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Osmosis and Osmotic Pressure of Solutions

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A number of natural and synthetic materials exhibit selective permeation, meaning that only molecules or ions of a certain size, shape, polarity, charge, and so forth, are capable of passing through (permeating) the material. Biological cell membranes provide elegant examples of selective permeation in nature, while dialysis tubing used to remove metabolic wastes from blood is a more simplistic technological example. Regardless of how they may be fabricated, these materials are generally...

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Updated: Jul 14, 2025

Ion-Exchange Membranes for the Fabrication of Reverse Electrodialysis Device

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Published on: July 20, 2021

A concise analytical model for the ideal reverse osmosis desalination processes.

¹Department of Civil, Environmental, and Construction Engineering, Texas Tech University, Lubbock, Texas, USA.

Water Environment Research : a Research Publication of the Water Environment Federation

|October 10, 2023

Summary

Determining permeate recovery in reverse osmosis (RO) systems is challenging. This study presents a concise analytical model and graphical solution, linking RO recovery to feed concentration, membrane characteristics, and pressure for easier performance assessment.

Keywords:

analytical model desalination graphical solution method permeate recovery reverse osmosis process

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Published on: February 13, 2016

Area of Science:

Water treatment technologies
Membrane separation processes

Background:

Permeate recovery is crucial for assessing and optimizing reverse osmosis (RO) performance.
Accurate and convenient determination of RO recovery from basic system parameters is a significant engineering challenge.

Purpose of the Study:

To develop a concise analytical model for calculating permeate recovery in ideal RO systems.
To establish a rigorous link between RO recovery and fundamental system parameters.
To introduce a graphical method for effortless recovery calculation.

Main Methods:

Development of a concise analytical model for RO permeate recovery.
Rigorous derivation relating recovery to feed water salt concentration, membrane characteristics, and driving pressure.
Introduction of a graphical solution method for direct recovery determination.

Main Results:

The presented model accurately predicts permeate recovery without empirical coefficients or complex calculations.
The graphical solution provides an effortless means to determine recovery rates.
The model and method are validated across various operational conditions.

Conclusions:

The developed concise model and graphical solution offer a powerful tool for simulating and improving RO process performance.
This approach simplifies the assessment of permeate recovery in ideal RO desalination systems.
The findings facilitate a better understanding and optimization of RO systems for engineers.