Oscillatory Marangoni convection around the air bubble in a vertical surfactant stratificationConvection de Marangoni oscillante autour d'une bulle d'air dans une stratification verticale surfactante

The solutocapillary Marangoni convection around a gas bubble in the inhomogeneous binary mixture of miscible fluids with a vertical surfactant concentration gradient was studied experimentally. A new phenomenon, the oscillatory instability of the surfactant mass transfer, near the bubble boundary, was detected and investigated. The interpretation of this effect as an interaction between the surfactant adsorption at the bubble free surface and solutocapillary and buoyancy convective mechanisms is proposed. The experimental data on oscillation period in relation to bubble dimensions, time, liquid layer thickness, physico-chemical fluid parameters and concentration gradients are presented and discussed. To cite this article: K. Kostarev et al., C. R. Mecanique 332 (2004).     

Mean curvature bounds and eigenvalues of Robin Laplacians

We consider the Laplacian with attractive Robin boundary conditions,

$$\begin{aligned} Q^\Omega _\alpha u=-\Delta u, \quad \dfrac{\partial u}{\partial n}=\alpha u \text { on } \partial \Omega , \end{aligned}$$

in a class of bounded smooth domains \(\Omega \in \mathbb {R}^\nu \); here \(n\) is the outward unit normal and \(\alpha >0\) is a constant. We show that for each \(j\in \mathbb {N}\) and \(\alpha \rightarrow +\infty \), the \(j\)th eigenvalue \(E_j(Q^\Omega _\alpha )\) has the asymptotics

$$\begin{aligned} E_j(Q^\Omega _\alpha )=-\alpha ^2 -(\nu -1)H_\mathrm {max}(\Omega )\,\alpha +{\mathcal O}(\alpha ^{2/3}), \end{aligned}$$

where \(H_\mathrm {max}(\Omega )\) is the maximum mean curvature at \(\partial \Omega \). The discussion of the reverse Faber-Krahn inequality gives rise to a new geometric problem concerning the minimization of \(H_\mathrm {max}\). In particular, we show that the ball is the strict minimizer of \(H_\mathrm {max}\) among the smooth star-shaped domains of a given volume, which leads to the following result: if \(B\) is a ball and \(\Omega \) is any other star-shaped smooth domain of the same volume, then for any fixed \(j\in \mathbb {N}\) we have \(E_j(Q^B_\alpha )>E_j(Q^\Omega _\alpha )\) for large \(\alpha \). An open question concerning a larger class of domains is formulated.

     

Phase Diagrams of Semicrystalline Polymer–Crystalline Substances: Polyolefins–1,2,4,5-Tetrachlorobenzene

The full phase diagrams of low-density polyethylene (LDPE), high-density polyethylene (HDPE), and isotactic polypropylene (i-PP) mixtures with 1,2,4,5-tetrachlorobenzene (TeCB), including the solubility curve of TeCB in a solid polymer, were constructed by an optical method. The diagrams contain a eutectic point that corresponds to the situation when the crystallization of TeCB out of its solution in a polyolefin is accompanied by the crystallization of monomer units of the macromolecules. As a result, the polymer acquires a gel structure with crystallites as crosslinks and amorphous regions saturated with TeCB. It is demonstrated that the eutectic point position on the phase diagram can be used for ranking polymers with respect to their thermodynamic affinity to a solvent. For the studied systems, the affinity to TeCB was decreased in the order i-PP, HDPE, and LDPE. Direct experimental evidence was obtained that TeCB crystals can be dissolved in a solid polymer via a vapor phase mechanism, which leads to the polymer amorphization.     

A feasibility study of X‐ray phase‐contrast mammographic tomography at the Imaging and Medical beamline of the Australian Synchrotron

Results are presented of a recent experiment at the Imaging and Medical beamline of the Australian Synchrotron intended to contribute to the implementation of low‐dose high‐sensitivity three‐dimensional mammographic phase‐contrast imaging, initially at synchrotrons and subsequently in hospitals and medical imaging clinics. The effect of such imaging parameters as X‐ray energy, source size, detector resolution, sample‐to‐detector distance, scanning and data processing strategies in the case of propagation‐based phase‐contrast computed tomography (CT) have been tested, quantified, evaluated and optimized using a plastic phantom simulating relevant breast‐tissue characteristics. Analysis of the data collected using a Hamamatsu CMOS Flat Panel Sensor, with a pixel size of 100 µm, revealed the presence of propagation‐based phase contrast and demonstrated significant improvement of the quality of phase‐contrast CT imaging compared with conventional (absorption‐based) CT, at medically acceptable radiation doses.     

Reactions of 1H-pyrano[3,4-c]pyran-7-ium perchlorates with ammonium acetate and amines: synthesis of 2,7-naphthyridines and pyrano[3,4-c]pyridinium salts

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