Transition from dripping to jetting

1999 ◽  
Vol 383 ◽  
pp. 307-326 ◽  
Author(s):  
CHRISTOPHE CLANET ◽  
JUAN C. LASHERAS
Keyword(s):  
Weber Number ◽  
Free Edge ◽  
Newtonian Liquid ◽  
Inviscid Limit ◽  
Inertia Effects ◽  
Wide Range ◽  
Critical Weber Number ◽  
Experimental Values ◽  
Outside Diameter ◽  
Good Agreement

We consider the critical Weber number (Wec≡ ρV20D/σ) at which the transition from dripping to jetting occurs when a Newtonian liquid of density ρ and surface tension σ is injected with a velocity V0 through a tube of diameter D downward into stagnant air, under gravity g. We extend Taylor's (1959) model for the recession speed of a free edge, and obtain in the inviscid limit an exact solution which includes gravity and inertia effects. This solution provides a criterion for the transition which is shown to occur at a critical Weber numberformula herewhere Bo and Boo are the Bond numbers (Bo≡[ρgD2/(2σ)]1/2), respectively based on the inside and outside diameter of the tube, and K is a constant equal to 0.37 for the case of water injected in air. This critical Weber number is shown to be in good agreement with existing experimental values as well as with new measurements performed over a wide range of Bond numbers.

scholarly journals DFT calculation and assignment of vibrational spectra of aryl and alkyl chlorophosphates

2014 ◽  
Vol 12 (2) ◽  
pp. 153-163
Author(s):  
Viktor Anishchenko ◽  
Vladimir Rybachenko ◽  
Konstantin Chotiy ◽  
Andrey Redko
Keyword(s):  
Vibrational Spectra ◽  
Basis Sets ◽  
Heavy Atoms ◽  
Wide Range ◽  
Complete Assignment ◽  
Key Factor ◽  
Polarization Functions ◽  
Experimental Values ◽  
Semi Empirical ◽  
Good Agreement

AbstractDFT calculations of vibrational spectra of chlorophosphates using wide range of basis sets and hybrid functionals were performed. Good agreement between calculated and experimental vibrational spectra was reached by the combination of non-empirical functional PBE0 with both middle and large basis sets. The frequencies of the stretching vibrations of the phosphate group calculated using semi-empirical functional B3LYP for all basis sets deviate significantly from the experimental values. The number of polarization functions on heavy atoms was shown to be a key factor for the calculation of vibrational frequencies of organophosphates. The importance of consideration of all the stable rotamers for a complete assignment of fundamental modes was shown.

scholarly journals Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

2021 ◽  
Vol 9 (11) ◽  
pp. 1253
Author(s):  
Yuriy N. Savchenko ◽  
Georgiy Y. Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Solution Process ◽  
Cavity Flow ◽  
Surface Tension Effect ◽  
Force Coefficient ◽  
Hodograph Method ◽  
Wide Range ◽  
Critical Weber Number ◽  
Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

VLE Determination of Carbon Dioxide Loaded Aqueous Alkanolamine Mixtures Using Modified Kent Eisenberg Model

2017 ◽  
Vol 231 (11-12) ◽  
Author(s):  
Humbul Suleman ◽  
Abdulhalim Shah Maulud ◽  
Zakaria Man
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Model Parameters ◽  
Thermodynamic Models ◽  
Carbon Dioxide Absorption ◽  
Proposed Model ◽  
Wide Range ◽  
Experimental Values ◽  
Good Agreement

AbstractA computationally simple thermodynamic framework has been presented to correlate the vapour-liquid equilibria of carbon dioxide absorption in five representative types of alkanolamine mixtures. The proposed model is an extension of modified Kent Eisenberg model for the carbon dioxide loaded aqueous alkanolamine mixtures. The model parameters are regressed on a large experimental data pool of carbon dioxide solubility in aqueous alkanolamine mixtures. The model is applicable to a wide range of temperature (298–393 K), pressure (0.1–6000 kPa) and alkanolamine concentration (0.3–5 M). The correlated results are compared to the experimental values and found to be in good agreement with the average deviations ranging between 6% and 20%. The model results are comparable to other thermodynamic models.

An Analytical Examination of the Behavior of Oil Sand Fragments in Heated Streams

1982 ◽  
Vol 104 (2) ◽  
pp. 121-129
Author(s):  
A. Hanafi ◽  
G. A. Karim
Keyword(s):  
Analytical Study ◽  
Chemical Processes ◽  
Operating Conditions ◽  
Transient Effects ◽  
Oil Sand ◽  
Wide Range ◽  
Experimental Values ◽  
Physical And Chemical ◽  
Simultaneous Heat ◽  
Good Agreement

The physical and chemical processes that occur typically within and around an oil sand fragment are considered when the fragment is suddenly introduced into a hot, low-uniform velocity, gaseous oxidizing stream. In this analytical study, the extent of bitumen volatilization was obtained from a consideration of the simultaneous heat and mass transfer within spherical oil sand fragments combined with a simplified cracking scheme of the heavy oil and asphaltene into coke and distillate. The resulting system of equations together with the boundary conditions arising from subjecting the fragments to hot convective streams were solved using Laplace transformation. The transient concentrations of bitumen and temperature within the fragments were then obtained under a wide range of operating conditions. The similarity of the expression obtained for the extent of bitumen volatilization to the expression derived from simplified analysis, based on a dropletlike model, was demonstrated for cases where the transient effects within the fragments were considered to be negligible. The results of the theoretical analysis show relatively good agreement with their corresponding experimental values at high stream temperatures, while they showed relatively inferior agreement at low temperatures.

Splashing of droplets impacting superhydrophobic substrates

2019 ◽  
Vol 870 ◽  
pp. 175-188 ◽  
Author(s):  
Enrique S. Quintero ◽  
Guillaume Riboux ◽  
José Manuel Gordillo
Keyword(s):  
Interfacial Tension ◽  
Critical Condition ◽  
Weber Number ◽  
Atmospheric Conditions ◽  
Ohnesorge Number ◽  
A Value ◽  
Consistent Model ◽  
Self Consistent ◽  
Critical Weber Number ◽  
Good Agreement

A drop of radius $R$ of a liquid of density $\unicode[STIX]{x1D70C}$, viscosity $\unicode[STIX]{x1D707}$ and interfacial tension coefficient $\unicode[STIX]{x1D70E}$ impacting a superhydrophobic substrate at a velocity $V$ keeps its integrity and spreads over the solid for $V<V_{c}$ or splashes, disintegrating into tiny droplets violently ejected radially outwards for $V\geqslant V_{c}$, with $V_{c}$ the critical velocity for splashing. In contrast with the case of drop impact onto a partially wetting substrate, Riboux & Gordillo (Phys. Rev. Lett., vol. 113, 2014, 024507), our experiments reveal that the critical condition for the splashing of water droplets impacting a superhydrophobic substrate at normal atmospheric conditions is characterized by a value of the critical Weber number, $We_{c}=\unicode[STIX]{x1D70C}\,V_{c}^{2}\,R/\unicode[STIX]{x1D70E}\sim O(100)$, which hardly depends on the Ohnesorge number $Oh=\unicode[STIX]{x1D707}/\sqrt{\unicode[STIX]{x1D70C}\,R\,\unicode[STIX]{x1D70E}}$ and is noticeably smaller than the corresponding value for the case of partially wetting substrates. Here we present a self-consistent model, in very good agreement with experiments, capable of predicting $We_{c}$ as well as the full dynamics of the drop expansion and disintegration for $We\geqslant We_{c}$. In particular, our model is able to accurately predict the time evolution of the position of the rim bordering the expanding lamella for $We\gtrsim 20$ as well as the diameters and velocities of the small and fast droplets ejected when $We\geqslant We_{c}$.

Lattice-Dynamical Estimation of Atomic Displacement Parameters in Carbonates: Calcite and Aragonite CaCO3, Dolomite CaMg(CO3)2 and Magnesite MgCO3

1998 ◽  
Vol 54 (5) ◽  
pp. 515-523 ◽  
Author(s):  
T. Pilati ◽  
F. Demartin ◽  
C. M. Gramaccioli
Keyword(s):  
Structure Refinement ◽  
Atomic Displacement ◽  
Empirical Potentials ◽  
Wide Range ◽  
Anisotropic Displacement Parameters ◽  
The Stability ◽  
Experimental Values ◽  
Atomic Displacement Parameters ◽  
Good Agreement ◽  
Raman And Ir Spectra

Using crystallographic information and empirical potentials derived from fitting the vibrational frequencies of all the substances under study, together with those of a group of silicates and oxides, a Born–von Karman rigid-ion lattice-dynamical model has been applied to the whole Brillouin zone in calcite, aragonite (α- and β-CaCO3, respectively), magnesite (MgCO3) and dolomite [CaMg(CO3)2]. The Raman and IR spectra are satisfactorily reproduced and interpreted by these calculations; there is also very good agreement with atomic anisotropic displacement parameters (a.d.p.'s) derived from accurate crystal structure refinement by various authors and with the experimental values of thermodynamic functions over a wide range of temperatures. On these vibrational grounds, the stability of calcite with respect to aragonite at high temperature can be accounted for.

Numerical Simulation of Droplet Flows and Evaluation of Interfacial Area

2002 ◽  
Vol 124 (3) ◽  
pp. 576-583 ◽  
Author(s):  
T. Watanabe ◽  
K. Ebihara
Keyword(s):  
Lattice Boltzmann ◽  
Weber Number ◽  
Volume Fraction ◽  
Interfacial Area ◽  
Force Balance ◽  
Two Phase ◽  
Critical Weber Number ◽  
Boltzmann Method ◽  
Droplet Flows ◽  
Good Agreement

Droplet flows with coalescence and breakup are simulated numerically using the lattice Boltzmann method. It is shown that the rising velocities are in good agreement with those obtained by the force balance and the empirical correlation. The breakup of droplets after coalescence is simulated well in terms of the critical Weber number. A numerical method to evaluate the interfacial area and the volume fraction in two-phase flows is proposed. It is shown that the interfacial area corresponds to the shape, the number and the size of droplets, and the proposed method is effective for numerical evaluation of interfacial area even if the interface changes dynamically.

A Thermodynamic Analysis of the Rich Flammability Limits of Fuel-Diluent Mixtures in Air

1995 ◽  
Vol 117 (3) ◽  
pp. 239-242 ◽  
Author(s):  
S. O. Bade Shrestha ◽  
I. Wierzba ◽  
G. A. Karim
Keyword(s):  
Atmospheric Temperature ◽  
Flammability Limit ◽  
Flammability Limits ◽  
Wide Range ◽  
Temperature And Pressure ◽  
The Rich ◽  
Predicted Values ◽  
Experimental Values ◽  
Good Agreement ◽  
Propane Butane

A simple approach is described for the calculation of the rich flammability limits of fuel-diluent mixtures in air for a wide range of initial temperatures based only on the knowledge of the flammability limit of the pure fuel in air at atmospheric temperature and pressure conditions. Various fuel-diluent mixtures that include the fuels methane, ethylene, ethane, propane, butane, carbon monoxide, and hydrogen, and the diluents nitrogen, carbon dioxide, helium, and argon have been considered. Good agreement is shown to exist between predicted values of the rich flammability limits and the corresponding available experimental values for the fuel-diluent mixtures.

A Thermodynamic Analysis of the Lean Flammability Limits of Fuel-Diluent Mixtures in Air

1994 ◽  
Vol 116 (3) ◽  
pp. 181-185 ◽  
Author(s):  
I. Wierzba ◽  
S. O. Bade Shrestha ◽  
G. A. Karim
Keyword(s):  
Thermodynamic Analysis ◽  
Initial Mixture ◽  
Flammability Limits ◽  
Temperature Range ◽  
Gaseous Fuels ◽  
Wide Range ◽  
Predicted Values ◽  
Experimental Values ◽  
Good Agreement

A procedure is described for calculating the lean flammability limits of fuel-diluent mixtures in air over a wide range of fuel-diluent combinations and for different initial mixture temperatures. Good agreement is shown to exist between the predicted values of the limits with the corresponding experimental values for some common gaseous fuels that include CH4, C2H6, C2H4, C3H8, C4H10, H2, and CO and the diluents CO2, N2, He, and Ar over the temperature range of −60°C up to 400°C.

Experimental Values of Solubility of Organic Compounds in Water for a Wide Range of Temperature Values − A New Experimental Technique

2010 ◽  
Vol 297-301 ◽  
pp. 1244-1249 ◽  
Author(s):  
João M.P.Q. Delgado ◽  
M. Vázquez da Silva
Keyword(s):  
Salicylic Acid ◽  
Benzoic Acid ◽  
Organic Compounds ◽  
Experimental Technique ◽  
Empirical Correlations ◽  
Wide Range ◽  
Set Up ◽  
Experimental Values ◽  
Good Agreement

This paper describes a simple experimental technique, easy to set-up in a laboratory, for the measurement of solute solubility in liquids (or gases). Experimental values of solubility were determined for the dissolution of benzoic acid in water and salicylic acid in water, at temperatures between 5°C and 70°C. The solubility experimental values obtained are in good agreement with the theoretical values of solubility and the empirical correlations presented in literature. The results show that it is possible to obtain good results for solubility values, using a simple and inexpensive experimental technique.

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