# NO Separation Characteristics in Integrated Electromigration Membrane Reactor
## 2 Experiments
### Process Description and Calculation  
The separation process of NO in the integrated electromigration membrane reactor can be divided into three steps:  
(1) Formation of NO negative ions:  
The N and O atoms in the NO molecule are hybridized with _sp_ orbitals to form a 6 bond, a \(\uppi\) bond, and a large two-center three-electron \(\pi_{2}^{3}\) bond which contains an unpaired electron. In the reactor, NO gas molecule collides with low-energy electrons are generated by gas discharge, capturing electrons to form NO negative ions, which can be briefly described as follows [19; 20]:  
\[\mathrm{e}+\mathrm{NO}\rightarrow\mathrm{NO}^{-},\] (R1)  
\[\mathrm{e}+\mathrm{NO}+\mathrm{M}\rightarrow\mathrm{NO}^{-}+\mathrm{M},\] (R2)  
\[\mathrm{(NO)}_{\mathrm{n}}+\mathrm{e}(\approx 0\mathrm{eV})\ \rightarrow\mathrm{NO}^{-}+\mathrm{(n-1)}\cdot \mathrm{NO}.\] (R3)  
(2) Separation of NO from simulated mixture gas:  
Under the synergistic action of the concentration gradient and electric field force, the NO negative ions drift towards the interface of the gas membrane from the simulated mixture gas. Because the membrane is set up in the electric field, the NO negative ions continue to migrate through the membrane pores into the absorbent liquid side of the membrane due to the grounding electrode, which is immersed in the absorption solution. The total mass transfer flux (N) in the process can be expressed as follows [21]:  
\[N=-D\frac{dC}{dx}+vC, \tag{1}\]  
where \(C\) is the concentration of NO negative ions in the surface membrane; \(v\) is the migration velocity of negative ions in an electric field, \(v=\mu E\), m\(\cdot\)s\({}^{-1}\); \(\mu\) is the ion migration velocity at the unit electric-field intensity, m\({}^{2}\)V\({}^{-1}\)s\({}^{-1}\); \(D\) is the gas diffusion coefficient, m\({}^{2}\cdot\)s\({}^{-1}\). In the coexistence process of gas diffusion and electromigration, according to [PERSON]'s equation, the relationship of the gas diffusion coefficient and its electromigration rate can be expressed as follows [22]:  
\[\frac{\mu}{D}=\frac{\mathrm{e}}{kT}, \tag{2}\]  
where \(k\) is the Boltzmann constant, \(1.38\times 10^{-23}\) J/K; \(T\) is experimental temperature, K; \(e\) is the charge amount of an electron, \(1.6\times 10^{-19}\) C.  
In T \(<25\)\({}^{\circ}\)C, it can be concluded that the electromigration rate of an NO negative ion (\(\mu\)) is about 39 times higher than its own diffusion coefficient (\(D\)). Thus, the effect of molecule diffusion on the NO separation efficiency is negligible. Therefore, the separation of NO in the reactor is mainly depended on the electromigration movement. (3) Absorption of NO in the absorption solution:  
NO negative ions through the membrane are absorbed by aqueous solutions, such as NaClO\({}_{2}\) or KMnO\({}_{4}\)/NaOH aqueous solution. The absorption reactions for NO removal can be briefly expressed as follows in the experimental process [23; 24]:  
\[\mathrm{NO(g)}\leftrightarrow\mathrm{NO(aq)},\] (R4)  
\[\mathrm{NO+MnO^{-}_{4}+2 OH\to NO^{-}_{2}+MnO^{2-}_{4}+H_{2}O},\] (R5)  
\[\mathrm{NO^{-}_{2}+2 MnO^{-}_{4}+2 OH^{-}\to NO^{-}_{3}+2 MnO^{2-}_{4}+H_{2}O},\] (R6)  
\[4\mathrm{NO+3 ClO^{-}_{2}+2H_{2}O\to 4 HNO_{3}+3 Cl^{-}}.\] (R7)  
In the study, the separation efficiency and the total mass transfer coefficient are used to evaluate the performance of the integrated electromigration membrane separation reactor on the NO separation from mixture gas, and are calculated by the following formulas [25; 26] ([PERSON] et al. 2009; [PERSON] et al. 2008):  
\[\eta=\frac{C_{\mathrm{in}}-C_{out}}{C_{in}}\times 100\%, \tag{3}\]  
\[\mathrm{e}+\mathrm{NO}+\mathrm{M}\rightarrow\mathrm{NO}^{-}+\mathrm{M},\]0  
where \(\eta\) is the separation efficiency of NO, %; \(K\) is the total mass transfer coefficient of NO, m\(\cdot\)s\({}^{-1}\); \(Q\) is the gas flow rate, L\(\cdot\)min\({}^{-1}\); \(C_{\mathrm{in}}\) and \(C_{\mathrm{out}}\) are the inlet and outlet concentration of NO in the reactor, mg\(\cdot\)m\({}^{-3}\); \(A\) is the membrane surface area, m\({}^{2}\).