An Alternate Derivation of the Excess Pressure Inside a Spherical Drop

1962 ◽  
Vol 30 (7) ◽  
pp. 528-528
Author(s):  
Samuel C. Wheeler
Keyword(s):  
Excess Pressure ◽  
Spherical Drop

To the theory analysis of tightness of tank of pressure testing

2019 ◽  
Vol 5 (4) ◽  
pp. 129-142
Author(s):  
Vladislav Sh. Shagapov ◽  
Ismagilyan G. Khusainov ◽  
Emiliya V. Galiakbarova ◽  
Zulfya R. Khakimova
Keyword(s):  
Relaxation Time ◽  
Three Dimensional ◽  
Petroleum Products ◽  
Technical Condition ◽  
Excess Pressure ◽  
Soil Parameters ◽  
Theory Analysis ◽  
Pressure Testing ◽  
Tank Pressure ◽  
Over Time

This article studies the process of relaxation of the pressure in a tank with the damaged area of the wall after pressure-testing. The authors use different methods for the diagnosis of the technical condition of objects of petroleum products storage. Pressure testing is one of nondestructive methods. The rate of pressure decrease is characteristic of the system tightness. This article studies the cases of ground and underground location of the tank. Pressure testing involves excess pressure inside of a tank and observing its decrease. Over time, one can assess the integrity of the system. This has required creating mathematical models to account the filtration of the liquid depending on the location of the tank. The results include the analytical solution of the task and the formulas for describing the dependence of the relaxation time of pressure in the tank from the liquid and soil parameters, geometry of the tank, and the damaged portion of the wall. The two- and three-dimensional cases of liquids filtration for the case of underground location of the tank were considered. The results of some numerical calculations of the dependence of reduction time and the time of half-life pressure from the area of the damaged portion of the wall were shown. The obtained solutions allow assessing the extent of the damaged area by the pressure testing with known values of tank, liquid, and soil.

scholarly journals Laminar condensation on a moving drop. Part 1. Singular perturbation technique

1984 ◽  
Vol 139 ◽  
pp. 105-130 ◽  
Author(s):  
J. N. Chung ◽  
P. S. Ayyaswamy ◽  
S. S. Sadhal
Keyword(s):  
Singular Perturbation ◽  
Perturbation Technique ◽  
Continuous Phase ◽  
Transport Processes ◽  
Forced Flow ◽  
Saturated Steam ◽  
Singular Perturbation Technique ◽  
Spherical Drop ◽  
Coupled Equations ◽  
Induced Velocity

In this paper, laminar condensation on a spherical drop in a forced flow is investigated. The drop experiences a strong, radial, condensation-induced velocity while undergoing slow translation. In view of the high condensation velocity, the flow field, although the drop experiences slow translation, is not in the Stokes-flow regime. The drop environment is assumed to consist of a mixture of saturated steam (condensable) and air (non-condensable). The study has been carried out in two different ways. In Part 1 the continuous phase is treated as quasi-steady and the governing equations for this phase are solved through a singular perturbation technique. The transient heat-up of the drop interior is solved by the series-truncation numerical method. The solution for the total problem is obtained by matching the results for the continuous and dispersed phases. In Part 2 both the phases are treated as fully transient and the entire set of coupled equations are solved by numerical means. Validity of the quasi-steady assumption of Part 1 is discussed. Effects due to the presence of the non-condensable component and of the drop surface temperature on transport processes are discussed in both parts. A significant contribution of the present study is the inclusion of the roles played by both the viscous and the inertial effects in the problem treatment.

A comprehensive analysis of the evaporation of a liquid spherical drop

2015 ◽  
Vol 438 ◽  
pp. 306-317 ◽  
Author(s):  
B. Sobac ◽  
P. Talbot ◽  
B. Haut ◽  
A. Rednikov ◽  
P. Colinet
Keyword(s):  
Comprehensive Analysis ◽  
Spherical Drop

scholarly journals Liquid toroidal drop under uniform electric field

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160633 ◽  
Author(s):  
Michael Zabarankin
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Dielectric Constants ◽  
Uniform Electric Field ◽  
Normal Velocity ◽  
Spherical Drop ◽  
Electric Stress ◽  
Freely Suspended ◽  
Major Radius ◽  
External Forces

The problem of a stationary liquid toroidal drop freely suspended in another fluid and subjected to an electric field uniform at infinity is addressed analytically. Taylor’s discriminating function implies that, when the phases have equal viscosities and are assumed to be slightly conducting (leaky dielectrics), a spherical drop is stationary when Q =(2 R 2 +3 R +2)/(7 R 2 ), where R and Q are ratios of the phases’ electric conductivities and dielectric constants, respectively. This condition holds for any electric capillary number, Ca E , that defines the ratio of electric stress to surface tension. Pairam and Fernández-Nieves showed experimentally that, in the absence of external forces (Ca E =0), a toroidal drop shrinks towards its centre, and, consequently, the drop can be stationary only for some Ca E >0. This work finds Q and Ca E such that, under the presence of an electric field and with equal viscosities of the phases, a toroidal drop having major radius ρ and volume 4 π /3 is qualitatively stationary—the normal velocity of the drop’s interface is minute and the interface coincides visually with a streamline. The found Q and Ca E depend on R and ρ , and for large ρ , e.g. ρ ≥3, they have simple approximations: Q ∼( R 2 + R +1)/(3 R 2 ) and Ca E ∼ 3 3 π ρ / 2   ( 6  ln  ⁡ ρ + 2  ln ⁡ [ 96 π ] − 9 ) / ( 12  ln  ⁡ ρ + 4  ln ⁡ [ 96 π ] − 17 )   ( R + 1 ) 2 / ( R − 1 ) 2 .

Surfaces, Interfaces, and Changing Shapes in Multilayered Films

MRS Bulletin ◽  
1999 ◽  
Vol 24 (2) ◽  
pp. 39-43 ◽  
Author(s):  
Daniel Josell ◽  
Frans Spaepen
Keyword(s):  
Free Energy ◽  
Excess Free Energy ◽  
External Pressure ◽  
Electronic Density ◽  
Spherical Drop ◽  
Crystal Anisotropy ◽  
Fundamental Quantity ◽  
The Difference ◽  
Image Position ◽  
Work Done

It is generally recognized that the capillary forces associated with internal and external interfaces affect both the shapes of liquid-vapor surfaces and wetting of a solid by a liquid. It is less commonly understood that the same phenomenology often applies equally well to solid-solid or solid-vapor interfaces.The fundamental quantity governing capillary phenomena is the excess free energy associated with a unit area of interface. The microscopic origin of this excess free energy is often intuitively simple to understand: the atoms at a free surface have “missing bonds”; a grain boundary contains “holes” and hence does not have the optimal electronic density; an incoherent interface contains dislocations that cost strain energy; and the ordering of a liquid near a solid-liquid interface causes a lowering of the entropy and hence an increase in the free energy. In what follows we shall show how this fundamental quantity determines the shape of increasingly complex bodies: spheres, wires, thin films, and multilayers composed of liquids or solids. Crystal anisotropy is not considered here; all interfaces and surfaces are assumed isotropic.Consideration of the equilibrium of a spherical drop of radius R with surface free energy γ shows that pressure inside the droplet is higher than outside. The difference is given by the well-known Laplace equation:This result can be obtained by equating work done against internal and external pressure during an infinitesimal change of radius with the work of creating a new surface.

Experimental method of evaluation of performance easily disposable construction

2020 ◽  
pp. 127-137
Author(s):  
V.V. Nizhnyk ◽  
◽  
O.F. Nikulin ◽  
S.V. Pozdeev ◽  
D.O. Dobriak ◽  
...  
Keyword(s):  
Experimental Evaluation ◽  
Building Materials ◽  
Excess Pressure ◽  
Design Parameters ◽  
Building Structures ◽  
Confined Space ◽  
Technical Parameters ◽  
Experimental Stand ◽  
Working Volume ◽  
Method Of Evaluation

This article presents the current state of affairs in cases of explosions in Ukraine and preventive measures to protect against them. The relevance of studies on the substantiation of the methodology for calculating the parameters of easily disposable structures for explosive and fire hazardous premises has been determined. The analysis of domestic and foreign regulatory documents for the design and installation of window openings in buildings for various purposes is carried out. The permissible values of the overpressure of the explosion, which does not cause significant damage to building structures and is safe for people, are considered. The subject of the study is the effect of the amount of gas on the design parameters of the research stand for the experimental evaluation of easily disposable structures. The purpose of this work is to substantiate the design and the main technical parameters of the research stand for assessing the performance of easily sisposable structures. The essence of the proposed research method is to create an excess pressure from the explosion of a mixture of propane-butane with air in the working volume and to study the effect of this excess pressure of the explosion on a prototype of an easily disposable structure. An experimental stand for studying the processes of the influence of the magnitude of the overpressure of an explosion in a confined space on the design parameters of easily disposable structures is simple in design, provides an imitation of a part of a building (structure) fragment and makes it possible to study the possibility of using certain building materials with different geometric parameters as easily disposable structures, which, in turn, allows the researcher to obtain more reliable data for analysis. The existing experimental methods for evaluating the parameters of easily disposable structures are analyzed. The dimensions of the research stand and the parameters of its enclosing structures, the critical values of the overpressure of the explosion, which the stand should create, and the minimum amount of gas, the combustion of which will provide the necessary overpressure of the explosion in the stand, are substantiated. A fundamentally new stand for the experimental evaluation of the parameters of easily disposable structures, a program and experimental research methodology have been developed.

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