An addition to the oxoacid family: H2B12(OH)12

The acid H(2)B(12)(OH)(12) can be isolated as a crystalline solid by protonation of the hydroxylated borane anion, B(12)(OH)(12)(2)(-). This acidic compound has low solubility in water, conducts protons in the solid state, and has thermal stability to a temperature of 400 degrees C. The conductivity mechanism is a Grotthuss mechanism with a low activation enthalpy (9-13 kcal/mol). This new acid represents an addition to the class of oxoacids, of which sulfuric and phosphoric acid are the most prominent examples.     

Theory-enforced Re-investigation of the Origin of the Large Metal–Carbon Bond Strength in PdCH2I+ and its reactions with unsaturated hydrocarbons

State-of-the-art ab initio studies demonstrate that the reaction Pd⁺ + CH₃I → PdCH₂I⁺ + H^. is endothermic by ca. 20 kcal/mol, which translates into a bond dissociation energy (BDE) of ca. 83 kcal/mol for the Pd⁺? CH₂I bond. This figure is in agreement with an experimental bracket of 68 kcal/mol < BDE(Pd⁺? CH₂I) < 92 kcal/mol. Based on these findings, the previously studied Pd⁺/CH₃I system was re-investigated, and double-resonance experiments demonstrate that the formation of PdCH₂I⁺ occurs stepwise via PdCH as a reactive intermediate. Further, ion/molecule reactions of PdCH₂I⁺ with unsaturated hydrocarbons are studied, which reveal the formation of carbon–carbon bonds in the gas phase.     

The influence of viscoelasticity on the collapse of cavitation bubbles near a rigid boundary

An understanding of the phenomena associated with cavitation is important in many areas of science and engineering. This paper is concerned with the influence of viscoelasticity on the dynamics of cavitation bubbles near rigid boundaries. Viscoelastic effects are modelled using a Maxwell constitutive equation, and a generalized Bernoulli equation is derived. The governing equations are solved using the boundary element method in which both the bubble surface and the potential are represented by cubic splines. The numerical scheme is validated through comparisons with results in the literature for the inviscid case. The introduction of viscoelasticity introduces some interesting bubble dynamics including the occurrence of oscillations during collapse. Most importantly, it is shown that viscoelasticity can serve to suppress the formation of a liquid jet. The subsequent reduced pressures compared with the inviscid case suggest that viscoelasticity has a mitigating effect on cavitation damage.     

A global equilibrium as the foundation of quantum randomness

We analyze the origin of quantum randomness within the framework of a completely deterministic theory of particle motion—Bohmian mechanics. We show that a universe governed by this mechanics evolves in such a way as to give rise to the appearance of randomness, with empirical distributions in agreement with the predictions of the quantum formalism. Crucial ingredients in our analysis are the concept of the effective wave function of a subsystem and that of a random system. The latter is a notion of interest in its own right and is relevant to any discussion of the role of probability in a deterministic universe.Research supported in part by NSF Grant DMS-9105661.     

Drag reduction in bubbly Taylor-Couette turbulence

In Taylor-Couette flow the total energy dissipation rate and therefore the drag can be determined by measuring the torque on the system. We do so for Reynolds numbers between Re=7 x 10(4) and Re=10(6) after having injected (i) small bubbles (R=1 mm) up to a volume concentration of alpha=5% and (ii) buoyant particles (rhop/rhol=0.14) of comparable volume concentration. In case (i) we observe a crossover from little drag reduction at smaller Re to strong drag reduction up to 20% at Re=10(6). In case (ii) we observe at most little drag reduction throughout. Several theoretical models for bubbly drag reduction are discussed in view of our findings.     

The Smoluchowski limit for a simple mechanical model

We consider a vertical stick constantly accelerated along thex-axis by a forceF and which elastically collides with point particles of the same mass (atoms). The atoms are initially Poisson distributed and are allowed to have four velocities only. It is shown that under suitable scaling of the system the displacementQ(t) of the stick satisfies a nontrivial CLT:Q(t)=vFt+D ^1/2 W(t) (Smoluchowski equation), where the values ofv andD depend on the fact that one atom may collide several times.     

"Compression-only" behavior: a second-order nonlinear response of ultrasound contrast agent microbubbles

Oscillating phospholipid-coated ultrasound contrast agent microbubbles display a so-called "compression-only" behavior, where it is observed that the bubbles compress efficiently while their expansion is suppressed. Here, a theoretical understanding of the source of this nonlinear behavior is provided through a weakly nonlinear analysis of the shell buckling model proposed by Marmottant et al. [J. Acoust. Soc. Am. 118, 3499-3505 (2005)]. It is shown that the radial dynamics of the bubble can be considered as a superposition of a linear response at the fundamental driving frequency and a second-order nonlinear low-frequency response that describes the negative offset of the mean bubble radius. The analytical solution deduced from the weakly nonlinear analysis shows that the compression-only behavior results from a rapid change of the shell elasticity with bubble radius. In addition, the radial dynamics of single phospholipid-coated microbubbles was recorded as a function of both the amplitude and the frequency of the driving pressure pulse. The comparison between the experimental data and the theory shows that the magnitude of compression-only behavior is mainly determined by the initial phospholipids concentration on the bubble surface, which slightly varies from bubble to bubble.     

Knudsen gas provides nanobubble stability

We provide a model for the remarkable stability of surface nanobubbles to bulk dissolution. The key to the solution is that the gas in a nanobubble is of Knudsen type. This leads to the generation of a bulk liquid flow which effectively forces the diffusive gas to remain local. Our model predicts the presence of a vertical water jet immediately above a nanobubble, with an estimated speed of ～3.3 m/s, in good agreement with our experimental atomic force microscopy measurement of ～2.7 m/s. In addition, our model also predicts an upper bound for the size of nanobubbles, which is consistent with the available experimental data.     

Effect of an entrained air bubble on the acoustics of an ink channel

Piezo-driven inkjet systems are very sensitive to air entrapment. The entrapped air bubbles grow by rectified diffusion in the ink channel and finally result in nozzle failure. Experimental results on the dynamics of fully grown air bubbles are presented. It is found that the bubble counteracts the pressure buildup necessary for the droplet formation. The channel acoustics and the air bubble dynamics are modeled. For good agreement with the experimental data it is crucial to include the confined geometry into the model: The air bubble acts back on the acoustic field in the channel and thus on its own dynamics. This two-way coupling limits further bubble growth and thus determines the saturation size of the bubble.