation is helpful for sensor selection and for uncertainty estimate. In addition, the distribution of gas dwell time usually differs from the response expected for an ideal probe. This deviation results from the dependence of the dwell time error on the piercing location. The dwell time distribution can be used to infer the dependence of the dwell time on the piercing location. Finally, the deformation of long fibers during the bubble-probe interaction significantly increases the measurement error. Observed results are consistent with data of Andreotti (2009), which were measured in an airlift flow, suggesting that present results are applicable also to the case of moving liquid. Conclusions of this study could be applied also to conductivity probes or more generally to the interaction of a bubble with any kind of thin, intrusive sensor or fiber.     

A moment method for splashing and evaporation processes of polydisperse sprays

A new moment method for the modelling of polydisperse sprays is proposed that simultaneously takes into account the dispersion in droplet size and droplet velocity. For the derivation of this Eulerian method the kinetic spray equation is used which constitutes a partial differential equation for the probability density function of droplets. To reduce the complex kinetic spray equation to a form that can be managed with the available numerical procedures, moment transforms with respect to the droplet velocity and the droplet size are conducted. The resulting moment equations are closed by choosing an approximate probability density function which applies to polydisperse sprays. The method is successfully tested for configurations in which a polydisperse spray is either splashed, evaporated or effected by a Stokes drag force. The tests are organised in such a way that crossing of two spray distributions is always included. The new method is able to capture the polydisperse nature of sprays as well as the bi-(or multi-) modal character of the droplet velocity distribution function, for example, when droplets cross each other.     

Sobolev Periodic Solutions of Nonlinear Wave Equations in Higher Spatial Dimensions

We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C ^k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash–Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large “clusters of small divisors”.     

Flow-induced polymer degradation probed by a high throughput microfluidic set-up

A complex fluid submitted to strong flows can endure irreversible changes in its structure. This is the case for long chain polymer additives that are commonly used as viscosity enhancers in industry, notably for oil recovery. These polymers break in solution when submitted to high deformation rates, eventually causing a serious viscosity loss. This problem of practical importance is though difficult to handle from a fundamental point of view given its complexity. We introduce here a new tool, based on microfluidic technology, for the screening of the degradation of solutions in the model situation of the flow through a constriction. We integrate two functions in a single set-up, a micro-fabricated constriction and an on-chip viscosimeter. This tool enables us to probe rapidly the viscosity loss imparted by flowing through the constriction at a given flow rate. Thanks to microfluidics, the sample preparation and measurement time are significantly lower than those implied by classical measurement protocols (reduction by up to two orders of magnitude). In addition, confinement provides control of the flow in terms of inertia. To illustrate the potential of this approach in a screening perspective, we use this tool to study the degradation of a series of semi-dilute aqueous solutions of PEO of varying molecular weights and concentrations. For each solution we identify a threshold flow rate for polymer degradation. The corresponding critical deformation rate decreases with molecular weight and concentration, as expected (the mass dependence is in line with previous reports and theories for dilute solutions). In addition we characterize the viscosity loss for larger deformation rates and find that, despite the polydispersity of our solutions, the observations for the various solutions can be roughly recast on a master curve by renormalization of the imposed deformation rates according to a law $M_w^{?1.7\pm 03}{c}^{?0.7\pm 03}$.     

Labelling and binding of poly-( -lysine) to functionalised gold surfaces. Combined FT-IRRAS and XPS characterisation

We compare herein the interfacial reactivity of self-assembled monolayers (SAMs) of 11-mercaptoundecanoic acid (MUA), 1-undecanethiol (UDT) and 11-mercaptoundecanol (MUD) on gold surfaces towards aqueous solutions of poly-( -lysine) (PL). Liquid-phase labelling of PL with the alkyne dicobalt hexacarbonyl cluster 1 combined with analysis of the substrates by Fourier transform infrared reflection–absorption spectroscopy (FT-IRRAS) and X-ray photoelectron spectroscopy (XPS) revealed that irreversible binding of PL occurred in all cases. However, the mechanism of binding involved differed markedly from one monolayer to the other. The main mode of interaction of PL to MUA SAM was of electrostatic nature between the terminal carboxylate of MUA and the ammonium groups of PL. For a similar number of bound thiolate molecules, the UDT adsorbed layer was found less continuous than the MUA one, allowing a higher fraction of PL to directly bind to the gold surface. As for MUD, very little thiolate molecules were adsorbed, leaving bare gold surface areas for non specific adsorption of PL.     

A new electrochemical cell adapted to quartz crystal microbalance measurements

As the resonance frequency of an oscillating quartz changes upon the deposition of a given mass to the crystal surface, it can be used as a very sensitive mass measuring device. Despite a growing interest in the use of electrochemical quartz crystal microbalance (EQCM), there is still no commercial available measurement cell which can satisfy all the conditions needed in electrochemical investigations. The design and characteristics of a new electrochemical cell adapted to EQCM measurements are presented. The sensitivity of the microbalance, which is determined by several calibration runs of silver electrodeposition is (183.2±2.9) Hz μg⁻¹ cm². This value, which is close to the theoretical one, confirms the validity of the system we have developed. The calibration procedure and the EQCM using range are then discussed.     

Neutral bis­(ethyl­enedi­thio)­tetra­thia­fulvalene at 100 K

The low‐temperature crystal structure of bis­(ethyl­enedi­thio)­tetra­thia­fulvalene (BEDT‐TTF), C₁₀H₈S₈, is similar to its high‐temperature structure. The room‐temperature central bond lengths of this mol­ecule are often used as reference in empirical methods to estimate the charge carried by the (BEDT‐TTF)_xⁿ⁺ cations in the BEDT‐TTF mol­ecule‐based organic conductors. We show that the method we previously reported can still be used with low‐temperature BEDT‐TTF salts data. Moreover, we confirm the purely thermal origin of the ordering of the ethyl­ene group.     

L1 Continuous Dependence Property¶for Systems of Conservation Laws

This paper is concerned with the uniqueness and L¹ continuous dependence of entropy solutions for nonlinear hyperbolic systems of conservation laws. We study first a class of linear hyperbolic systems with discontinuous coefficients: Each propagating shock wave may be a Lax shock, or a slow or fast undercompressive shock, or else a rarefaction shock. We establish a result of L¹ continuous dependence upon initial data in the case where the system does not contain rarefaction shocks. In the general case our estimate takes into account the total strength of rarefaction shocks. In the proof, a new time-decreasing, weighted L¹ functional is obtained via a step-by-step algorithm. To treat nonlinear systems, we introduce the concept of admissible averaging matrices which are shown to exist for solutions with small amplitude of genuinely nonlinear systems. Interestingly, for many systems of continuum mechanics, they also exist for solutions with arbitrary large amplitude. The key point is that an admissible averaging matrix does not exhibit rarefaction shocks. As a consequence, the L¹ continuous dependence estimate for linear systems can be extended to nonlinear hyperbolic systems using a wave-front tracking technique.     

A Sobolev mapping property of the Bergman kernel

We prove that if D is a pseudoconvex domain with Lipschitz boundary having an exhaustion function such that is plurisubharmonic, then the Bergman projection maps the Sobolev space boundedly to itself for any . Received March 10, 1999 / Published online May 8, 2000