scholarly journals Coalescence of sessile drops

2002 ◽  
Vol 453 ◽  
pp. 427-438 ◽  
Author(s):  
C. ANDRIEU ◽  
D. A. BEYSENS ◽  
V. S. NIKOLAYEV ◽  
Y. POMEAU
Keyword(s):  
Relaxation Time ◽  
Vapour Phase ◽  
Theoretical Description ◽  
Characteristic Relaxation Time ◽  
Late Time ◽  
Spherical Cap ◽  
Water Drops ◽  
Exponential Relaxation ◽  
Kinetics Of ◽  
Latent Heat Of Vaporization

We present an experimental and theoretical description of the kinetics of coalescence of two water drops on a plane solid surface. The case of partial wetting is considered. The drops are in an atmosphere of nitrogen saturated with water where they grow by condensation and eventually touch each other and coalesce. A new convex composite drop is rapidly formed that then exponentially and slowly relaxes to an equilibrium hemispherical cap. The characteristic relaxation time is proportional to the drop radius R* at final equilibrium. This relaxation time appears to be nearly 107 times larger than the bulk capillary relaxation time tb = R*η/σ, where σ is the gas–liquid surface tension and η is the liquid shear viscosity.In order to explain this extremely large relaxation time, we consider a model that involves an Arrhenius kinetic factor resulting from a liquid–vapour phase change in the vicinity of the contact line. The model results in a large relaxation time of order tb exp(L/[Rscr ]T) where L is the molar latent heat of vaporization, [Rscr ] is the gas constant and T is the temperature. We model the late time relaxation for a near spherical cap and find an exponential relaxation whose typical time scale agrees reasonably well with the experiment.

scholarly journals Late-time theory for the effects of a conserved field on the kinetics of an order-disorder transition

1991 ◽  
Vol 44 (13) ◽  
pp. 6673-6688 ◽  
Author(s):  
K. R. Elder ◽  
B. Morin ◽  
Martin Grant ◽  
R. C. Desai
Keyword(s):  
Late Time ◽  
Disorder Transition ◽  
Kinetics Of ◽  
Time Theory

Induced polarization and pore radius — A discussion

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D519-D526 ◽  
Author(s):  
Andreas Weller ◽  
Zeyu Zhang ◽  
Lee Slater ◽  
Sabine Kruschwitz ◽  
Matthias Halisch
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Diffusion Coefficients ◽  
Pore Radius ◽  
Mercury Porosimetry ◽  
Induced Polarization ◽  
Reliable Estimate ◽  
Characteristic Relaxation Time ◽  
A Value ◽  
Apparent Diffusion

Permeability estimation from induced polarization (IP) measurements is based on a fundamental premise that the characteristic relaxation time [Formula: see text] is related to the effective hydraulic radius [Formula: see text] controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We have examined the link between a widely used single estimate of [Formula: see text] and [Formula: see text] for an extensive database of sandstone samples, in which mercury porosimetry data confirm that [Formula: see text] is reliably determined from a modification of the Hagen-Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of one or two distinct representative diffusion coefficients but instead demonstrates strong evidence for six orders of magnitude of variation in an apparent diffusion coefficient that is well-correlated with [Formula: see text] and the specific surface area per unit pore volume [Formula: see text]. Two scenarios can explain our findings: (1) the length scale defined by [Formula: see text] is not equal to [Formula: see text] and is likely much longer due to the control of pore-surface roughness or (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g., silica and clays) making up the rock. In either case, the estimation of [Formula: see text] (and hence permeability) is inherently uncertain from a single characteristic IP relaxation time as considered in this study.

scholarly journals Thermodynamic Analysis of Relaxation Model for Non-Equilibrium Phase Behavior of Hydrocarbon Mixtures

2021 ◽  
Vol 2090 (1) ◽  
pp. 012138
Author(s):  
I M Indrupskiy ◽  
P A Chageeva
Keyword(s):  
Relaxation Time ◽  
Phase Behavior ◽  
Relaxation Process ◽  
Thermodynamic Analysis ◽  
Balance Equation ◽  
Equilibrium Phase ◽  
Characteristic Relaxation Time ◽  
Relaxation Model ◽  
Entropy Balance ◽  
Non Equilibrium

Abstract Mathematical models of phase behavior are widely used to describe multiphase oil and gas-condensate systems during hydrocarbon recovery from natural petroleum reservoirs. Previously a non-equilibrium phase behavior model was proposed as an extension over generally adopted equilibrium models. It is based on relaxation of component chemical potentials difference between phases and provides accurate calculations in some typical situations when non-instantaneous changing of phase fractions and compositions in response to variations of pressure or total composition is to be considered. In this paper we present a thermodynamic analysis of the relaxation model. General equations of non-equilibrium thermodynamics for multiphase flows in porous media are considered, and reduced entropy balance equation for the relaxation process is obtained. Isotropic relaxation process is simulated for a real multicomponent hydrocarbon system with different values of characteristic relaxation time using the non-equilibrium model implemented in the PVT Designer module of the RFD tNavigator simulation software. The results are processed with a special algorithm implemented in Matlab to calculate graphs of the total entropy time derivative and its constituents in the entropy balance equation. It is shown that the constituents have different signs, and the greatest influence on the entropy is associated with the interphase flow of the major component of the mixture and the change of the total system volume in the isotropic process. The characteristic relaxation time affects the rate at which the entropy is approaching its maximum value.

CATIONIC COPOLYMERIZATION OF ISOBUTYLENE WITH ISOPRENE: KINETICS OF THE PROCESS AND DETERMINATION OF KINETIC CONSTANTS

2015 ◽  
Vol 88 (4) ◽  
pp. 574-583 ◽  
Author(s):  
N. V. Ulitin ◽  
K. A. Tereshchenco ◽  
D. A. Shiyan ◽  
G. E. Zaikov
Keyword(s):  
Experimental Data ◽  
Molecular Weight ◽  
Cationic Polymerization ◽  
Methyl Chloride ◽  
Theoretical Description ◽  
Kinetic Constants ◽  
Molecular Weight Characteristics ◽  
Cationic Copolymerization ◽  
Kinetics Of

ABSTRACT A theoretical description has been developed of the kinetics of isobutylene with isoprene (IIR) cationic polymerization in the environment of methyl chloride on aluminum trichloride as the catalyst. Based on experimental data on the kinetics of copolymerization (isobutylene conversion curve) and the molecular weight characteristics of the copolymer of IIR, kinetic constants for the process were found. Adequacy of the developed theoretical description of the kinetics of the IIR copolymerization process was confirmed by comparing the experimental molecular-weight characteristics calculated by this description, independent characteristics, and IIR unsaturation.

INFLUENCE OF NATURAL MOISTURE ON THE CHARACTERISTIC TIME OF METHANE DESORPTION FROM COALS OF VARIOUS DEGREES OF METAMORPHISM

2020 ◽  
pp. 23-32
Author(s):  
Vsevolod Vasylkivskyi ◽  
◽  
Leonid Stefanovich ◽  
Oksana Chesnokova ◽  
◽  
...  
Keyword(s):  
Methane Emission ◽  
Characteristic Time ◽  
Practical Significance ◽  
Characteristic Relaxation Time ◽  
Storage Vessel ◽  
Compressed Gas ◽  
Three Stages ◽  
Methane Desorption ◽  
Kinetics Of ◽  
Metamorphic Series

Goal. To study the effect of natural internal moisture content on the kinetics of methane desorption from coals of varying degrees of metamorphization. Methodology. For the research, coal was used after a long (more than 100 days) preliminary exposure in a dry, closed indoors. The measurements were carried out on several samples of Donbass coals with different volatile content. Two groups of coal samples were used - dry, with natural internal humidity and one sample with artificial humidity of 1.5%. The volumetric method was used for measurements. The method includes three stages: 1st  saturation of coal with compressed methane, 2nd  preliminary discharge of compressed gas from a container with coal after its saturation, and 3rd  collection of methane released by coal into a storage vessel. Before registration of desorption, pressurized gas was discharged from the free volume of containers into the atmosphere. The desorption unit contains a low-temperature trap (78°C) for water vapor and a warming radiator for methane entering the storage vessel. To determine the numerical values of the characteristic time of desorption of methane from coal, we used information on the change in gas pressure in the storage vessel during desorption. To analyze the results, a method based on the concept of a change in the characteristic relaxation time of desorption during methane emission was used. Results. Experimental results show that in wet coals the ratio between the amount of methane in coal and the intensity of its outflow at any desorption site is less than in dry coals. It was found that in coals of the metamorphic series the presence of natural moisture leads to a decrease in the intensity of methane emission, a decrease in the characteristic desorption time and a decrease in the activation energy of methane desorption by 0.4 - 2.5 kJ / mol. The features of the kinetics of desorption indicates competition energetics of interactions between methane and water with the surface of the pores of coal. Scientific novelty. It was found that even without artificial humidification, but in the presence of natural internal moisture in coal, the degassing time during desorption is reduced (in comparison with dry coal). Practical significance. The research results can be used to optimize the duration of hydraulic saturation of the coal seam and the water consumption during coal degassing.

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