@article{11808d1d8b404318a98b390aa6aabf88,
title = "Quantitative insight into the effect of ions size and electrodes pores on capacitive deionization performance",
abstract = "In this work, effect of ions size is combined with the influence of pore size to provide a quantitative simulation method to evaluate CDI desalination performance. The method is capable of simulating the equilibrium and dynamic behaviours of the CDI. The simulation provides instructive observations that are important to enhance the current state of the art in CDI research and facilitate its implantation into industrial scale. For example, the desalination performance of CDI for high salinity water can be enhanced by using electrodes with small pore size (less than 2nm), while electrodes with higher pore size performs better for lower salinity water. From design respective it is therefore recommended to use electrodes with different pore sizes for multi-stage CDI process, as the salinity of water will increase from one stage to another. For electrolyte of a given concentration, the specific desalination capacity increases when the pore size becomes smaller till approach a threshold pore size and then dramatically decreases, particularly this is most severe for high salinity water. Therefore, careful and precise design approach for the electrode pore size is crucial. As ions of smaller volume can accumulate more for the same pore size limit, the analysis inspires us an innovative approach: to enhance the CDI performance through reducing the size of ions by weakening the hydration, which has been achieved by employing the electromagnetic wave in our experiments.",
keywords = "Capacitive deionization, Desalination efficiency, Electrical double layer, Electromagnetic wave, Ions size, Simulation",
author = "Pei Shui and Emad Alhseinat",
note = "Funding Information: The authors gratefully acknowledge the financial support from Khalifa University for KUIRF L2 project, award No. 8431000012 . Appendix For steady status simulation, the numerical scheme is: • Calculation level I: When V a p p is given, 1 Provide an initial estimate of σ; 2 Calculate V S t from Eq (7) ; 3 Calculate V d i f f from Eq (6) (Process Calculation level II ); 4 Examine if V S t and V d i f f satisfy Eq (10) , if not, update σ and iterate from step 2. • Calculation level II: In this calculation level, Eq (7) is discretized and solved in the diffusive layer. The length of diffusive layer is set to x d i f f and the grid numbers is 300 ( Figure 17 ). The discretization leads to Eq (25) and Eq (26) , which can be solved with the boundary condition Eq (27) : (25) d 2 V d x 2 = d V ′ d x ≈ V n + 1 {\textquoteright} − V n {\textquoteright} x n + 1 − x n = − 1 ε ∑ i e z i c i (26) V ′ = d V d x ≈ V n + 1 − V n x n + 1 − x n (27) V s t a r t {\textquoteright} = − 1 ε σ e , V e n d = V b u l k 1 Obtain boundary condition Eq (27) from σ; 2 Provide an initial estimate of V s t a r t at x S t ; 3 Calculate Eq (25) and Eq (26) to obtain V e n d (Process Calculation level III ); 4 Examine if V e n d = V b u l k , if not, update V s t a r t and iterate from step 3. • Calculation level III: This calculation level aims to solve the local concentration of ion species i under the effect of general excess term η. In this work, η is used for ions size effect defined by Eq (4) . Consider an electrolyte containing i different types of ion, its concentration matrix is: (28) c = [ c 1 ⋯ c i ] T And it needs to be solved through: (29) F ( c ) = [ f 1 ⋮ f i ] = [ ln c 1 + z 1 V V r e f + η − ln c 1 , b u l k − z 1 V b u l k V r e f − η b u l k ⋮ ln c i + z i V V r e f + η − ln c i , b u l k − z i V b u l k V r e f − η b u l k ] = [ 0 ⋮ 0 ] Eq (29) can be solved by Newton{\textquoteright}s method: (30) c n e w = c o l d − J a c − 1 [ F ( c o l d ) ] ⋅ F ( c o l d ) where J a c is the Jacobian matrix of F ( c ) . Iterate Eq (30) until it converges. • Dynamic process modification: Here are modifications for simulating the transient problems. 1 In Calculation level I , the σ is given by initial condition; 2 Process Calculation level I with given σ and obtain V S t and V d i f f ; 3 Obtain V m t l from Eq (10) to Eq (11) by given V a p p and calculated V S t , V d i f f ; 4 Calculate dynamic response through Eq (14) to Eq (18) . We notice there were some research also calling Debye length x D e b as the diffuse layer length, which may cause ambiguity. In fact, since the end of diffuse layer is where the solution achieves electroneutrality (the bulk solution), there is no clear boundary for diffuse layer. By experience, x d i f f F = 3 x D e b is broad enough to accommodate the diffuse layer and is used in this paper. The following figure is the independence test of this x d i f f F setting: In Figure 18 , it is clear that x d i f f F = x D e b is problematic and 3 x D e b or even larger diffuse layer length provides acceptable results. The Independency of the grid number ( = 300 ) has been examined as well. Fig. 17 Discretized calculation domain for diffuse layer region. The profile is the electrical potential solved discretely, as well as the local concentration of each ion species. Fig. 17 Fig. 18 Independency test of x d i f f F . x d i f f F varies from 3 x D e b to 6 x D e b . GCS model without ion size effect, C S t = 0.2 F / m 2 , c b u l k = 10 m M , no porous structure. Fig. 18 Appendix A Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",
year = "2020",
month = jan,
day = "1",
doi = "10.1016/j.electacta.2019.135176",
language = "British English",
volume = "329",
journal = "Electrochimica Acta",
issn = "0013-4686",
publisher = "Elsevier Ltd",
}
