Partial Coalescence of Particles in Chains

When two silica particles unite in water, they grow together because the solubility of silica in the crevice at the point of contact is less than that of the silica over the surface of the particle. The neck joining the particles therefore increases in diameter, until the difference in solubility becomes small. There is, of course, no true equilibrium, since the equilibrium condition would be represented when the two particles became fused together, first into an oval and finally inter one large spherical particle. 

The rate of thickening of the neck between the two particles will become very slow after a certain point. This point can be estimated by the following reasoning  

Under the given conditions, the rate of growth of the neck will become very slow when the effective negative radius of curvature, r , at the neck, is numerically greater than a certain value. The solubility at the neck S will be less than S, / since Sn/S, f = exp(/T/r ) and / has a negative value. 

It seems logical to believe that if the growth of discrete particles becomes slow when 5a - 5 reaches a low value, then under the same aging conditions the neck between two particles will likewise grow only slowly when St - 5 reaches the same low value. Thus 

Using the equation given later in this chapter for relating solubility to particle diameter  

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