Page 377 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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v
Hg
P
H 2O 8. APPLICATIONS: ESTIMATION OF TRANSPORT PROPERTIES 357
v
h P
Nonwetting P v P v
θ Wetting h
θ
Liquid
FIG. 8.16—The contact angle of a
liquid surface and concept of wetta- a-Wetting Fluid b-Nonwetting Fluid
bility.
FIG. 8.17—Wetting and nonwetting liquids
wettability. Consider droplets of water and mercury on a solid in capillary tubes.
surface as shown in Fig. 8.16. For mercury θ> 90 and it
◦
is called a nonwetting fluid, while for water with θ< 90 is radius of tube decreases the height of liquid rise increases. In
◦
an example of a wetting liquid. For other liquids θ is varying the case of oil and water, Eq. (8.82) becomes
between 0 and 180 and have different degrees of wettability. 2σ wo Cosθ
◦
Equation (8.80) was derived on the assumption that the (8.83) h = (ρ − ρ ) gr
o
w
droplet is spherical. However, when a liquid is in contact with
a solid surface where the liquid curvature is not fully spherical where σ wo is the interfacial tension between oil and water
o
W
the above equation is corrected as phases. ρ and ρ are density of water and oil, respectively.
3
In this equation, if σ wo is in N/m and ρ is in kg/m , then h and
2σ Cosθ
V
L
(8.81) P − P = r must be in m.
r The instrument that measures surface tension of a liquid
For a fully nonwetting liquid θ = 180 ◦ (or Cosθ =−1), is called tensiometer, which may be manual or digital. Most
Eq. (8.81) reduces to Eq. (8.80). If a wetting liquid (i.e., water) commonly used methods of measuring surface tension in-
and a nonwetting liquid (i.e., mercury) are placed in two cap- clude classical ring method, capillary rise, pendant drop, and
illary tubes of radius r (diameter 2r), the wetting liquid rises bubble pressure. The pendant method is most commonly used
while nonwetting liquid depresses in the tube, as shown in to measure surface tension of liquid oils. Schematic of appa-
Fig. 8.17. The height of liquid rise is determined from the ratus to measure interfacial tension using the pendant drop
V
L
V
L
pressure difference P − P [= (ρ − ρ )gh] in which by sub- method is shown in Fig. 8.18 [59]. Millette et al. [60] recom-
stituting into Eq. (8.81) one can get: mend maximum bubble pressure method to measure surface
tension of hydrocarbons at high temperatures and pressures.
2σ Cosθ
(8.82) h = Most advanced instruments can measure surface tension with
V
(ρ − ρ ) gr
L
an accuracy of ±0.001 mN/m.
V
L
where ρ and ρ are the liquid and vapor density, respectively, Surface tension usually decreases with both pressure and
2
and g is the acceleration of gravity (9.8 m/s ). At low or atmo- temperature. Effect of temperature is greater than effect of
V
spheric pressures where ρ
ρ , for simplicity ρ can be ne- pressure on surface tension. As pressure increases the dif-
V
L
V
L
L
V
glected. At high pressures, the pressure difference (P − P ) ference between (ρ − ρ ) decreases and as a result surface
causes liquid rise and it is called capillary pressure shown by tension also decreases, according to Eq. (8.82). The effect of
P cap . For nonwetting liquids, such as mercury, where θ> 90 , pressure on IFT is discussed later. Surface tension increases
◦
Cosθ< 0 and according to Eq. (8.81) the liquid depresses in with increase in molecular weight of a compound within a ho-
the tube as shown in Fig. 8.17. From this equation, when the mologous hydrocarbon group. Some values of surface tension
FIG. 8.18—Schematic of apparatus to measure interfacial tension using the
pendant drop method. Taken with permission from Ref. [59].
(1) anti-vibration table; (2) light source; (3) optical rail; (4) light diffuser; (5)
iris; (6) green filter; (7) thermostated interfacial tension cell with optical flats;
(8) syringe to form pendant drops; (9) thermostat; (10) photomacrographic
Tessovar zoom lens; (11) CCD camera; (12) computer with digitizing board.
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