Electrohydrodynamics Near Hydrophobic Surfaces

We show that an electro-osmotic flow near the slippery hydrophobic surface depends strongly on the mobility of surface charges, which are balanced by counterions of the electrostatic diffuse layer. For a hydrophobic surface with immobile charges, the fluid transport is considerably amplified by the existence of a hydrodynamic slippage. In contrast, near the hydrophobic surface with mobile adsorbed charges, it is also controlled by an additional electric force, which increases the shear stress at the slipping interface. To account for this, we formulate electrohydrodynamic boundary conditions at the slipping interface, which should be applied to quantify electro-osmotic flows instead of hydrodynamic boundary conditions. Our theoretical predictions are fully supported by dissipative particle dynamics simulations with explicit charges. These results lead to a new interpretation of zeta potential of hydrophobic surfaces.

Figure 1

Sketch of the system in the case of an asymmetric channel with one no-slip wall. In the case of a symmetric channel, both slippery walls are equal. Fixed surface charges are in the walls; mobile surface charges are adsorbed to the neutral walls. This is important for a definition of $H$ in simulations, but not in the theory, where ions are pointlike, so that $d$ is infinitesimally thin.

Figure 2

Top: Lennard-Jones adsorption potential applied in simulations. Bottom: a concentration profile of adsorbed ions and the model with homogeneous charge distribution inside the adsorbed layer.

Figure 3

(a) Fluid velocity profiles simulated at $q_2/q_1=1$ and $\kappa H=12$ (symbols). Circles correspond to a hydrophilic channel; squares and triangles represent a channel with a hydrophobic surface, $b/H=1.2$, with $\mu =1$ and 0. Solid curves show solutions of linearized Eq. (4); dotted lines are predictions of Eq. (5). (b) Corresponding cation (filled symbols) and anion (open symbols) profiles obtained in simulations with the theoretical expectations (dotted curves).

Figure 4

Fluid velocity profiles simulated at $\kappa H=12$, $b/H=1.2$, $q_2/q_1=0,1,2,3$, and $\mu =0$. Solid curves show theoretical results; dotted lines are predictions of Eq. (5).

Figure 5

Fluid velocity profiles simulated at $\kappa H=12$, $q_2/q_1=2$, and $\mu =0$ (symbols). From top to bottom, $b/H=0$, 1.2, and $\infty$. Solid curves show theoretical results; dotted lines are predictions of Eq. (5).

Figure 6

Fluid velocity profiles in a symmetric channel simulated at $\kappa H=11$ and $\mu =0$ (symbols). Upper curves were simulated at $b/H=0$, 0.08, 1.3, and 2.4; bottom curve corresponds to $b/H=\infty$. Solid curves show theoretical results; upper dotted lines are predictions of Eq. (7); and lower dotted lines are predictions of Eq. (8).