Enhanced electroosmotic flow in a nano-channel patterned with curved hydrophobic strips

We consider the electroosmotic flow (EOF) in a nano-channel in which the channel walls are modulated with a periodic array of curved hydrophobic patches. The objective is to achieve an enhanced flow compared to a slit nano-channel. The shape of the hydrophobic strips are considered to be of sinusoidal form, which resembles the situation in which the channel indentations are filled with immiscible nonconducting fluid over which the electrolyte is considered to be in metastable Cassie state. The homogeneous no-slip portions of the channel walls are considered to posses a constant surface-potential (zeta-potential) or constant surface charge density, while the hydrophobic regions are uncharged. A mathematical model based on the Nernst-Planck-Navier-Stokes equations are considered to analyze the present EOF. A coordinate transformation is adopted to map the irregular physical domain to a regular computational domain. A pressure-correction based control volume approach is adopted to solve the governing equations. We have studied the EOF by varying the amplitude of the hydrophobic region. Our results show that an enhancement in EOF compared to a slit-channel is possible when the Debye length is in the order of the channel height. The EOF in the patterned channel varies with the planform length of the hydrophobic region as well as the relative span of the slip and no-slip regions. A comparison with the pressure-driven flow is also presented to analyze the hindrance created by the electric body force of the unbalanced ions.