Memory Effects in Contact Line Friction

TL;DR

This work reveals that dynamic wetting involves strong non-Markovian contact-line friction arising from coupling to bulk hydrodynamics rather than fast single-molecule processes. By formulating a generalized Langevin equation and extracting the memory kernel from equilibrium fluctuations, the authors obtain the full frequency-dependent friction $ζ(ω)$ and identify a long-time power-law decay $t^{-2/3}$ governed by hydrodynamic modes. Friction decreases with frequency beyond a characteristic scale, leading to predominantly elastic response at high frequencies and linking nanoscale dissipation to macroscopic hydrodynamics. The proposed Mori-Zwanzig framework provides a practical protocol to predict dynamic wetting behavior from equilibrium data and challenges traditional Markovian or molecular-kinetic models of contact-line motion.

Abstract

When a drop of liquid comes into contact with a solid surface, it relaxes towards an equilibrium configuration, either wetting the surface or remaining in a droplet-like shape with a finite contact angle. The force driving the process towards equilibrium is the corresponding out-of-balance Young's force. However, the speed with which the liquid front advances depends strongly on an opposing friction force arising from dissipative processes due to the moving solid-liquid-gas contact line. In analogy to the treatment of hydrodynamic friction we present an exact method, based on the Mori-Zwanzig formalism, to extract this friction from equilibrium data. We find that the contact line exhibits long-lasting memory with a characteristic power-law decay due to coupling to the systems hydrodynamic modes. Within linear response regime, we obtain the frequency-dependent dissipative and elastic response of the contact line to an external perturbation, including a frequency-dependent friction coefficient. Similar to hydrodynamic friction in liquids, we find that the friction decreases beyond a characteristic frequency and the system exhibits predominantly elastic behavior.

Figures (3)

• Figure 1: (a) A simulation snapshot of the water–graphene liquid bridge viewed in the $xz$-plane. (b) A schematic illustration of how the density field is calculated to obtain a continuously changing field in time. The black dots indicate the center of each grid cell with cell length $l$ and $\Delta x$ and $\Delta z$ the distance of the particle to the lower left cell along the $x$- and $z$-axis respectively. The contribution of a particle (blue circle) to the density field is distributed to the four nearest grid cells via bilinear interpolation, e.g., the contribution to the bottom left cell is given by $(l-\Delta x)(l-\Delta z)/l^2$. (c) The instantaneous density profile $\rho(x, z)$ in the $xz$-plane and (d) its ensemble average $\expval{\rho(x, z)}$. (e) The density profile along $x$ at $z_{\mathrm{Cl}}$ for the instantaneous density (dotted blue line) and its time average (dashed blue line). Both profiles are approximated with Eq. \ref{['eq:fit']} (solid red lines) to determine the contact line position from the interfacial position. (f) The resulting trajectory of the contact line position $X$.
• Figure 2: (a) the VACF and (c) the corresponding memory kernel $K$ for an LJ-octamer fluid confined between generic solid plates, and (b) the VACF and (d) the corresponding memory kernel for water confined between graphene sheets. For both systems, the VACF and, to a lesser extent, the memory kernel are well captured by a short-time expansion of the form $1 - (t\omega_0)^2$ (dotted black lines) with the slope approaching zero for $t\rightarrow 0$. This indicates that the contact line velocity is a well-defined observable. At long times, both the VACF and memory kernel decay according to a power law (dashed black lines) with an exponent of $2/3$.
• Figure 3: The dissipative $\Re(\hat{\Upsilon})$ (solid red lines) and elastic $\Im(\hat{\Upsilon})$ (solid purple lines) response of the contact line of a) an LJ-octamer fluid confined between generic solid plates, and b) water confined between graphene sheets. The real part of the half-sided Fourier transform of the memory kernel $\Re(\hat{K}_{+})$, corresponding to the frequency-dependent contact line friction $\zeta(\omega)$ (solid yellow lines), and the imaginary part of the transform $\Im(\hat{K}_{+})$ of c) an LJ-octamer fluid confined between generic solid plates, and d) water confined between graphene sheets.