Dynamic surface tension density

For a pure liquid in eqmlibrium with its vapor, the number density and orientation of molecules at the surface will be different from that of bulk molecules (Fig. 8.2). When new surface is created, it is reasonable to assume that a finite amount of time will be required for new molecules to diffuse to the surface and to return the system to equilibrium. In that interim, as short as it may be, the measured surface tension of the system will be different from that of the system in equilibrium. The surface tension of such new surface is referred to as the dynamic surface tension. 

Temperature Density Kinematic Dynamic Surface tension in at atmosphmc... 

It was noted in connection with Eq. III-56 that molecular dynamics calculations can be made for a liquid mixture of rare gas-like atoms to obtain surface tension versus composition. The same calculation also gives the variation of density for each species across the interface [88], as illustrated in Fig. Ill-13b. The density profiles allow a calculation, of course, of the surface excess quantities. 

Alejandre J, Tildesley D J and Chapela G A 1995 Molecular dynamics simulation of the orthobaric densities and surface tension of water J. Chem. Phys. 102 4574-83... 

Spray Correlations. One of the most important aspects of spray characterization is the development of meaningful correlations between spray parameters and atomizer performance. The parameters can be presented as mathematical expressions that involve Hquid properties, physical dimensions of the atomizer, as well as operating and ambient conditions that are likely to affect the nature of the dispersion. Empirical correlations provide useful information for designing and assessing the performance of atomizers. Dimensional analysis has been widely used to determine nondimensional parameters that are useful in describing sprays. The most common variables affecting spray characteristics include a characteristic dimension of atomizer, d Hquid density, Pjj Hquid dynamic viscosity, ]ljj, surface tension. O pressure, AP Hquid velocity, V gas density, p and gas velocity, V. ... 

Dynamic similarity requires that the rado of input force, viscosity, density, and surface tension be equal. For the same fluid, only two of these four forces need be equal, because the density and viscosity will be the same [34, 29]. 

Dynamic viscosity Kinematic viscosity Density Surface tension Shear stress Vapor quality Contact angle Shear viscosity Shear rate... 

In the above equations, p, p. and a are the density, dynamic viscosity and surface tension respectively of the liquid PA, N and DA are the power consumption, rotational speed and diameter respectively of the agitator. 

In contrast to Section IV,M, where the turbulent diffusivity was employed to derive an expression for the mass transfer coefficient, in this section expression (401), which is based on a physical model, constitutes the starting point. Concerning the renewal frequency s, the following dimensional considerations can lead to useful expressions. The state of turbulence near the interface can be characterized by a characteristic velocity ua = (gSf)i/2, the dynamic viscosity rj, the surface tension a, and the density p. Therefore... 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

Gallium(III) bromide is a hygroscopic, white solid which sublimes readily and melts at 122.5° to a covalent, dimeric liquid. The solid is ionic and its electrical conductivity at the melting point is twenty-three times that of the liquid.5 The vapor pressure of the liquid at T°K is given by the equation log p(mm.) = 8.554 — 3129/T and the heat of dissociation of the dimer in the gas phase is 18.5 kcal./mol.3 At 125° the liquid has the following properties 5,6 density, 3.1076 dynamic viscosity, 2.780 c.p. surface tension, 34.8 dynes/cm. and specific conductivity, 7.2 X 10-7 ohm-1 cm.-1 Gallium(III) bromide readily hydrolyzes in water and forms addition compounds with ligands such as ammonia, pyridine, and phosphorus oxychloride. 

The fundamental units of dynamics are those of mass, length, and time. These units are denoted by the symbols [M], [L], and [T], respectively. The magnitude of these units may be fixed arbitrarily but all other units are derived from them, and depend upon them alone. The various derivative units are developed simply. For example, unit-density is unit-mass contained in a unit-volume. In terms of the fundamental units it is therefore [M/L8] or [ML-8]. Again, unit-velocity is unit-distance divided by unit-time, or [L/T]. By means of these units the terms in a given equation may be checked, inasmuch as all terms added to a given expression must be of the same kind and therefore of the same dimensions. If, for illustration, it is desired to determine the units of surface tension, a, from the capillary equation... 

The surface tension a and the dynamic viscosity of the liquid /i (as long as it is low) do affect gas flowrate. For viscosities greater than 0.5 PaS, however, the use of hollow stirrers for aeration becomes meaningless. Since aeration deals with a material system with large density differences, the operation is strongly influenced by the parameter gAp/p g at normal pressure, and therefore by the Froude number. 

SEPRAN package (Cuvelierefci/., 1986). Recently Delnoij etal. (1997b) applied the VOF method to study the dynamics of single gas bubbles rising in a quiescent Newtonian liquid. They were able to demonstrate that the predicted bubble shape and the induced flow patterns in the liquid phase could be predicted very well as a function of the key physical properties of the liquid phase such as density, viscosity, and surface tension (see Section VI.D). The results reported by Tomiyama et al. are discussed in more detail below. 

The most common variables in fluid mechanics problems are force, length, velocity, mass density, dynamic coefficient of viscosity, acceleration of gravity, speed of sound, and surface tension. Along with their dimensions they are as... 

Temp. r. c Saturation Pressure P. kPa Density 0. ke/m Enthalpy of Vaporization Specific Heat Ce, J/kg K Thermal Conductivity k. V m K Dynamic Viscosity fi, kg/m 5 Prandll Number Pr VoluiTie Expansion CocIficienI 0.1/K Liquid Surface Tension, N/m... 

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