The mean velocity profile of near-wall turbulent flow: is there anything in between the logarithmic and power laws?

The question of possible analytical forms for the mean velocity profile in a near-wall turbulent flow is addressed. An approach based on the use of dispersion relations for the flow velocity is developed in the context of a two-dimensional channel flow. It is shown that for an incompressible flow conserving vorticity, there exists a decomposition of the velocity field into rotational and potential components, such that the restriction of the former to an arbitrary cross section of the channel is a functional of the vorticity and velocity distributions over that cross section, while the latter is divergence-free and bounded downstream thereof. By eliminating the unknown potential component with the help of a dispersion relation, a nonlinear integro-differential equation for the flow velocity is obtained. It is then analysed within an asymptotic expansion in the small ratio v_*/U of the friction velocity to the mean flow velocity. Upon statistical averaging in the lowest nontrivial order, this equation relates the mean velocity to the cross-correlation function of the velocity fluctuations. Analysis of the equation reveals existence of two continuous families of solutions, one having the power-law near-wall asymptotic U ～ yⁿ, where y is the distance to the wall, n > 0, and the other, U ～ ln?^p(y/y₀), with y₀ = const and p ≥ 1. In the limit of infinite channel height, the exponent n turns out to be asymptotically a universal function of the Reynolds number, n ～ 1/ln?Re, whereas p → 1. Thus, the logarithmic profile (p = 1) is found to be a member of the power-log family whose members with p > 1 are intermediate between the power- and logarithmic-law profiles with respect to their slopes at large y. These results are discussed in the light of the existing controversy regarding experimental verification of the law of the wall.     

Faster,More Reproducible DESI-MS for Biological Tissue Imaging

A new, more robust sprayer for desorption electrospray ionization (DESI) mass spectrometry imaging is presented. The main source of variability in DESI is thought to be the uncontrolled variability of various geometric parameters of the sprayer, primarily the position of the solvent capillary, or more specifically, its positioning within the gas capillary or nozzle. If the solvent capillary is off-center, the sprayer becomes asymmetrical, making the geometry difficult to control and compromising reproducibility. If the stiffness, tip quality, and positioning of the capillary are improved, sprayer reproducibility can be improved by an order of magnitude. The quality of the improved sprayer and its potential for high spatial resolution imaging are demonstrated on human colorectal tissue samples by acquisition of images at pixel sizes of 100, 50, and 20 μm, which corresponds to a lateral resolution of 40–60 μm, similar to the best values published in the literature. The high sensitivity of the sprayer also allows combination with a fast scanning quadrupole time-of-flight mass spectrometer. This provides up to 30 times faster DESI acquisition, reducing the overall acquisition time for a 10 mm × 10 mm rat brain sample to approximately 1 h. Although some spectral information is lost with increasing analysis speed, the resulting data can still be used to classify tissue types on the basis of a previously constructed model. This is particularly interesting for clinical applications, where fast, reliable diagnosis is required.

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Solvothermal Synthesis of [Cr7S8(en)8Cl2]Cl3 ⋅ 2H2O with Magnetically Frustrated [Cr7S8]5+ Double-Cubes**

A novel transition metal chalcohalide [Cr₇S₈(en)₈Cl₂]Cl₃ ⋅ 2H₂O, with [Cr₇S₈]⁵⁺ dicubane cationic clusters, has been synthesized by a low temperature solvothermal method, using dimethyl sulfoxide (DMSO) and ethylenediamine (en) solvents. Ethylenediamine ligand exhibits bi- and monodentate coordination modes; in the latter case ethylenediamine coordinates to Cr atoms of adjacent clusters, giving rise to a 2D polymeric structure. Although magnetic susceptibility shows no magnetic ordering down to 1.8 K, a highly negative Weiss constant, θ=−224(2) K, obtained from Curie-Weiss fit of inverse susceptibility, suggests strong antiferromagnetic (AFM) interactions between S=3/2 Cr(III) centers. Due to the complexity of the system with (2S+1)⁷=16384 microstates from seven Cr³⁺ centers, a simplified model with only two exchange constants was used for simulations. Density-functional theory (DFT) calculations yielded the two exchange constants to be J₁=−21.4 cm⁻¹ and J₂=−30.2 cm⁻¹, confirming competing AFM coupling between the shared Cr³⁺ center and the peripheral Cr³⁺ ions of the dicubane cluster. The best simulation of the experimental data was obtained with J₁=−20.0 cm⁻¹ and J₂=−21.0 cm⁻¹, in agreement with the slightly stronger AFM exchange within the triangles of the peripheral Cr³⁺ ions as compared to the AFM exchange between the central and peripheral Cr³⁺ ions. This compound is proposed as a synthon towards magnetically frustrated systems assembled by linking dicubane transition metal-chalcogenide clusters into polymeric networks.     

Low‐Temperature Isolation of the Bicyclic Phosphinophosphonium Salt [Mes*2P4Cl][GaCl4]

The reaction of [ClP(μ‐PMes*)]₂ ( 1 ) with the Lewis acid GaCl₃ yielded a hitherto unknown tetraphosphabicyclo[1.1.0]butan‐2‐ium salt, [Mes*P₄(Cl)Mes*][GaCl₄] ( 3 [GaCl₄]), which incorporates a positively charged phosphonium center within its bicyclic P₄ scaffold. The formation of the title compound was studied by means of low‐temperature NMR experiments. This led to the identification of an intermediate cyclotetraphosphenium cation, which was trapped by reaction with dimethylbutadiene (dmb). All of the compounds were fully characterized by experimental and computational methods.     

Strong Negative Synergism of Ion Pair Extinction Coefficients in Chloroform–Acetone and Methylene Dichloride–Acetone Mixtures

The heteroselective preferential solvation of the iodides of N-heterocyclic aromatic cations in acetone–chloroalkane (chloroform and dichloromethane) binary mixtures results in not only a shift in the maxima of outer-sphere charge transfer absorption bands but also a considerable decrease in the molar extinction coefficients of ion pairs.     

Synthetic Modification of 1,3-Thiazolidin-4-One 1,1-Dioxides

Abstract

The reactivity of EWG (electron withdrawing group)-activated methylene group in 1,3-thiazolidin-4-one 1,1-dioxides were investigated. Novel derivatives of 1,3-thiazolidin-4-one 1,1-dioxides were prepared (the heterocyclic core was modified with carboxamide and carboxthioamide moieties as carbonyl group analogues). The products, which have functional groups for possible future modifications, are described and characterized.     

Synthesis Derivatives of 2‐Amino‐4‐quinolones from 1,2,3,4‐Tetrahydroquinoline‐8‐carboxylic acids

A simple and efficient method is developed. Novel 2‐amino‐4‐quinolone derivatives are synthesized. The products that have several functional groups for possible future modifications are described.