An integrated model based on transient flow and the nanoconfinement effect of water transport through nanopores

The property of water confined in nanopores is significantly different from that of bulk water, resulting in a great influence on the rate of water development during the unsteady state. In this study, we focused on the unsteady behavior of water transport in nanopores. We established a transient equation and applied the Laplace transform and Bessel function of the imaginary argument according to the time-dependent momentum conservation equation of Poiseuille-flow. The apparent density, apparent viscosity, and slip of the confined water were modeled by considering the water-wall interactions and the pore size. Moreover, the transient transport equation was modified by these three models to obtain a transient analytical model, which considered the effect of the nanoconfinement effect. We verified the credibility of the proposed model compared with other models as well as through experiments and molecular dynamics simulations. The results indicated that the development rate of water confinement in the superhydrophobic nanopores was much greater than that in intermediate wettability and hydrophilic pores, and its velocity profile behaved as an approximately straight line throughout the unsteady state. Slip in the intermediate wettability pores was more likely to transmit its effects to the pore center than in hydrophilic pores. We found that small hydrophilic pores were dominated by the apparent density and apparent viscosity in the unsteady state, whereas large hydrophilic pores were dominated by slip in the initial state, which gradually changed to apparent density and apparent viscosity with time. For the superhydrophobic pores, regardless of pore size, slip was the main controlling factor in the unsteady state. Additionally, the sensitivity of confined water stabilization time to pore size was much greater in the superhydrophobic pores than in the hydrophilic pores.