New exact solutions for the evaporation flux density of a small droplet on a flat horizontal substrate with a contact angle in the range of 135-180 degrees

Previously [arXiv:2103.15582v3], an expression was proposed for the evaporation flux density of a small liquid droplet having the shape of an axisymmetric spherical segment deposited on a horizontal substrate. The dependence of the flux density on the polar angle was established for arbitrary contact angles. This formula has the form of an integral and is rather complicated for use in modeling algorithms. An approximate expression was obtained for the evaporation flux density at small contact angles. However, the question of which simplified formulas should be appropriate to apply in other ranges of contact angles, for example, in the case of obtuse angles remains open. In this paper, we propose new exact solutions for the set of discrete "hydrophobic" contact angles. As an example, very simple exact expressions are obtained explicitly for the evaporation flux density for droplets with contact angles 135 and 150 degrees that do not contain integral dependencies. They can also be used as approximate solutions for a narrow range of contact angles around the specified values.Comment: 7 pages, 2 figure

Wavefunction Collapse Broadens Molecular Spectrum

Spectral lines in the optical spectra of atoms, molecules, and other quantum systems are characterized by a range of frequencies ω or a range of wavelengths λ=2πc/ω, where c is the speed of light. Such a frequency or wavelength range is called the width of the spectral lines (linewidth). It is influenced by many specific factors. Thermal motion of the molecules results in broadening of the lines as a result of the Doppler effect (thermal broadening) and by their collisions (pressure broadening). The electric fields of neighboring molecules lead to Stark broadening. The linewidth to be considered here is the so-called parametric broadening (PB) of spectral lines in the optical spectrum. PB can be considered the fundamental type of broadening of the electronic vibrational–rotational (rovibronic) transitions in a molecule, which is the direct manifestation of the basic concept of the collapse of a wavefunction that is postulated by the Copenhagen interpretation of quantum mechanics. Thus, that concept appears to be not only valid but is also useful for predicting physically observable phenomena

Evaporation of Small Sessile Drop Deposited on a Horizontal Solid Surface: New Exact Solutions and Approximations

Evaporating a liquid sessile drop deposited on a horizontal surface is an important object of applications (printing technologies, electronics, sensorics, medical diagnostics, hydrophobic coatings, etc.) and theoretical investigations (microfluidics, self-assembly of nanoparticles, crystallization of solutes, etc.). The arsenal of formulas for calculating the slow evaporation of an axisymmetric drop of capillary dimensions deposited on a flat solid surface is reviewed. Characteristics such as vapor density, evaporation flux density, and total evaporation rate are considered. Exact solutions obtained in the framework of the Maxwellian model, in which the evaporation process of the drop is limited by vapor diffusion from the drop surface to the surrounding air, are presented. The summary covers both well-known results obtained during the last decades and new results published by us in the last few years, but practically unknown to the wider scientific community. The newest formulas, not yet published in refereed publications, concerning exact solutions for a number of specific contact angles are also presented. In addition, new approximate solutions are presented (total evaporation rate and mass loss per unit surface area per unit time in the whole range of contact angles θ∈[0, π), drop lifetime in constant contact radius evaporation regime and constant contact angle mode), which can be used in modeling without requiring significant computational resources

Evaporation dynamics and Marangoni number estimation for sessile picoliter liquid drop of binary mixture solution

We propose the evaporation model of picoliter sessile drop of binary solvent mixture (with infinitely soluble in each other components) based on Hu and Larson solution for single solvent sessile drop and Raoult law for saturated vapor density of components of binary mixture in wide range of undimensional molar binary concentration of the components. Concentration Marangoni number estimation for such a system is also considered for prediction of liquid flows structure for further applications in dissipative particle dynamics in binary mixture evaporating drop

Evaporation dynamics and Marangoni number estimation for sessile picoliter liquid drop of binary mixture solution

We propose the evaporation model of picoliter sessile drop of binary solvent mixture (with infinitely soluble in each other components) based on Hu and Larson solution for single solvent sessile drop and Raoult law for saturated vapor density of components of binary mixture in wide range of undimensional molar binary concentration of the components. Concentration Marangoni number estimation for such a system is also considered for prediction of liquid flows structure for further applications in dissipative particle dynamics in binary mixture evaporating drop

Evolution of pi(0) Suppression in Au plus Au Collisions from root s(NN)=39 to 200 GeV

Neutral-pion pi(0) spectra were measured at midrapidity (vertical bar y vertical bar < 0.35) in Au + Au collisions at root s(NN) = 39 and 62.4 GeV and compared with earlier measurements at 200 GeV in a transverse-momentum range of 1 < p(T) < 10 GeV/c. The high-p(T) tail is well described by a power law in all cases, and the powers decrease significantly with decreasing center-of-mass energy. The change of powers is very similar to that observed in the corresponding spectra for p + p collisions. The nuclear modification factors (RAA) show significant suppression, with a distinct energy, centrality, and p(T) dependence. Above p(T) = 7 GeV/c, R-AA is similar for root sNN = 62.4 and 200 GeV at all centralities. Perturbative-quantum-chromodynamics calculations that describe R-AA well at 200 GeV fail to describe the 39 GeV data, raising the possibility that, for the same p(T) region, the relative importance of initial-state effects and soft processes increases at lower energies. The p(T) range where pi(0) spectra in central Au + Au collisions have the same power as in p + p collisions is approximate to 5 and 7 GeV/c for root sNN = 200 and 62.4 GeV, respectively. For the root sNN = 39 GeV data, it is not clear whether such a region is reached, and the x(T) dependence of the x(T)-scaling power-law exponent is very different from that observed in the root sNN = 62 and 200 GeV data, providing further evidence that initial-state effects and soft processes mask the in-medium suppression of hardscattered partons to higher p(T) as the collision energy decreases

Measurement of transverse-single-spin asymmetries for midrapidity and forward-rapidity production of hadrons in polarized p+p collisions at s=\sqrt{s}=200 and 62.4 GeV

451 authors, 16 pages, 11 figures, and 10 tables. Submitted to Phys. Rev. D. Plain text data tables for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htmlMeasurements of transverse-single-spin asymmetries ($A_{N}$) in $p$$+$$p$ collisions at $\sqrt{s}=$62.4 and 200 GeV with the PHENIX detector at RHIC are presented. At midrapidity, $A_{N}$ is measured for neutral pion and eta mesons reconstructed from diphoton decay, and at forward rapidities, neutral pions are measured using both diphotons and electromagnetic clusters. The neutral-pion measurement of $A_{N}$ at midrapidity is consistent with zero with uncertainties a factor of 20 smaller than previous publications, which will lead to improved constraints on the gluon Sivers function. At higher rapidities, where the valence quark distributions are probed, the data exhibit sizable asymmetries. In comparison with previous measurements in this kinematic region, the new data extend the kinematic coverage in $\sqrt{s}$ and $p_T$, and it is found that the asymmetries depend only weakly on $\sqrt{s}$. The origin of the forward $A_{N}$ is presently not understood quantitatively. The extended reach to higher $p_T$ probes the transition between transverse momentum dependent effects at low $p_T$ and multi-parton dynamics at high $p_T$

Low-mass vector-meson production at forward rapidity in p plus p collisions at root s=200 GeV

The PHENIX experiment at the Relativistic Heavy Ion Collider has measured low-mass vector-meson ,omega, rho, and phi, production through the dimuon decay channel at forward rapidity (1.2 mu mu) = 80 +/- 6(stat) +/- 12(syst)nb and d sigma/dy(phi -> mu mu) = 27 +/- 3(stat) +/- 4(syst)nb. These results are compared with midrapidity measurements and calculations