Abstract
The osmotically driven flow across a semipermeable membrane under a constant static pressure difference is revisited with reference to previous reports on reverse osmosis. The osmosis due to the local solute concentration difference across the membrane induces solvent seeping flow, which advects solutes in a layer in contact with the membrane and reduces the osmosis itself as a result of nonlinear feedback. A few mathematical techniques for obtaining approximate solutions of the seeping flow and the layer thickness, such as that for inverse problems used in the field of heat transfer, are presented with an emphasis on nonlinear boundary conditions and the time-dependent solvent flow rate. We determined that the layer on the membrane forms rapidly and spontaneously through osmosis at a timescale of and that the layer thickness increases with no upper limit in an infinite time interval. Based on the obtained solution, we also discuss the thermodynamic output work in an irreversible process, which is extracted from the seeping flow as an osmotic engine.
Highlights
Osmosis in membrane transport is a physical mechanism underlying a variety of engineering or biological phenomena[3]
“forward” osmosis means the spontaneous flow through a membrane mainly driven by concentration difference across the membrane subject to a small external hydrostatic pressure difference, which leads to the concentration relaxation attributed to the physics principle, increase of entropy
We revisited a nonlinear partial differential equation describing the osmotically driven flow across a semi-permeable membrane under a constant static pressure difference, which was previously investigated for reverse osmosis[1, 2]
Summary
Osmosis in membrane transport is a physical mechanism underlying a variety of engineering or biological phenomena[3]. The solvent spontaneously starts to seepage across the membrane from the pure solvent side (trans-side) into the solution side (cisside) due to the osmotic pressure, which virtually originates to the Brownian motion of molecules from the microscopic viewpoint[9, 10, 11] This transmembrane volume flux of solvent from trans-side to cisside is sustained unless the equilibrium is achieved where the static hydraulic pressure difference across the membrane cancels the osmotic pressure. In the forward osmosis, the decrease of solute concentration difference across membrane is inevitably followed by the reduction of the effective osmotic pressure and the transmembrane volume flux, the development of the layer may be suppressed either by mechanical mixing with crossflow or by supply of solute molecules in the bulk region in cis-side
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
