Contact Angle

The equilibrium state for the attached bubble is described by the contact angle, 6, as indicated in Figure 2. The contact angle for this three-phase equilibrium is related to the respective interfacial tensions by Young's equation,

The attachment process should be spontaneous for all finite contact angles, but generally a contact angle of at least 20° is required for bubble attachment and flotation. The greater the contact angle, the greater the hydrophobicity. Of course contact angles much greater than 20° are desired in order to make effective flotation separations. Generally the characteristic contact angles for flotation systems rarely exceed 100°. Typical values for naturally hydrophobic minerals are given in Table 2. Larger contact angles are

Figure 2 Equilibrium state for water drop at a hydrophobic surface.
Table 2 Naturally hydrophobic minerals and respective contact angles

Mineral

Composition

Surface

Contact angle

plane

(degrees)

Graphite

C

0001

86

Coal

Complex hydrocarbon

20-60

Sulfur

S

85

Molybdenite

MoS2

0001

75

Stibnite

Sb2S3

010

Pyrophyllite

Ah(Si4O10)(OH)2

001

Talc

Mg^SuO^OH^

001

88

Iodyrite

AgI

20

possible for specially prepared surfaces which are highly water repellant. For example, water contact angles exceeding 150° have been observed for specially prepared surfaces as shown in Figure 3.

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Solar Panel Basics

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