Particle Deposition at Surface Features

Interpretation of numerical results obtained in this case is facilitated by the fact that a few analytical solutions exist in the limit of line segments and infinitely long lines (thin stripes). Also, useful analytical expressions can be derived for surface features whose surface area is considerably larger than the particle cross-section area [57]. 

This value of 0=oid, referred to as the jamming limit in one dimension, was obtained originally by Renyi and others [59, 60]. Interestingly, a very similar value of the jamming limit (i.e. 0.7506) was obtained in the diffusion RSA process solved analytically in Ref [61]. 

Knowing 0ooid one can predict that in the limit I/d 3 1 (infinitely long line), the averaged number of particles adsorbed on the collector is given by  

In contrast, for 2D collectors (circles, rectangles), one can predict that in the case when adsorbing particles are much smaller than the collector characteristic dimension, that is, if L/d 3 1, the limiting expression for the averaged number of adsorbed particles is given by 

With an intermediate range of the L/d and hjd parameters, meaningful results can be obtained by numerical simulations only, which have been performed for line segments, either rectilinear or bent [56], as well as for circles, rectangles and stripes [57]. 

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Figure 11.5 Schematic representation of particle deposition at surface features.

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