Hidden microscopic life of the moving contact line of a waterlike liquid

We have used large-scale molecular dynamics (MD) simulations to investigate the contact-line friction of a waterlike liquid interface moving across a flat solid surface. The dynamic contact angle ${\theta }_D$ has been measured as a function of contact-line speed $U_{cl}$ using two configurations: a liquid drop spreading spontaneously on a stationary solid surface and a liquid bridge in Couette flow between two solid surfaces moving in opposite directions at a range of steady speeds. The wettability of the solid surface was systematically varied to give a range of equilibrium contact angles ${\theta }^0$ from 38 to 126 deg. The coefficient of contact-line friction $\zeta$ was determined from the expression $\zeta U_{cl}={\gamma }_L(cos{\theta }^0-cos{\theta }_D)$, where ${\gamma }_L$ is the surface tension of the liquid. This simple linear equation, which maybe derived from the molecular-kinetic theory (MKT) of dynamic wetting, is predicted to apply at sufficiently low values of $U_{cl}$. In addition, we have applied a Langevin formalism to extract the coefficients of contact-line friction directly from the equilibrium fluctuations of the contact line, without any additional theoretical interpretation or model. Both approaches yield the same values for the coefficient within the probable uncertainty, confirming that this intriguing property is determined only by equilibrium properties. Overall, our results show that contact-line friction is a real phenomenon, intrinsic to wetting and applicable to real liquids such as water. Thus, models of dynamic wetting that ignore it are incomplete. From a practical perspective, the concept of a simple linear relationship between surface tension driving force and contact-line velocity may provide a useful simplification in many areas such as nanotechnology where contact-line speeds can be low. Another finding from our study is that slip between water and a molecularly flat, partially wetted solid surface is minimal, with slip lengths of little more than the diameter of a water molecule for equilibrium contact angles of 90 deg or less. Furthermore, we have confirmed a mechanistic link between the coefficients of slip and contact-line friction, specifically $\beta =\zeta /\delta$, where $\delta$ is the thickness of the contact line when viewed at the molecular scale. Thus measurements of the dynamic contact angle or contact-line fluctuations may potentially be used to predict slip and vice versa.

Figure 1

(a), (b), and (c): Snapshots of drop spreading simulations at successive times $t=0, 0.09,$ and $1.1$ ns, respectively. (d), (e), and (f): Snapshots of capillary bridge simulations for plate velocities $U_{\mathrm{plate}}=0$, 16, and 24 m/s, respectively. All correspond to a solid-liquid interaction coupling $C_{SL}=9$.

Figure 2

(a) Drop profile and circular fit at equilibrium for $C_{SL}=11$. (b) Bridge profile and circular fits at equilibrium for $C_{SL}=11$. (c) Comparison of the equilibrium contact angles obtained for the spontaneous spreading and liquid-bridge simulations.

Figure 3

Evolution of (a) radius of contact $x_{cl}\left(t\right)$ and (b) dynamic contact angle ${\theta }_D\left(t\right)$ for spreading drop simulations with five different solid-liquid affinities $C_{SL}$.

Figure 4

Spreading drop simulations. The main chart shows the capillary driving force ${\gamma }_L(cos{\theta }^0-cos{\theta }_D)$ plotted vs contact-line velocity $U_{cl}$ for coupling $C_{SL}=11$. The dashed line is the fit to Eq. (2) (open symbols). The inset shows the contact-line friction ${\zeta }_{SP}$ for all couplings studied vs the corresponding equilibrium contact angle.

Figure 5

(a) Ratio of $U_{1L}/U_{\mathrm{plate}}$ and (b) the slip length $L_{\mathrm{slip}}$ for simulations of a liquid bridge between moving plates. Both are plotted vs the equilibrium contact angle. Also plotted in (b) are the slip lengths obtained using Eq. (8), with $\delta =1.06$ nm, ${\eta }_L=0.64$ mPa s, and averaged values of $\zeta$ from Table 1. The solid line is the correlation proposed by Huang et al. [45].

Figure 6

Forced wetting of a liquid bridge between moving plates. The main chart shows the capillary driving force ${\gamma }_L(cos{\theta }^0-cos{\theta }_D)$ plotted vs the contact-line velocity $U_{cl}=-(U_{\mathrm{plate}}+U_{\mathrm{slip}})$ for each coupling $C_{SL}$ studied. The inset shows the corresponding coefficients of contact-line friction ${\zeta }_{MP}$ vs the equilibrium contact angle.

Figure 7

Probability density function (PDF) of the contact-line position about its mean location computed from the Gaussian fits (lines) to the density histograms (symbols) for a contact line of length $\mathrm{\Delta }y=L_y$ and solid-liquid couplings $C_{SL}\in [5,14]$. Inset: Computed ${\sigma }^2{L}_y$ parameters vs the average equilibrium contact angle.

Figure 8

Normalized self-correlation function ${\langle x_{cl}(t+t_0)x_{cl}\left(t_0\right)\rangle }_{t_0}/{\sigma }^2$ vs time $t$ for $C_{SL}=5$ and the fit to Eq. (6). Inset: Decay parameter $b$ vs the average equilibrium contact angle.

Figure 9

Comparison of the contact-line friction coefficients measured by our three different simulation methods vs the equilibrium contact angle ${\theta }^0$: spontaneous spreading ${\zeta }_{SP}$, moving plates ${\zeta }_{MP}$, and fluctuations ${\zeta }_F$.