Henry’s law constants (IUPAC Recommendations 2021)

Henry’s law states that the abundance of a volatile solute dissolved in a liquid is proportional to its abundance in the gas phase. It applies at equilibrium and in the limit of infinite dilution of the solute. For historical reasons, numerous different definitions, names, and symbols are used in the literature to express the proportionality coefficient, denoted the “Henry’s law constant”. Here, a consistent set of recommendations is presented. An important distinction is made between two new recommended reciprocal quantities: “Henry’s law solubility constant” (H s) and “Henry’s law volatility constant” (H v). Eight recommended variants of H s and H v are described and relations among them presented.

Distribution of the Proportionality Coefficient of Winter Route Accounting

In previous studies it was shown that the coefficient of proportionality of the winter route count (WRC) of animals included in the formula of WRC in the form of a constant multiplier π/2, is actually a random variable – the same as the average number of intersections account route traces per unit length, and the average length of the diurnal animals. The value π/2 is the mathematical expectation value of the proportionality factor, provided that the count route equiprobably crosses the daily footprint at any place and at any angle from 0 to 2π during a winter route counting of animals. At the same time, both the nature of the distribution of the coefficient as a random variable and the values of its variance as its other statistical characteristics remained unknown. In this study, it was found that when the above-mentioned count conditions are met, the distribution of the proportionality coefficient of WRC as a random variable will be exponential or power-like. This allows calculating the values of its variance and relative statistical error in advance without collecting additional count data.

Experimental Study on the Flow Around a Rotating Cylinder

The flow around a rotating cylinder has been investigated at the experimental water basins. The tangential velocity generated by the rotation of the cylinder decreases linearly with the logarithmic value of the distance from the cylinder surface, and has a constant distribution in the radial direction regardless of the rotation speed. The distance at which the tangential velocity becomes zero is about 4.35 times of the cylinder radius from the cylinder center. The energy transfer is greater near the cylinder than far from the cylinder and proportional to the proportionality coefficient A of the linear equation of velocity distribution. In a narrow water basin, the influence of the rotation is not absorbed completely to the water and a flow was formed in the water basin.

On the Evaluation of the Proportionality Coefficient between the Turbulence Temperature Spectrum and Structure Parameter

The turbulence temperature spectrum and structure parameter are related through a widely adopted proportionality coefficient. We formally derive this expression, and present further evidence, to demonstrate that this coefficient is too large by a factor of 2.

A Mathematical Model of Winter Route Counting: Checking for Falsification

In the course of our model experiment, an attempt was made to falsify (refute) a consequence from the mathematical justification of the winter route counting of hunting animals (WRC) – the consequence of the mathematical expectation of the proportionality coefficient of this counting being equal to π/2. A simulation was carried out in the MapInfo program. The essence of our digital experiment was as follows: in several places of the model territory, which was a circle 5 km in diameter, daily tracks of animals were placed. Next, a grid of parallel routes oriented along 12 equally spaced directions relative to each other was applied to the model territory. The frequency of the route grid (the distance between parallel routes) for different tracks was chosen so that the total number of all intersections of a single track in all directions was not less than a thousand. In total, 19 electronic daily tracks of various animal species were used. 95 different actual values of the proportionality coefficient were obtained for various locations of the tracks in the model territory, no violations of the above mentioned consequence were found. The results of our experiment made it possible to formulate a corollary arising from the fundamental properties of Euclidean geometry on the directly proportional dependence between the number of intersections between the lines of daily animal tracks and route lines and the product of the total lengths of these lines. The mathematical justification of WRC has once again passed a simulation test, already using the means of geographical information systems and data from satellite navigators. At present, there are no grounds for abandoning the practical use of winter route counting for game animals. All possible discrepancies in the estimates of the numbers of game animals determined by the WRC method with their actual values should be attributed to shortcomings in the direct organization of this counting rather than to its mathematical justification.

Effects of crystallinity on sintering of metal nanoparticles

Regularities and mechanisms of coalescence of Au nanodroplets and sintering of solid Au nanoparticles have been investigated by using molecular dynamics and some theoretical models. It has been established that the characteristic time of coalescence t is proportional to radius r0 of initial nanodroplets. Both the above conclusion and some quantitative estimations of the proportionality coefficient between t and r0 agree with Frenkels theory (1946) though this theory was rut forward to describe coalescence of macroscopic droplets.

Влияние химической модификации поверхности углеродных нанотрубок на их теплопроводность

An effect of partial chemical modification of the surface of a single-walled carbon nanotube on its thermal conductivity is studied. Numerical simulation of heat transfer showed that partial hydrogenation (fluorination) of a nanotube (addition of hydrogen and fluorine atoms from its outer side) can lead to more than a tenfold decrease in thermal conductivity. When the length of the nanotube increases, its thermal conductivity increases in proportion to the logarithm of the length, whereas the proportionality coefficient decreases with an increase in density of hydrogen or fluorine atoms attached. A thermal conductivity reduction coefficient does not depend on the length of the nanotube, but depends on temperature (the lower the temperature, the stronger the decrease) and density of the attached atoms p . When p < 0.25, an increase in density monotonically decreases the thermal conductivity. A decrease is maximum, when density p is 0.25. If only one half of the nanotube is hydrogenated, this half has a lower thermal conductivity. Such a nanotube becomes anisotropic and can be used as a heat transfer rectifier with no more than two percent rectification efficiency.

INTENSIFIED HEAT EXCHANGE AT THE TURBULENT CURRENT IN PIPES WITH TURBULIZERS WITH THE APPLICATION OF THE FOUR-LAYER MODEL OF THE TURBULENT BORDER LAYER DEPENDING ON THE NUMBER PRANDTLE

The main aspects of mathematical modeling of intensified heat transfer in turbulent flow in pipes with turbulators with the use of a four-layer model of a turbulent boundary layer are analyzed in the article, depending on the Prandtl number. The advantage of the law of the "fourth" degree is shown for large Prandtl numbers for the calculation of heat transfer in tubes with turbulators; It is shown that for tubes with turbulators the proportionality coefficient in this law is much higher than in smooth tubes, which indicates an increased level of turbulence in them at the boundary of the viscous and buffer sublayers. The results of calculating heat transfer for large Prandtl numbers have shown that the relative heat exchange with increasing Prandtl number increases rather insignificantly, especially after Pr>102; after Pr>103 it almost stabilizes

Entropy in a d-dimensional charged black hole

Christodoulou and Rovelli have shown that the interior volume of a Schwarzschild black hole grows linearly with time. The entropy of a scalar field in this interior volume of a Schwarzschild black hole has been calculated and shown to increase linearly with the advanced time too. In this paper, considering Hawking radiation from a d-dimensional charged black hole, we investigate the proportional relation between the entropy of the scalar field in the interior volume and the Bekenstein–Hawking entropy using the method of our previous work. We also derive this proportionality relation using Hamiltonian analysis and find a consistent result. We then investigate the proportionality coefficient with respect to d and find that it gradually decreases as the dimension of space–time increases.