Edge pinch instability of liquid metal sheet in a transverse high-frequency AC magnetic field

We analyze the linear stability of the edge of a thin liquid metal layer subject to a transverse high-frequency AC magnetic field. The layer is treated as a perfectly conducting liquid sheet that allows us to solve the problem analytically for both a semi-infinite geometry with a straight edge and a thin disk of finite radius. It is shown that the long-wave perturbations of a straight edge are monotonically unstable when the wave number exceeds some critical value $k_c,$ which is determined by the surface tension and the linear density of the electromagnetic force acting on the edge. The higher the density of electromagnetic force, the shorter the critical wavelength. The perturbations with wavelength shorter than the critical are stabilized by the surface tension, whereas the growth rate of long wave perturbations reduces as $\sim k$ for wave numbers $k\to 0$. Thus, there is the fastest growing perturbation with the wave number k_\max=2/3 k_c. By applying the general approach developed for the semi-infinite sheet, we find that a circular disk becomes linearly unstable with respect to exponentially growing perturbation with the azimuthal wave number $m=2$ when the magnetic Bond number exceeds $Bm_c=3\pi$. The instability characteristics agree well with the experimental data.Comment: 11 pages, 11 figures, minor grammatical changes; to appear in Phys. Rev.

Simultaneous Determination of Various Isothiocyanates by RP-LC Following Precolumn Derivatization with Mercaptoethanol

Numerous isothiocyanates (ITCs) are poorly soluble in water which causes their precipitation in aqueous mobile phases used in reversed phase liquid chromatography (RP-LC), thus impacting the accuracy of the quantification. By comparing the amounts of ITCs injected and released from the column, losses could be estimated at 5–32% depending on polarities and concentrations. Results could be dramatically improved in terms of separation and quantification using RP-LC with a mercaptoethanol precolumn derivatization aimed at avoiding ITCs precipitation. The cancer chemoprotective allyl-ITC and sulforaphane were found in cabbage extracts at 1.2 and 2.7 μg g−1 fresh weight, respectively

The consistency conditions for density limits of hypoplastic constitutive law

The so-called phase diagram of grain skeletons illustrates the range of possible void ratios between the pressure dependent bounds ei and ed. It can be shown that in the framework of the actual hypoplastic model these bounds can be surpassed by particular deformation paths. This inconsistency is particularly acute in recently proposed FE-calculations with density fluctuations. Here we propose a modification to render the formulation consistent