PDF Publication Title:
Text from PDF Page: 004
fluxes together to get the electric current density: N i = zkFJk, (2) k=1 where F is the Faraday constant. The conservation of species k leads to ∂ck +∇·Jk =Rk, (3) ∂t where Rk is the volumetric reaction rates of species k. In this work, we assume no reaction for salt ions, and only water dissociation reaction for water ions. So ∂ck +∇·Jk =0 {k=1,2,···,Ns}, (4) ∂t ∂cw +∇·Jw =0, (5) ∂t where cw = cNs+1 − cNs+2 and Jw = JNs+1 − JNs+2 are respectively the difference of concentration and flux of the two water ions (H+ and OH−). Assuming fast dissociation of water, cNs+1cNs+2 = Kw, (6) where Kw is the water dissociation constant. On the other hand, the flow is not only driven by a pressure gradient, but also by an electric force. A typical shock ED system involves an incompressible fluid and operates at low Reynolds number, hence the Stokes equations can be applied for momentum conservation: μ∇2u − ∇p − ρe∇ψ = 0, (7) where ρe is the local charge density. In addition, the continuity equation should be satisfied: ∇ · u = 0. (8) Finally, the electric potential should satisfy the Poisson equation: N ǫ∇2ψ=−ρe =−zkFck, (9) k=1 where ǫ is the permittivity of the solution and is assumed to be a constant. To summarize, Eq.(4)-(9) provide N +5 equations so the system should be solvable with proper boundary conditions. 2.2. Thin channel assumption In this part, we will simplify the full model in Sec.2.1 under the assumption of thin channels. The assumption includes two aspects. First, the z-dimension (less than 10 μm) is much smaller than the x- and y-dimensions (∼ mm), and thus we can assume | ∂ | ≫ | ∂ |, | ∂ | and parallel flow (w = 0), which means ∂z ∂x∂y that we can neglect the electroosmotic instability and electroosmotic vortices in xz or yz planes [11, 27]. Second, the P ́eclet number Pek = |u|h/Dk, which represents the convection in the x- and y-directions over the diffusion in z-direction, is so small (≪ 1) that we can neglect Taylor-Aris dispersion [28] and assume local equilibrium (Jz,k = 0) to a virtual reservoir (where ρe = 0) at each (x, y) position [29, 26]. We define cvk(x, y), ψv(x, y), pv(x, y) as the concentration, electric potential, and pressure in the virtual reservoirs. In the following, we will denote u = (u,v) and Jk = (Jx,k,Jy,k) since w = 0 and Jz,k = 0, and we will denote ψ ̃ = ψ/VT for simplicity. 4PDF 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 | RSS | AMP |