Figure 1

Molecular configuration, velocity fields, and density profiles of fluids flowing through a patterned nanochannel. (a) A steady state snapshot of the dense system of 120 chain molecules in an $x\mathrm{\text{−}}z$ projection. (b) and (c) The velocity fields in the $x\mathrm{\text{−}}z$ plane for the dense and rarefied systems, respectively. The darker vectors represent velocities larger than the average speed at the center point of the system. In (b), the channel effectively widens leading to lower speeds on the right. In (c), the speed is higher in the repulsive region in spite of the increased effective width. (d) The density profiles for the dense (top) and rarefied (bottom) fluids. Three locations along the channel are shown for each case: the dotted, broken, and solid lines are for $x/\sigma$ around 5.6 (denoted by A), 13.8 (B), and 21 (C) corresponding to attractive walls, the transition region, and repulsive walls, respectively. The atoms of the inner walls are at the edges of the figure. In the wetting region, two monolayers form and make the effective width narrower. In the nonwetting region, the adsorption is absent thus the effective midpoint density falls on moving from A to C. This decrease [not discernible in (d)] is inconsequential for the dense case but explains the anomalous behavior of the velocity field in the rarified case.Reuse & Permissions

Figure 2

Nanoflow attributes for the dense (left panels) and rarefied (right panels) regimes. (a) The velocity profiles for the $x$ components of the flow velocity as averaged in strips located at points A (asterisks), B (squares), and C (circles) as in Fig. 1d. The lines are guides to the eye. One sees the Poiseuelle parabolic flow at A and B changing to plug flow at C. Dissipation at the attractive walls leads to stationarity of the flow that is missing for purely repulsive walls. (b) The slip length, $\zeta$, along the length of the channel. The arrow shows the location of the switchover in wettability. $\zeta$ is obtained as a linear extrapolation of the flow profile and is a measure of the distance from the wall at which the extrapolated velocity vanishes. Positive (negative) $\zeta$ indicates that the extrapolated velocity vanishes outside (inside) the channel. $\zeta$ is negative for the attractive region but becomes positive and large when the fluid is within repulsive walls. The effective viscosity, as measured from the curvature of the velocity profiles at the midpoint of the channel, is also a function of location along the channel and it follows the behavior of $\zeta$. (c) The maximum velocity, $v_{x,\max }$, occurring halfway between the walls, as a function of $x$. It grows on crossing the wettability step in the rarefied case but decreases in the dense case.Reuse & Permissions

Figure 3

Snapshots of droplets on a solid substrate. The pictures show a view (projection) from the top and a three-dimensional depiction of the droplet in a side view (bottom). The left pictures refer to a patterned substrate with periodic squares with $A=A_1=3/8$ superposed on a background of $A=A_2=1/4$ while those on the right depict a homogeneous surface with $A=3/8$ corresponding to partial wetting. Smaller values of $A$ typically lead to the detachment of the droplet. The choice of the $A_1$ and $A_2$ coefficients was dictated by the requirement of marginal attachment. Note that the contact angle is larger for the patterned substrate resulting in “superhydrophobicity.” In some of our runs with the patterned substrate, the droplet detaches when pushed laterally.Reuse & Permissions

Figure 4

The “lotus” effect. Top: the time dependence of the longitudinal displacement of the center of mass of the droplets pushed with $g=0.002{\tau }^2/\sigma$ along the $x$ direction averaged over four runs. For the homogeneous substrate the droplet hardly moves but the motion is rapid for the patterned substrate. Bottom: the time dependence of height $z$ above the substrate of droplet atoms (two on the left, one on the right) which are initially close to the surface of the droplet and the wall. The nearly horizontal line indicates the location of the center of mass of the droplet and provides a reference. The pictures suggest rolling motion [18] combined with diffusion for the patterned substrate (left) and pure diffusion for the homogenous substrate.Reuse & Permissions