Surface tension defined

The surface tension defined above was related to an interface that behaved mechanically as a membrane stretched uniformly and isotropically by a force which is the same at all points on the surface. A surface property defined this way is not always applicable to the surfaces of solids and the surface energy of planar surfaces is defined to take anisotropy into account. The surface energy is often in the literature interchanged with surface tension without further notice. Although this may be useful in practice, it is strictly not correct. 

Change in superficial velocity of continuous phase Surface tension Defined in Eq. (72)... 

The wetting of a surface can be described in thermodynamic terns. Important parameters that could have an effect on adhesion development and the interfacial bond include the surface energetics of both the sohd coating and the substrate as well as the surface tension of the coating in its liquid state (Lee, 1991 KendaU, 2001). The spreading coefficient, which is related to the surface tension, defines the capabUity of a liquid to wet and spread on a sofid. The surface teision of both substances (fiquid and sofid) will determine whether a given coating will wet a sofid surface. 

The chemical nature of the substrate, combined with the liquid surface tension, defines the liquid CA on a perfectly clean, flat surface. To control the wettability of surfaces, often (hydrophobic) polymers with specific low surface tension end-groups are used. The surface tension of typical substituent end-groups decreases in the following order CH2(36dyn/cm) > CH3(30dyn/cm) > CF2(23dyn/cm) >... 

Before approaching the problem of dynamics of contact line, we shall briefly review the equilibrium properties of gas-liquid interfaces and their dependence on the proximity to solid surfaces. We shall consider the simplest one-component system a liquid in equilibrium with its vapor. Thermodynamic equilibrium in a two-phase system implies equilibrium of the interphase boundary, which tends to minimize its area. The thermodynamic quantity that expresses additional energy carried by the interface is surface tension, defined as the derivative of the Helmholtz or Gibbs free energy with respect to interfacial area E ... 

The presence of the transition zone between a drop or a bubble and thin liquid interlayers can be described in terms of line tension, x, a concept first introduced by Gibbs (see for example [22]). In the case of surface tension, the transition zone between the liquid and vapor is replaced by a plane of tension with excess surface energy, y. By analogy, the transition zone between a drop or a bubble and the thin liquid interlayer may be replaced by a three-phase contact line with an excess linear energy, x. In contrast to surface tension defined always as positive, the value of the line tension may be positive and negative. When positive, it contracts the wetting perimeter, whereas the perimeter expands if the line tension is negative [33-36]. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

It has been pointed out [138] that algebraically equivalent expressions can be derived without invoking a surface solution model. Instead, surface excess as defined by the procedure of Gibbs is used, the dividing surface always being located so that the sum of the surface excess quantities equals a given constant value. This last is conveniently taken to be the maximum value of F. A somewhat related treatment was made by Handa and Mukeijee for the surface tension of mixtures of fluorocarbons and hydrocarbons [139]. 

The surface tension of an aqueous solution varies with the concentration of solute according to the equation y = 72 - 350C (provided that C is less than 0.05Af). Calculate the value of the constant k for the variation of surface excess of solute with concentration, where k is defined by the equation V = kC. The temperature is 25°C. 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

A direct measurement of surface tension is sometimes possible from the work of cleaving a crystal. Mica, in particular, has such a well-defined cleavage plane that it can be split into large sheets of fractional millimeter thickness. Orowan... 

In figure A3.3.9 the early-time results of the interface fonnation are shown for = 0.48. The classical spinodal corresponds to 0.58. Interface motion can be simply monitored by defining the domain boundary as the location where i = 0. Surface tension smooths the domain boundaries as time increases. Large interconnected clusters begin to break apart into small circular droplets around t = 160. This is because the quadratic nonlinearity eventually outpaces the cubic one when off-criticality is large, as is the case here. 

Silanes can alter the critical surface tension of a substrate in a well-defined manner. Critical surface tension is associated with the wettabiUty or release qualities of a substrate. Liquids having a surface tension below the critical surface tension, y, of a substrate wet the surface. Critical surface tensions of a number of typical surfaces are compared to y of silane-treated surfaces in Table 2 (19). 

The Weber number. We, is defined as foUows and represents the ratio of the dismptive aerodynamic forces to the restoring surface tension forces. 

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

The Spreading process is governed by the spreading coefficient S defined as in equation 4 (30) where c is the surface tension of the foaming medium, C the surface tension of the defoamer, and C. the interfacial tension between them. 

Capillarity. The outer surface of porous material has pore entrances of various sizes. As surface Hquid is evaporated during constant rate drying, a meniscus forms across each pore entrance and interfacial forces are set up between the Hquid and material. These forces may draw Hquid from the interior to the surface. The tendency of Hquid to rise in porous material is caused pardy by Hquid surface tension. Surface tension is defined as the work needed to increase a Hquid s surface area by one square meter and has the units J/m. The pressure increase caused by surface tension is related to pore size ... 

The molecules in a gas-hquid interface are in tension and tend to contract to a minimum surface area. This tension may be quantified by the surface tension, which is defined as the force in the plane of the surface per unit length. Jasper" has made a critical evaluation of experimental surface tension data for approximately 2200 pure chem-ic s. He correlates surface tension C (mN/m = dyn/cm) with temperature T (°C) over a specified temperature range as... 

To find the equilibrium form of a crystal, the following Wullf construction [20] can be used, which will be explained here, for simplicity, in two dimensions. Set the centre of the crystal at the origin of a polar coordinate system r,6. The radius r is assumed proportional to the surface tension 7( ), where 6 defines the angle between the coordinate system of the crystal lattice and the normal direction of a point at the surface. The anisotropy here is given through the angular dependence. A cubic crystal, for example, shows in a two-dimensional cut a clover-leaf shape for 7( ). Now draw everywhere on this graph the normals to the radius vector r = The... 

Roy et al. (R3) define the critical solids holdup as the maximum quantity of solids that can be held in suspension in an agitated liquid. They present measurements of this factor for various values of gas velocity, gas distribution, solid-particle size, liquid surface tension, liquid viscosity, and a solid-liquid wettability parameter, and they propose the following two correlations in terms of dimensionless groups containing these parameters ... 

Figure 11 presents the surface tension of an aqueous solution of Cl4-C16 AOS vs. the expansion rate E defined as... 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

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