A micromechanical derivation of the differential equations of interfacial statics. III. Line tension

摘要: Abstract A continuum-mechanical theory of line-excess tension and adsorption is developed, quantitatively relating phenomena directly to the density-gradient intermolecular forces existing in neighborhood three-phase contact line. This purely mechanical (i.e., nonthermodynamic) rigorously derived via singular perturbation methods, utilizing a small parameter expansion involving ratio microscopic length scale over which act an appropriate macroscale associated with macroscopic attributes (depth, curvature, lens radius, etc.) bulk phases. “Slender-body” serves as geometrical basis scheme, “body” axis oriented along In sense matched asymptotic expansions, scheme automatically derives proper pair “boundary conditions” at common intersection phases, Specifically, these boundary conditions link together “outer” or stress fields within three interfaces separating Of two thereby by matching inner outer condition normal line found be identical so-called “generalized Neumann force balance” Buff Saltsburg, tension. The second condition, tangent line, arising from line-tension gradients, appears new. nonequilibrium circumstances (where this gradient not balanced external stress) it represents potential source lineal Marangoni flow phenomena, analogous comparable areal interfaces. Developments techniques reported herein constitute counterparts micromechanical surface-excess preceding papers series.