Adhesion Forces

Three primary adhesive forces are responsible for the aggregation of aerosols: van der Waals, electrostatic, and capillary [232,261] (Fig. 9). For dry powders, all three forces may play important roles. Interactions between particles in suspension include only van der Waals and electrostatic forces.

Figure 9 Comparison of primary adhesion forces between aerosol particles. (Reprinted from Ref. 261. Courtesy of Marcel Dekker, Inc.).

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Figure 9 Comparison of primary adhesion forces between aerosol particles. (Reprinted from Ref. 261. Courtesy of Marcel Dekker, Inc.).

The van der Waals (VDW) attractive forces are the principal forces between dry, noncharged spherical aerosol particles [262] and may reduce stability and cause flocculation of suspended particles. The VDW forces arise from the attractive forces between permanent dipoles (Keesom forces), induced dipoles (London forces), and dipole-induced dipoles (Debye forces). For nonpolar or slightly polar compounds, the force of attraction between two particles with diameter d separated by a distance h (where h < d) is:

where the Hamaker constant, A, is dependent on the particle surface chemistry and surface roughness, the fluid surrounding the particles, and the separation distance between the particle surfaces [263,264].

Two types of electrostatic forces are important for small particles: the electrostatic image (coulomb) force and the electric double-layer force. Electrostatic forces can accumulate during particle formulation and/or use in an inhaler [265]. However, it has been shown that electrostatic forces do not play an important role in the adhesion of dry uncharged particles, since VDW forces dominate [266]. In addition, large nonequilibrium charges on dry particles are necessary for electrostatic forces to become significant. Suspended particles can acquire a surface charge by interactions with molecules such as surfactants, the suspending liquid, and water.

Coulomb forces result from the interaction between a charged surface and another charged or neutral surface. These forces can be attractive or repulsive, depending on the charge of each surface, and are relevant for particles with diameters larger than 5 mm [267]. For two-point electric charges separated by a distance h, Coulomb's Law gives:

where qj and q2 are the electric charges on the particles and e0 is the dielectric constant of the medium. For particles in contact, with h ! d:

where sj and s2 are the surface charge densities of the particles and d is the diameter of the particles.

Electric double-layer forces result from the contact between two compounds of different contact potential. In a dry environment, electric double-layer forces are only significant for particles less than 5 mm in diameter [267]. Lewis acid-base interactions, determined by the chemical composition of the surface, may be used to alter the adhesion of particles. However, if capillary bridges are present between the particles in a dry environment, electric forces cannot develop [268]. For particles in suspension, the electric double layer forms when counterions in the solution balance the charge on the particle surface. The resultant forces are important for the stability of colloidal systems [255]. Two similarly charged surfaces will repel each other unless the distance between the surfaces is decreased to a critical distance, whereupon the surfaces will become adherent [255].

Capillary forces develop when liquid bridges are formed in small gaps between two surfaces. Above a critical relative humidity, capillary forces are the dominant attractive force between aerosol particles [269,270]. The magnitude of this force depends on other parameters as well, such as particle surface chemistry and size. For two particles attached by a liquid bridge, the adhesive force is [260]:

where R is the radius of the particles and gL is the liquid surface tension.

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