Some considerations of fluid interfaces in two dimensions (Q580129)

Basic assumptions of the capillary wave theory of fluid interfaces are examined critically as a function of space dimensionality d. When the predictions of capillary wave theory are compared with those of the nonclassical Maxwell-van der Waals theory, agreement is found in \(d=3\) and 4, but strong disagreement occurs in \(d=2\). It is shown that the total effective mass density obtained from the Hamiltonian describing the collective capillary wave excitations has a logarithmic divergence in \(d=2\). This result suggests the possibility of anomalous behavior for fluid interfaces in \(d=2\).