5. Single-Phase Velocity Profile Comparison between H-H and P-H Pores

This section focuses on the effect of the electric field single-phase velocities for different pore sizes for a fixed acceleration of 0.002 nm/ps2 in P-H and H-H pores. The results are shown in Fig. 14 indicating that the P-H nanopore exhibits flatter flow profiles at the pore center due to the presence of the electric field as shown in Fig.5.
Normally, adsorption is the result of van der Waals forces, covalent bonding and electrostatic attraction101. In this work, we do not consider covalent bonding102. Therefore, in our study, adsorption is solely due to the van der Waals force and electrostatic attraction. Adjacent to the surface, these forces impact fluid transport. However, van der Waals force quickly diminish for increasing distances from the pore surface 103, while the long-range electrostatic interaction can extend tens of nanometers32.
Therefore, in the P-H pore, fluid transport is controlled by the electric field and imposed acceleration, leading to a flat pattern as shown in Figs.14a-b. Increasing pore sizes for P-H pores increases the width of flat pattern as shown in Figs.14c-d because of the increase in the width of the zone dominated by the electric field. However, in H-H nanopore, there is a negligible electric field at the nanopore center. Therefore, classical parabolic shaped patterns are observed in H-H nanopores as shown in Fig.14.