Rough Particles with Many Edges

The work of emergence from the oil phase, of each of the configurations of this rough particle at the oil-water surface may be calculated in a similar manner to W° by using Equation 4.76 if due allowance is made for the relevant geometry. If again we assume that the particles are small relative to the size of the oil drops, then we find 

Calculations of W °/Cq X for a particle that satisfies both conditions 4.72 and 4.77, so that 

Work of Emergence into Oil-Water Surface w/ of an Axially Symmetrical Particle with Regular Rugosities 

Source Adapted from Garrett, P.R., Mode of action of antifoams, in Defoaming, Theory and Industrial Applications (Garrett, P.R., ed.), Marcel Dekker, New York, Chp 1, p 1 1993. 

We therefore have two sets of conditions for the effectiveness of a rough particle in rupturing air-water-oil pseudoemulsion films while not rupturing air-water-air foam films. For partial wetting oils with no spread oil layer at the air-water surface. 

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It is tempting to generalize from this example that for rough particles with many edges and asperities, the contact angle for destabilization cannot be specified with certainty so that antifoam effects will even occur with 0 < 90° (provided condition 4.62 is satisfied). However, destabilizing configurations for O w < 90° will occur only with low probability, so that the overall antifoam behavior will be relatively weak... 

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