Abstract

Purpose: This study aimed to characterize commercial nanofiltration membranes (NF90 and NP010) by determining their membrane parameters and estimating osmotic pressure using the virial equation.

Method: A comparison has been conducted using the Van't Hoff equation for both dilute and concentrated mixtures. Membrane parameters (σ, Ps, and ks) have been experimentally obtained, and osmotic pressure has been calculated using the virial equation, with results compared to the Van't Hoff equation. Various solutes, including lactose, Al³⁺, Mg²⁺, Na⁺, and Cl^-, have been tested at different concentrations to investigate the membrane behavior.

Result: The virial equation has shown better agreement with experimentally measured fluxes than the Van't Hoff equation. With an increase in solute concentration, σ has decreased, while Ps and ks have increased. Higher cation valency has increased rejection rates, with lactose exhibiting the highest rejection. The rejection rates have followed the order of R_Lactose > R_Al3+ > R_Mg2+ > R_Na > R_Cl. The order of σ values has been as follows: σ_Lactose > σ_Al3+ > σ_Mg2+ > σ_Na+ > Rσ_Cl. While the order of Ps and ks values has been Cl->Na⁺>Mg²⁺>Al³⁺>lactose.

Conclusion: The virial equation has proven to be more effective in estimating osmotic pressure. The findings have provided valuable insights into membrane behavior under varying conditions, optimizing the application of NF membranes across various industries.

Keywords: Mass transfer coefficient, nanofiltration membranes, solute permeability, Van't Hoff equation, volumetric flux, membrane technology.