Steady-state composition of a two-component gas bubble growing in a liquid solution: self-similar approach

The paper presents an analytical description of the growth of a two-component bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time dependence of the bubble radius and analytical expressions for the non-steady profiles of dissolved gases around the bubble. We show that the necessary condition for the self-similar regime of bubble growth is the constant, steady-state composition of the bubble. The equation for the steady-state composition is obtained. We reveal the dependence of the steady-state composition on the solubility laws of the bubble components. Besides, the universal, independent from the solubility laws, expressions for the steady-state composition are obtained for the case of strong supersaturations, which are typical for the homogeneous nucleation of a bubble.Comment: 12 pages, 2 figure

Dynamics of gas bubble growth in a supersaturated solution with Sievert's solubility law

This paper presents a theoretical description of diffusion growth of a gas bubble after its nucleation in supersaturated liquid solution. We study systems where gas molecules completely dissociate in the solvent into two parts, thus making Sievert's solubility law valid. We show that the difference between Henry's and Sievert's laws for chemical equilibrium conditions causes the difference in bubble growth dynamics. Assuming that diffusion flux is steady we obtain a differential equation on bubble radius. Bubble dynamics equation is solved analytically for the case of homogeneous nucleation of a bubble, which takes place at a significant pressure drop. We also obtain conditions of diffusion flux steadiness. The fulfillment of these conditions is studied for the case of nucleation of water vapor bubbles in magmatic melts.Comment: 22 pages, 3 figure

Metastable bound state of a pair of two-dimensional spatially separated electrons in anti-parallel magnetic fields

We propose a new mechanism for binding of two equally charged carriers in a double-layer system subjected by a magnetic field of a special form. A field configuration for which the magnetic fields in adjacent layers are equal in magnitude and opposite in direction is considered. In such a field an additional integral of motion - the momentum of the pair P arises. For the case when in one layer the carrier is in the zero (n=0) Landau level while in the other layer - in the first (n=1) Landau level the dependence of the energy of the pair on its momentum E(P} is found. This dependence turns out to be nonmonotonic one : a local maximum and a local minimum appears, indicating the emergence of a metastable bound state of two carrier with the same sign of electrical charge.Comment: 7 page

Theory of the nonsteady diffusion growth of a gas bubble in a supersaturated solution of gas in liquid

Using a self-similar approach a general nonsteady theory is elaborated for the case of the diffusion growth of a gas bubble in a supersaturated solution of gas in liquid. Due to the fact that the solution and the bubble in it are physically isolated, the self-similar approach accounts for the balance of the number of gas molecules in the solution and in the bubble that expells incompressible liquid solvent while growing. The rate of growth of the bubble radius in its dependence from gas solubility and solution supersaturation is obtained. There is a nonsteady effect of rapid increase of the rate of bubble growth simultaneous with the growth of the product of gas solubility and solution supersaturation. This product is supplied with a limitation from above, which also stipulates isothermal conditions of bubble growth. The smallness of gas solubility is not presupposed.Comment: 22 pages, 3 figure

Stages of steady diffusion growth of a gas bubble in strongly supersaturated gas-liquid solution

Gas bubble growth as a result of diffusion flux of dissolved gas molecules from the surrounding supersaturated solution to the bubble surface is studied. The condition of the flux steadiness is revealed. A limitation from below on the bubble radius is considered. Its fulfillment guarantees the smallness of fluctuation influence on bubble growth and irreversibility of this process. Under the conditions of steadiness of diffusion flux three stages of bubble growth are marked out. With account for Laplace forces in the bubble intervals of bubble size change and time intervals of these stages are found. The trend of the third stage towards the self-similar regime of the bubble growth, when Laplace forces in the bubble are completely neglected, is described analytically.Comment: 22 page

A multilaboratory comparison of calibration accuracy and the performance of external references in analytical ultracentrifugation.

Analytical ultracentrifugation (AUC) is a first principles based method to determine absolute sedimentation coefficients and buoyant molar masses of macromolecules and their complexes, reporting on their size and shape in free solution. The purpose of this multi-laboratory study was to establish the precision and accuracy of basic data dimensions in AUC and validate previously proposed calibration techniques. Three kits of AUC cell assemblies containing radial and temperature calibration tools and a bovine serum albumin (BSA) reference sample were shared among 67 laboratories, generating 129 comprehensive data sets. These allowed for an assessment of many parameters of instrument performance, including accuracy of the reported scan time after the start of centrifugation, the accuracy of the temperature calibration, and the accuracy of the radial magnification. The range of sedimentation coefficients obtained for BSA monomer in different instruments and using different optical systems was from 3.655 S to 4.949 S, with a mean and standard deviation of (4.304 ± 0.188) S (4.4%). After the combined application of correction factors derived from the external calibration references for elapsed time, scan velocity, temperature, and radial magnification, the range of s-values was reduced 7-fold with a mean of 4.325 S and a 6-fold reduced standard deviation of ± 0.030 S (0.7%). In addition, the large data set provided an opportunity to determine the instrument-to-instrument variation of the absolute radial positions reported in the scan files, the precision of photometric or refractometric signal magnitudes, and the precision of the calculated apparent molar mass of BSA monomer and the fraction of BSA dimers. These results highlight the necessity and effectiveness of independent calibration of basic AUC data dimensions for reliable quantitative studies