Very interesting, i am thinking about it deeply.

The efficiency of a bio-membrane or nanomembrane for wastewater treatment can be calculated using the following formula:

Efficiency = (C_in - C_out)/C_in * 100%

where C_in is the concentration of the pollutant in the wastewater feed, and C_out is the concentration of the pollutant in the effluent after passing through the membrane.

To determine the concentration of the pollutant, you can use analytical techniques such as UV-Vis spectroscopy, chromatography, or titration, depending on the nature of the pollutant.

The Thomas model assumes that the rate of adsorption is proportional to the concentration of the solute in the wastewater, and that the adsorbent capacity is finite. The Adam-Bohart model is a modification of the Thomas model that takes into account the flow rate of the wastewater through the adsorbent bed. The Langmuir model assumes that the adsorption process follows a monolayer adsorption isotherm, where the adsorbent can adsorb a finite amount of solute molecules.

To determine which model is most appropriate for your system, you need to consider several factors, including the type of adsorbent material, the concentration of the solute in the wastewater, and the contact time between the adsorbent and the wastewater. It is also important to validate the model by comparing its predictions with experimental data.

If you have access to software like MATLAB or Python, you can also use numerical methods like the finite element method or the finite difference method to solve the differential equations that describe the adsorption process. However, this requires a good understanding of the underlying mathematical and physical principles.

Dear Suraiya Naznin ,

The Thomas model, Adam-Bohart model and Langmuir model are all adsorption model according to the target compound(s) that you want to adsorb (soluble organics, metal ions, ...).

However membranes are separators which are characterized by their cut-off particle/molecular size (micro, ultra, nano, RO). If you want to model membrane separation, you will first need to define and characterize the target compounds in the wastewater matrix with their respective concentrations and particle/molecular sizes, then select the proper membrane cut-off, and then model it using the characteristic of the selected membrane.

You can use the prominent adsorption isotherm models namely Adam-bohart, Thomas, Yoon-Nelson, Clark model which basically designed according to the continuous column adsorption experiments indeed.

You need some particular parameters which help to interpret your experimental data set undoubtedly.