Figure 1

Segment of the MD simulation sample for an immiscible Couette flow with a $90°$ static contact angle. The small empty and solid circles indicate the instantaneous molecular positions of the two fluids projected onto the $xz$ plane. The horizontally aligned black and gray circles denote the wall molecules. Between the two fluids, the large hollow circles represent the time-averaged interface profile, defined by ${\rho }_1={\rho }_2$ ($\varphi =0$). The solid line is the interface profile calculated from the continuum hydrodynamic model.Reuse & Permissions

Figure 2

Log-log plot of the slip profiles showing the $1/x$ behavior. Here $v_x/V_w+1$ is the scaled slip velocity at the lower fluid-solid interface $z=0$, and $x/\sigma$ measures the distance from the MCL in units of $\sigma$. The wall is moving at $-V_w$; hence $v_x/V_w=0$ means complete slip and $v_x/V_w=-1$ means no slip. The $v_x$ profiles were obtained for five symmetric cases of identical wall-fluid interactions for the two fluids (both ${\delta }_{wf}=1$ and thus a $90°$ static contact angle). The five cases shown here used different values for $H$ but the same value for $V_w$ ($=0.05\sqrt{ϵ/m}$) and also the same parameters for densities and interactions. The symbols represent the MD results and the solid lines represent the continuum hydrodynamics results, obtained for $H=6.8\sigma$ (black circles and line), $H=13.6\sigma$ (red squares and line), $H=27.2\sigma$ (green diamonds and line), $H=54.4\sigma$ (blue up triangles and line), and $H=68\sigma$ (orange down triangles and line). There are two solid curves for each color, one curve for the slip profile left to the MCL and the other for the slip profile right to the MCL. The dashed line has the slope of $-1$, indicating that the $1/x$ behavior is approached for increasingly larger $H$. For $H=68\sigma$, the $1/x$ behavior extends from $|x|\approx 12\sigma \approx 6l_s$ to $50\sigma \approx 25l_s$, where $l_s$ was measured to be $2\sigma$. Inset: The scaled tangential velocity $v_x/V_w$ at $z=0$ is plotted as a function of $x/\sigma$.Reuse & Permissions

Figure 3

Log-log plot of the slip profiles showing the $1/x$ behavior. Here $v_x/V_w+1$ is the scaled slip velocity at the lower fluid-solid interface $z=0$, and $x/l_s$ measures the distance from the MCL in units of $l_s$. The wall is moving at $-V_w$; hence $v_x/V_w=0$ means complete slip and $v_x/V_w=-1$ means no slip. The black solid line denotes the case of $H=326\sigma$, $V_w=0.005\sqrt{ϵ/m}$, and $l_s=1.24\sigma$, the red dashed line denotes the case of $H=326\sigma$, $V_w=0.0025\sqrt{ϵ/m}$, and $l_s=1.24\sigma$, and the blue dotted line denotes the case of $H=326\sigma$, $V_w=0.0025\sqrt{ϵ/m}$, and $l_s=0.62\sigma$. The green dot-dashed line has the slope of $-1$, indicating a power-law region much wider than that in Fig. 2. Inset: Universal slip profile. The scaled tangential velocities $v_x/V_w$ at $z=0$ for all three cases are plotted as a function of the scaled coordinate $x/l_s$. It is seen that the slip profiles show a partial-slip region as large as hundreds of $l_s$. The relation $v_x/V_w=1/(1+|x|/2.14l_s)-1$ is also plotted by the orange dot-dashed line, showing an extremely good fit.Reuse & Permissions