surface tension

surface tension, property of a liquid surface displayed by its acting as if it were a stretched elastic membrane.

This phenomenon can be observed in the nearly spherical shape of small drops of liquids and of soap bubbles.

Because of this property, certain insects can stand on the surface of water. A razor blade also can be supported by the surface tension of water.

The razor blade is not floating: if pushed through the surface, it sinks through the water.

Surface tension depends mainly upon the forces of attraction

between the particles within the given liquid and also upon the gas, solid, or liquid in contact with it. The molecules in a drop of water, for example, attract each other weakly.

Water molecules well inside the drop may be thought of as being attracted equally in all directions by the surrounding molecules.

However, if surface molecules could be displaced slightly outward from the surface, they would be attracted back by the nearby molecules.

The energy responsible for the phenomenon of surface tension may be thought of as approximately equivalent to the work or energy required to remove the surface layer of molecules in a unit area.

Surface tension may be expressed, therefore, in units of energy (joules) per unit area (square metres). Water has a surface tension of 0.07275 joule per square metre at 20 °C (68 °F).

In comparison, organic liquids, such as benzene and alcohols, have lower surface tensions, whereas mercury has a higher surface tension.

An increase in temperature lowers the net force of attraction among molecules and hence decreases surface tension.

Surface tension is also viewed

as the result of forces acting in the plane of the surface and tending to minimize its area.

On this basis, surface tension is often expressed as an amount of force exerted in the surface perpendicular to a line of unit length.

The unit then is newtons per metre, which is equivalent to joules per square metre.

Physical Property of Liquids and Gases

(2-6)σ=σ1[Tc−TTc−T1]R

where σ₁ = surface tension at T_1°C, dynes/cm

T_c = critical temperature, K

T = temperature, K

R = correlation parameter

For water, the temperature range for which surface tension is valid is:

Temperature range 0°C to 100°C σ₁ = 71.97

Temperature range 100°C to 374.2°C σ₁ = 58.91

T₁ = 298.16 K, R = 0.8105 for 0°C to 100°C

T₁ = 373.16 K, R= 1.1690 for 100°C to 374.2°C

The surface tension has been correlated with other physical parameters such as liquid compressibility, viscosity, molar fractions, and the refractive index. Rao et al.

8] developed a linear relationship between the surface tension at normal boiling point (log σ_b) and the reduced boiling point temperature (T_br).

Hadden [9] presented a nomograph for hydrocarbons that enables rapid calculation of σ. For cryogenic liquids, Sprows and Prausnitz [10] introduced the equation

(2-7)σ=σ0(1−Tr)P

where σ = surface tension, dyne/cm

σ₀ and p were determined by a least-squares analysis of the measured data. The computer program PROG21 gives a routine for estimating the surface tension of liquids, and typical results for water are shown in Table 2-1.

Figure 2-5 demonstrates the surface tension of water from 0°C to its critical value of 374.2°C In general, the surface tension of a liquid in equilibrium with its own vapor decreases with temperature and becomes zero at the critical point.

In the reduced temperature range 0.45 to 0.65, σ for most organic liquids range from 20 to 40 dyne/cm. For water, σ = 71.97 dyne/cm at 25°C.

Heat transfer and fluid flow theory

2.3.2.5 Temperature dependence of surface tension

Surface tension decreases with increasing temperature, it is therefore important to take temperature effects into account if using the results of measurements at typical ambient temperatures.

Values of surface tension for over 2000 pure fluids have been tabulated by Jasper [5] and temperature corrections of the form σ=a+bT are suggested.

For water the following interpolating equation [6] gives good values of surface tension:

(2.12)σl=B(1−Tr)μ(1−b(1−Tr))

where T_r is the reducedtemperature=T/Tc, T_c=647.096 K, B=235.8 mN/m, b=0.625 and μ=1.256.

Equation (2.12) is valid between the triple point (0.01°C) and the critical temperature, and is in agreement with measured data to within experimental uncertainty.

Eötvös proposed a relationship which was later modified by Ramsay and Shields to give:

(2.13)σl(Mρl)2/3=H(Tc−6−T)

where M is the molecular weight, Tc is the critical temperature (K), T the fluid temperature (K) and H is a constant, the value of which depends upon the nature of the liquid.

The Eötvös–Ramsay–Shields equation does not give agreement with the experimentally observed behaviour of liquid metals.

and molten salts. Bohdanski and Schins [7] have derived an equation which applies to the alkali metals. While Fink and Leibowitz [8] recommended:

Petroleum Composition and Properties

6.3 Surface and Interfacial Tension

Surface tension is a measure of the force acting at a boundary between two phases.

If the boundary is between a liquid and a solid or between a liquid and a gas (air) the attractive forces are referred to as surface tension

but the attractive forces between two immiscible liquids are referred to as interfacial tension.

Temperature and molecular weight have a significant effect on surface tension of crude oil and crude oil products (Speight, 2014a, 2015b).

For example, in the normal hydrocarbon series, a rise in temperature leads to a decrease in the surface tension.

but an increase in molecular weight increases the surface tension.

A similar trend, that is, an increase in molecular weight causing an increase in surface tension, also occurs in the acrylic series and, to a lesser extent, in the alkyl benzene series.

Surface Tension and Its Measurement

2.7.2 Measurement for Solids: Liquid Homolog Series

Surface tension of solid plastics is determined indirectly, usually by contact angle methods.

A problem with the direct measurement of surface tension arises from the difficulty in the reversible formation of a solid surface.

Table 2.3 shows a list of methods that can be applied to measure the surface tension of solids.