**Assessment of the Total Volume Membrane Charge Density through Mathematical Modeling for Separation of Succinic Acid Aqueous Solutions on Ceramic Nanofiltration Membrane**

#### **Agata Marecka-Migacz 1, Piotr Tomasz Mitkowski 1,\*, Jerzy Antczak 2, Jacek Róza ´ ˙ nski 1 and Krystyna Prochaska 2**


Received: 8 July 2019; Accepted: 17 August 2019; Published: 23 August 2019

**Abstract:** Nanofiltration of aqueous solutions of succinic acid with the addition of sodium hydroxide or magnesium hydroxycarbonate has been investigated experimentally and modeled with the comprehensively described Donnan–Steric partitioning model. The experimental retentions of acid at the same pH varied between 16% and 78%, while the estimated total volume membrane charge densities were in the range of −35.73 and +875.69 mol/m3. This work presents a novel insight into the modeling of nanofiltration and investigates the relations between the estimated total volume membrane charge densities, ionic strength, and component concentration on the performance of ceramic membrane. In addition, this study takes into consideration other parameters such as pH regulation and viscosities of solutions.

**Keywords:** nanofiltration; total volume membrane charge density; modeling DSPM model; ceramic membrane; ionic strength
