Extension of continuummechanics to the nanoscale

This is an extension of continuum mechanics to the nanoscale (not the molecular scale). In the context of continuum mechanics, nanoscale problems always involve the immediate neighborhood of a phase interface or the immediate neighborhood of a three-phase line of contact or common line. While the presentation is new, it is based upon a long history of important developments beginning with that of Hamaker (Physica 4 (1937) 1058). We test this theory by using it to predict both the surface tensions of the n-alkanes and the static contact angles for the n-alkanes on PTFE and for several liquids on polydimethylsiloxane. In the case of surface tension and like the best previous theory, one adjustable parameter is required. For the contact angle predictions, no adjustable parameters are used. In both cases, the results are compared with previously published experimental data. The results for the contact angle analysis also provide a successful test of a previously derived form of Young’s equation for the true, rather than apparent, common line. 2004 Elsevier Ltd. All rights reserved.