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Examination of Fig. 4 reveals that d u z / d r, and hence d u ˜ z / d r, is steepest at the contact line, r ˜ = 1. In fact, for a substrate with infinite thickness, d I / d r is logarithmically singular at this point. The weak nature of this singularity, however, means that even large values of d / a produce d u ˜ z / d r ˜ that is of order 1. Furthermore, it is likely that local effects due to the contact line force and the surface tension of the solid will weaken the singularity [12].
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