Evaluation of Transport Properties and Energy Conversion of Bacterial Cellulose Membrane Using Peusner Network Thermodynamics

Abstract

We evaluated the transport properties of a bacterial cellulose (BC) membrane for aqueous ethanol solutions. Using the R^r version of the Kedem-Katchalsky-Peusner formalism (KKP) for the concentration polarization (CP) conditions of solutions, the osmotic and diffusion fluxes as well as the membrane transport parameters were determined, such as the hydraulic permeability (L_p), reflection (σ), and solute permeability (ω). We used these parameters and the Peusner (Rijr) coefficients resulting from the KKP equations to assess the transport properties of the membrane based on the calculated dependence of the concentration coefficients: the resistance, coupling, and energy conversion efficiency for aqueous ethanol solutions. The transport properties of the membrane depended on the hydrodynamic conditions of the osmotic diffusion transport. The resistance coefficients R11r, R22r, and Rdetr were positive and higher, and the R12r coefficient was negative and lower under CP conditions (higher in convective than nonconvective states). The energy conversion was evaluated and fluxes were calculated for the U-, F-, and S-energy. It was found that the energy conversion was greater and the S-energy and F-energy were lower under CP conditions. The convection effect was negative, which means that convection movements were directed vertically upwards. Understanding the membrane transport properties and mechanisms could help to develop and improve the membrane technologies and techniques used in medicine and in water and wastewater treatment processes.

Keywords: Kedem–Katchalsky–Peusner equations; Peusner coefficients of membranes; bacterial cellulose membrane; concentration polarization; energy conversion; membrane transport.

Figure 1

(a) The model of a single-membrane system: M—membrane; g—gravitational acceleration; $l_l^A$ and $l_h^A$ —the concentration boundary layers (CBLs) in configuration A; $l_l^B$ and $l_h^B$ —the CBLs in configuration B; P_h and P_l—mechanical pressures; $C_h$ and $C_l$ —total solution concentrations ($C_h$ > $C_l$ ); $C_l^A$, $C_h^A$, $C_l^B$, and $C_h^B$ —local (at boundaries between the membrane and CBLs) solution concentrations; $J_v^A$ —solute and volume fluxes in configuration A; $J_v^B$ —solute and volume fluxes in configuration B. (b) Interferometric images of concentration boundary layers for a membrane system that contains ethanol solutions of concentrations $C_l$ = 1 mol⋅m⁻³ and $C_h$ = 125 mol⋅m⁻³ at time 80 s; M—membrane [14].

Figure 2

(a) Measuring system (h and l—measuring vessels, N—external solution tank, s—mechanical stirrers, M—membrane, K—calibrated pipette, m—magnets, Z—plugs) [33]. (b) Image of a cross section of a Bioprocess membrane obtained from a scanning electron microscope (magnification: 10,000 times) [37].

Figure 3

Dependences $J_v^r=f\left(t\right)$ (a), $J_s^r=f\left(t\right)$ (b), $J_v^r=f\left(∆C\right)$ (c), and $J_s^r=f\left(∆C\right)$ (d): curves 1A and 1B were obtained for homogeneous solutions (mechanical mixing), and curves 2A and 2B were obtained for concentration polarization conditions (after excluding mechanical mixing of the solutions).

Figure 4

Time (a) and concentration (b) dependences of ${\zeta }_v^r$ and ${\zeta }_s^r$ for aqueous ethanol solutions.

Figure 5

Concentration dependences of the resistance coefficients (a) $R_{11}^r,$ (b) $R_{12}^r=R_{21}^r$, (c) $R_{22}^r$, and (d) $R_{det}^A$ for aqueous ethanol solutions.

Figure 6

Concentration dependencies of the coefficients ${({\varphi }_{ij}^r)}_R$ and (${\varphi }_{det}^r{)}_R$ (a) and the coefficients ${({\phi }_{ij})}_R$ and (${\phi }_{det}{)}_R$ (b) for aqueous ethanol solutions.

Figure 7

Concentration dependencies of ${({\Phi }_S^r)}_R$ (a) and maximum energy conversion efficiency coefficients ${(e_{12}^r)}_R={(e_{21}^r)}_R$ (b) for aqueous ethanol solutions.

Figure 8

Concentration dependencies of the flux of F-energy ${({\Phi }_F^r)}_R$ (a) and the flux of U-energy ${({\Phi }_U^r)}_R$ (b) for aqueous ethanol solutions.