PDF Publication Title:
Text from PDF Page: 009
2.6. Extension for stack of channels In this part, we will extend the depth-averaged model to stack of channels as shown in Fig.2. We assume hio ≪ L,H, which guarantees the validity of the thin channel assumption, and we further assume that the profiles of physical variables are identical in each charged channel. We only need to define a new parameter: porosity ǫp, which is the sum of all the space of charged channels in the z direction divided by hio. Then we can just replace the h ̃ by ǫp in the Nernst-Planck equation (Eq.(25), (26)) and the continuity equation (Eq.(28)). This is similar to the model for porous media, but here we use planner channels so the tortuosity is 1. However, since we only care about the steady states, we can choose an artificial porosity to imitate the real porous media. 3. Numerical simulation 3.1. Algorithms and parameters In this section, we present the simulation results of the depth-averaged model. The model is solved by the following procedure. First, we solve the PB equation and tabulate αEO, αDO, βP , βEO, βDO, δk, ck k k k kl and ζ in terms of cvk for pre-selected values of h and σ. We then discretize the depth-averaged equations using the finite volume method with nonuniform meshes because the membranes and electrode channels are much thinner in the y direction relative to the feed channel. Next, we solve the transient depth-averaged 0 ̃v,0 v,0 v equations until the steady-state solutions are obtained: (1) give the initial cˆk, ψ , and p ̃ , (2) find the ck corresponding to ck0, (3) find the αEO, αDO, βP , βEO, βDO, δk and ζ based on cv, (4) calculate the k ̃P , k k k kl k k ̃EO, and the diffuoosmotic flow uˆDO, (5) solve for the depth-averaged equations with fixed coefficients and k uˆk and get the cˆk, ψ , p ̃ for the new time step, (6) end the process if the difference between cˆk, ψ , p ̃ DO ̃v v 0 ̃v,0 v,0 0 ̃v,0 ̃v v,0 v ̃v v and cˆk, ψ , and p ̃ is smaller than a critical value, otherwise let cˆk = cˆk, ψ = ψ , p ̃ = p ̃ and repeat steps (2)-(6). To better understand the mechanisms, we simulate not only the full depth-averaged model, but also the reduced depth-averaged model with flow driven only by a pressure gradient (no electroosmosis and diffusioosmosis), the full homogenized model, and the reduced homogenized model with flow driven only by a pressure gradient. The above four models are named as DAfull, DAp, Hfull, and Hp, respectively, in this paper (as shown in Table 2). For given values of σ and hp, we solve the Grahame equation for a single EDL at cin to get a constant ζ for the Hfull model, and we solve the pore-scale profiles to get ζ as a function of k ck for the DAfull model. As a result, DAfull model has larger |ζ| in the ion-depleted zone. By comparing Hp and DAp, or Hfull and DAfull, we can learn how the pore-scale details influence the results. Also, by comparing DAfull and DAp, we can determine the roles of electroosmosis and diffusioosmosis. In addition, we reproduce the model of Schlumpberger et al.[20] and compare it with our models. Though the model is for planar channels, we can still choose parameters to imitate the experimental conditions. In this work, we aim to qualitatively and quantitatively compare the simulation results with the experiments by Schlumpberger et al. [8]. They used ultrafine borosilicate glass frits (Adams & Chittenden Scientific Glass), which had a nominal pore size of 0.9–1.4μm and a porosity of 48%. Therefore, the frit should have h = V /a ≈ 225–350nm and a hindrance factor ǫ /τ ≈ ǫ1.5 ≈ 33%. In this paper, we choose ppp pp hp = 250 nm and ǫp = 33% for the stack of planar charged channels. In addition, Schlumpberger et al. [8] used Nafion 115 (0.005 inches thick) as the membrane, which has 1 meq/g total acid capacity and 38% water uptake (by weight). Since water density is about 1g/cm3, the negative charge concentration in membrane cMs ≈ 1 × 1/0.38 ≈ 2.63 M. Nafion will also slightly expand in water, and the charge density can slightly vary with pH. In this paper, we simply fix cs = 2.63 M, HM = 130 μm for the membrane. We set hio = 2.5 μm, which is apparently different from the depth of the real prototype (W = 2 cm). However, we set uin = Q W Hio and uE = QE , where Q and QE is the experimental flow rate into the feed and electrode channels, to make WHE the flow rate per unit depth the same as experiments. Meanwhile, the dimensionless current I ̃ is independent of the depth in z direction. In addition, we set Hio = 0.6mm,HE = 0.65mm, Hs = 1mm, LI = 3mm, LO =2mm,andsetL,H,HF/(HF +HB)tobethesameasinexperiments. Finally,whencomparedwith experiments, we set σ based on the charge regulation model for glass [30] immersed in solution with ionic 9PDF Image | Theory of shock electrodialysis
PDF Search Title:
Theory of shock electrodialysisOriginal File Name Searched:
2012-05431.pdfDIY PDF Search: Google It | Yahoo | Bing
NFT (Non Fungible Token): Buy our tech, design, development or system NFT and become part of our tech NFT network... More Info
IT XR Project Redstone NFT Available for Sale: NFT for high tech turbine design with one part 3D printed counter-rotating energy turbine. Be part of the future with this NFT. Can be bought and sold but only one design NFT exists. Royalties go to the developer (Infinity) to keep enhancing design and applications... More Info
Infinity Turbine IT XR Project Redstone Design: NFT for sale... NFT for high tech turbine design with one part 3D printed counter-rotating energy turbine. Includes all rights to this turbine design, including license for Fluid Handling Block I and II for the turbine assembly and housing. The NFT includes the blueprints (cad/cam), revenue streams, and all future development of the IT XR Project Redstone... More Info
Infinity Turbine ROT Radial Outflow Turbine 24 Design and Worldwide Rights: NFT for sale... NFT for the ROT 24 energy turbine. Be part of the future with this NFT. This design can be bought and sold but only one design NFT exists. You may manufacture the unit, or get the revenues from its sale from Infinity Turbine. Royalties go to the developer (Infinity) to keep enhancing design and applications... More Info
Infinity Supercritical CO2 10 Liter Extractor Design and Worldwide Rights: The Infinity Supercritical 10L CO2 extractor is for botanical oil extraction, which is rich in terpenes and can produce shelf ready full spectrum oil. With over 5 years of development, this industry leader mature extractor machine has been sold since 2015 and is part of many profitable businesses. The process can also be used for electrowinning, e-waste recycling, and lithium battery recycling, gold mining electronic wastes, precious metals. CO2 can also be used in a reverse fuel cell with nafion to make a gas-to-liquids fuel, such as methanol, ethanol and butanol or ethylene. Supercritical CO2 has also been used for treating nafion to make it more effective catalyst. This NFT is for the purchase of worldwide rights which includes the design. More Info
NFT (Non Fungible Token): Buy our tech, design, development or system NFT and become part of our tech NFT network... More Info
Infinity Turbine Products: Special for this month, any plans are $10,000 for complete Cad/Cam blueprints. License is for one build. Try before you buy a production license. May pay by Bitcoin or other Crypto. Products Page... More Info
CONTACT TEL: 608-238-6001 Email: greg@infinityturbine.com (Standard Web Page)