Figure 1

(a) Cross-sectional view of the simulated system. Walls are made of silicon atoms. (b) A schematic showing patched wettability of the substrate.Reuse & Permissions

Figure 2

Water contact angle on (a) a Si atom wall (C${}_{\mathrm{Si}-\mathrm{water}}$ $=$ 1) (θ $=$ 48°) and (b) a modified Si atom wall (C${}_{\mathrm{Si}-\mathrm{water}}$ $=$ 0.548) (θ $=$ 119°), which may be perceived as a consequence of hydrophobic patterning on the Si.Reuse & Permissions

Figure 3

Schematic representation of (a) checkerbox patched, (b) vertically patched, and (c) horizontally patched patterns of substrate atoms, with red crosses denoting the atoms with lower strength of wettability (hydrophobic) or surface charge density. The solid circles represent atoms with higher strength of wettability (hydrophilic) or surface charge density. (d) SPC/E water molecule, ${\sigma }_{\mathrm{water}}$ $=$ 0.3166 nm.Reuse & Permissions

Figure 4

Water and Na${}^{+}$ concentration profile for (a) hydrophobic substrate with high surface charge density, (b) hydrophilic substrate with high surface charge density, (c) hydrophobic substrate with low surface charge density, (d) hydrophilic substrate with low surface charge density.Reuse & Permissions

Figure 5

Solvent concentration maps (in M) for the configuration [red crosses and circles described as per Figs. 3a, 3b, 3c] as follows: (a) horizontally patched [as Fig. 3c] over a uniformly hydrophobic surface that is negatively charged with crosses indicating low surface charge patch and circles indicating high surface charge patch, (b) checkered patched [as Fig. 3a] over a uniformly hydrophobic surface that is negatively charged with crosses and circles representing same as in (a), (c) vertically patched [as Fig. 3b] over a uniformly hydrophobic surface with crosses representing patches with low surface charge densities and circles representing patches with high surface charge density, (d) vertically patched [as Fig. 3b] over a surface with uniform high surface charge density and crosses representing hydrophobic and circles representing hydrophilic patches (e) checkered patched [as Fig. 3a] with crosses representing hydrophobic patches with low surface charge densities and circles representing hydrophilic patches with high surface charge density, (f) checkered patched [as Fig. 3a] with crosses representing hydrophobic patches with high surface charge density and circles representing hydrophilic patches with low surface charge density, (g) horizontally patched [as Fig. 3c] with crosses representing hydrophobic patches with low surface charge densities and circles representing hydrophilic patches with high surface charge density, and (h) horizontally patched [as Fig. 3b] with crosses representing hydrophobic patches with high surface charge density and circles representing hydrophilic patches with low surface charge density.Reuse & Permissions

Figure 6

Flow pattern over the surface, where (a)–(h) correspond to the cases present in Figs. 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h. The continuous lines indicate the streamlines of the flow [Re ∼ $O$(1)]. As in Fig. 5, the streamlines are computed by the binning technique in a 15 × 15 grid on the $x$-$y$ plane (parallel to the wall and positioned 0.5 nm away from it), time averaged over 1 ns.Reuse & Permissions

Figure 7

Slip length (in nm) contours where cases (a)–(h) correspond to cases presented in Figs. 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h.Reuse & Permissions

Figure 8

Dimensionless vorticity ($C_z$) where cases (a)–(h) correspond to cases presented in Figs. 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h in the same order.Reuse & Permissions

Figure 9

Nondimensional vorticity contours and transverse velocity ($V_z$) maps over patched substrates where case (a) corresponds to uniform wettability (hydrophobic) substrate with vertically patterned surface charge densities, case (b) corresponds to uniform wettability (hydrophobic) substrates with checkerbox patterned surface charge density, case (c) corresponds to uniform high surface charge density substrates with vertically patterned wettability, and case (d) corresponds to uniform low surface charge density substrates with horizontally patterned wettability. The flow is in the positive $x$ direction.Reuse & Permissions