Local orientations of fluctuating fluid interfaces

Abstract

Thermal fluctuations cause the local normal vectors of fluid interfaces to deviate from the vertical direction defined by the flat mean interface position. This leads to a nonzero mean value of the corresponding polar tilt angle which renders a characterization of the thermal state of an interface. Based on the concept of an effective interface Hamiltonian we determine the variances of the local interface position and of its lateral derivatives. This leads to the probability distribution functions for the metric of the interface and for the tilt angle which allows us to calculate its mean value and its mean square deviation. We compare the temperature dependences of these quantities as predicted by the simple capillary wave model, by an improved phenomenological model, and by the microscopic effective interface Hamiltonian derived from density functional theory. The mean tilt angle discriminates clearly between these theoretical approaches and emphasizes the importance of the variation of the surface tension at small wave lengths. Also the tilt angle two-point correlation function is determined which renders an additional structural characterization of interfacial fluctuations. Various experimental accesses to measure the local orientational fluctuations are discussed.

Brownian diffusion of a partially wetted colloid

“…The line segment λ here corresponds to the correlation lengths of capillary waves, λ ≈ 1/k max (ref. 27), which represents the typical deformation size induced by fluctuating capillary waves. In the expression for the friction coefficient γ T,L (equation (2)), α ∼ 1 is now the average angle of the interface with respect to the horizontal because of capillary waves 27 (Fig.…”

Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves

“…(20), where σ ∞ was cleared of CW using Eq. (28). This is a prediction considered as correct, because, as discussed in Sec.…”

“…(20) based on the "bare" surface tension of the planar phase interface that was obtained from the experimental surface tension using Eq. (28). (See Appendix B for more information about the experimental surface tensions.)…”

“…Meunier's approach, developed for planar phase interfaces, is used in this work to estimate the effect of CW on the surface tension for droplets (clusters) relevant to nucleation. Mecke, Dietrich and Napiórkowski [26][27][28] derived an effective Hamiltonian combining the effect of DFT and CW and surface tension depending on the wavenumber q. Their complex CW model differs significantly from the traditional 21 approach.…”

“…and bare surface tension σ bare , Eqs (20). and(28). Inset is the detail of the beginning where the lines cross.…”