Modeling Disjoining Pressures in Submicrometer Liquid-Filled Cylindrical Geometries

摘要

This work develops models for calculating the disjoining pressures of a cylindrical fluid "plug," specifically in submicrometer cylindrical pores. This modeling produces closed-form, cylindrical-pore disjoining pressures for London/van der Waals and solute-pore-wall adsorption interactions, which are the slit-pore models with the characteristic pore size replaced by the radius and multiplied by 6, resulting in a 48-fold or more increase in magnitude. In addition, this work contains a numerical solution for electrostatic interactions. The result of the numerical solution was a 9-fold increase inthe modeled disjoining pressure compared to that in the slit-pore model. The cylindrical models may apply to the chemical coating of the interior walls of cylindrical pores or to the thermodynamics within droplets after the breakup of a fluid coating a surface. However, the application used as the base case in this paper is the extension of transport and thermodynamic laws for porous media, previously developed with capillary pressure models, to fully saturated porous media with submicrometer-sized pores. As such, the models could apply to mass transport in ultrafiltration, nanofiltration, and reverse-osmosis membranes.