Theoretical Investigation of Boundary Condition Effects on Chemical Osmosis-Induced Water Flow and Solute Concentration Variation in a Horizontal Layer of the Solution-Saturated Semi-permeable Medium
摘要
The chemical osmosis is commonly defined as the solvent (such as water) flow that is driven by the solute concentration gradient in a semi-permeable medium. Although the previous theoretical studies have been conducted to deal with the chemical osmosis-induced water flow and solute concentration variation problem in a horizontal layer of the solution-saturated semi-permeable medium, there are two conceptual errors involved in the mathematical model of the considered problem. The first conceptual error is that a phenomenological model, rather than a theoretical model, is used to express the constitutive relationship between the porosity variation rate with time and the solute concentration variation rate with time, while the second conceptual error is that the solute is allowed to transport in the semi-permeable medium, which is contradictory to the definition of the semi-permeable medium itself. The main purpose of this study is first to correct these two conceptual errors involved in the previous studies and then to derive analytical solutions for the corrected mathematical model of the chemical osmosis-induced water flow and solute concentration variation problem in a horizontal layer of the solution-saturated semi-permeable medium. In particular, three different boundary conditions are taken into account to investigate their effects on the chemical osmosis-induced water flow and solute concentration variation problem in a horizontal layer of the solution-saturated semi-permeable medium.