Journal articles on the topic 'Poisson-Nernst-Planck-Navier-Stokes equations'
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1
Ma, Haitao. "Global Large Solutions to the Navier-Stokes-Nernst-Planck-Poisson Equations." Acta Applicandae Mathematicae 157, no. 1 (March 1, 2018): 129–40. http://dx.doi.org/10.1007/s10440-018-0167-0.
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Liu, Xiaoling, and Chuanju Xu. "Efficient Time-Stepping/Spectral Methods for the Navier-Stokes-Nernst-Planck-Poisson Equations." Communications in Computational Physics 21, no. 5 (March 27, 2017): 1408–28. http://dx.doi.org/10.4208/cicp.191015.260816a.
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AbstractThis paper is concerned with numerical methods for the Navier-Stokes-Nernst-Planck-Poisson equation system. The main goal is to construct and analyze some stable time stepping schemes for the time discretization and use a spectral method for the spatial discretization. The main contribution of the paper includes: 1) an useful stability inequality for the weak solution is derived; 2) a first order time stepping scheme is constructed, and the non-negativity of the concentration components of the discrete solution is proved. This is an important property since the exact solution shares the same property. Moreover, the stability of the scheme is established, together with a stability condition on the time step size; 3) a modified first order scheme is proposed in order to decouple the calculation of the velocity and pressure in the fluid field. This new scheme equally preserves the non-negativity of the discrete concentration solution, and is stable under a similar stability condition; 4) a stabilization technique is introduced to make the above mentioned schemes stable without restriction condition on the time step size; 5) finally we construct a second order finite difference scheme in time and spectral discretization in space. The numerical tests carried out in the paper show that all the proposed schemes possess some desirable properties, such as conditionally/unconditionally stability, first/second order convergence, non-negativity of the discrete concentrations, and so on.
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Saurabh, Kumar, and Maxim Solovchuk. "Mathematical and computational modeling of electrohydrodynamics through a nanochannel." AIP Advances 13, no. 1 (January 1, 2023): 015205. http://dx.doi.org/10.1063/5.0131073.
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Fluid-ion transport through a nanochannel is studied to understand the role and impact of different physical phenomena and medium properties on the flow. Mathematically, the system is described through coupled fourth order Poisson–Nernst–Planck–Bikerman and Navier–Stokes equations. The fourth order-Poisson–Nernst–Planck–Bikerman model accounts for ionic and nonionic interactions between particles, the effect of finite size of the particles, polarization of the medium, solvation of the ions, etc. Navier–Stokes equations are modified accordingly to include both electroviscous and viscoelectric effects and the velocity slip. The governing equations are discretized using the lattice Boltzmann method. The mathematical model is validated by comparing the analytical and experimental ion activity while the numerical model is validated by comparing the analytical and numerical velocity profiles for electro-osmotic flow through a microchannel. For a pressure driven flow, the electroviscous and viscoelectric effects decrease the fluid velocity while the velocity slip enhances it. The acidity of the medium also influences the fluid velocity by altering the ζ potential and ion concentration. The finite size of the particle limits the concentration of ionic species, thus, reducing electroviscous effects. As the external concentration decreases, the impact of finite size of particles also reduces. The inhomogeneous diffusion coefficient also influences electroviscous effects as it changes the concentration distribution. The variation in external pressure does not influence the impact of steric and viscoelectric effects significantly. The maximum impact is observed for ΔP = 0 (electro-osmotic flow).
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Shen, Rong, and Yong Wang. "Stability of the nonconstant stationary solution to the Poisson–Nernst–Planck–Navier–Stokes equations." Nonlinear Analysis: Real World Applications 67 (October 2022): 103582. http://dx.doi.org/10.1016/j.nonrwa.2022.103582.
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Shobukhov, Andrey. "Mathematical Model for the Electrokinetic Instability of Electrolyte Flow." EPJ Web of Conferences 224 (2019): 02003. http://dx.doi.org/10.1051/epjconf/201922402003.
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We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.
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Longaretti, Massimo, Giovambattista Marino, Bice Chini, Joseph W. Jerome, and Riccardo Sacco. "Computational Models in Nano-Bioelectronics: Simulation of Ionic Transport in Voltage Operated Channels." Journal of Nanoscience and Nanotechnology 8, no. 7 (July 1, 2008): 3686–94. http://dx.doi.org/10.1166/jnn.2008.18334.
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In this article, a novel mathematical and computational model is proposed for the numerical simulation of Voltage Operated ionic Channels (VOC) in Nano-bioelectronics applications. This is a first step towards a multi-physics description of hybrid bio-electronical devices such as bio-chips. The model consists of a coupled system of nonlinear partial differential equations, comprising a Poisson-Nernst-Planck system to account for electro-chemical phenomena, and a Navier-Stokes system to account for fluid-mechanical phenomena. Suitable functional iteration techniques for problem decoupling and finite element methods for discretization are proposed and discussed. Numerical results on realistic VOCs illustrate the validity of the model and its accuracy by comparison with relevant computed channel equivalent electrical parameters with measured data.
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Wang, Shu, Limin Jiang, and Chundi Liu. "Quasi-neutral limit and the boundary layer problem of Planck-Nernst-Poisson-Navier-Stokes equations for electro-hydrodynamics." Journal of Differential Equations 267, no. 6 (September 2019): 3475–523. http://dx.doi.org/10.1016/j.jde.2019.04.011.
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Mirbozorgi, S. A., H. Niazmand, and M. Renksizbulut. "Electro-Osmotic Flow in Reservoir-Connected Flat Microchannels With Non-Uniform Zeta Potential." Journal of Fluids Engineering 128, no. 6 (March 24, 2006): 1133–43. http://dx.doi.org/10.1115/1.2353261.
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The effects of non-uniform zeta potentials on electro-osmotic flows in flat microchannels have been investigated with particular attention to reservoir effects. The governing equations, which consist of a Laplace equation for the distribution of external electric potential, a Poisson equation for the distribution of electric double layer potential, the Nernst-Planck equation for the distribution of charge density, and modified Navier-Stokes equations for the flow field are solved numerically for an incompressible steady flow of a Newtonian fluid using the finite-volume method. For the validation of the numerical scheme, the key features of an ideal electro-osmotic flow with uniform zeta potential have been compared with analytical solutions for the ionic concentration, electric potential, pressure, and velocity fields. When reservoirs are included in the analysis, an adverse pressure gradient is induced in the channel due to entrance and exit effects even when the reservoirs are at the same pressure. Non-uniform zeta potentials lead to complex flow fields, which are examined in detail.
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Flores-Rivera, Ciro-Filemon. "Modeling and Behavior Analysis of a Membraneless Fuel Cell." ISRN Applied Mathematics 2012 (February 9, 2012): 1–24. http://dx.doi.org/10.5402/2012/695167.
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Membraneless fuel cells are examples of microelectromechanical systems (MEMSs) that can be considered as alternate energy sources. Applications include microfluidic-based devices like miniaturized laboratories, sensors, or actuators to be used in medicine or agronomy. This paper presents a mathematical model for this type of cells based on the governing physical laws. It includes fluid dynamics, electric charge distribution and electrostatics modeled by the Navier-Stokes, Nernst-Planck, and Poisson equations, respectively. A robust numerical algorithm is proposed to solve the model. Two cases are discussed: allowing electrochemical reactions on one of the electrodes and the simpler situation of null exchange current density. An initial characterization for the behavior of membraneless fuel cells is achieved concerning to prevalence of velocity and electric field, use of non-Newtonian fluids, relationship to initial conditions for some variables, general profile for conductivity and electric density, and linear dependence on current density under specific conditions.
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Sheu, Tony W. H., Yogesh G. Bhumkar, S. T. Yuan, and S. C. Syue. "Development of a High-Resolution Scheme for Solving the PNP-NS Equations in Curved Channels." Communications in Computational Physics 19, no. 2 (February 2016): 496–533. http://dx.doi.org/10.4208/cicp.230914.040615a.
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AbstractA high-order finite difference scheme has been developed to approximate the spatial derivative terms present in the unsteady Poisson-Nernst-Planck (PNP) equations and incompressible Navier-Stokes (NS) equations. Near the wall the sharp solution profiles are resolved by using the combined compact difference (CCD) scheme developed in five-point stencil. This CCD scheme has a sixth-order accuracy for the second-order derivative terms while a seventh-order accuracy for the first-order derivative terms. PNP-NS equations have been also transformed to the curvilinear coordinate system to study the effects of channel shapes on the development of electroos-motic flow. In this study, the developed scheme has been analyzed rigorously through the modified equation analysis. In addition, the developed method has been computationally verified through four problems which are amenable to their own exact solutions. The electroosmotic flow details in planar and wavy channels have been explored with the emphasis on the formation of Coulomb force. Significance of different forces resulting from the pressure gradient, diffusion and Coulomb origins on the convective electroosmotic flow motion is also investigated in detail.
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Falk, Guido, Alexander Nold, and Birgit Wiegand. "Advances in Microscale and Nanoscale Mechanisms of Electrophoretic Deposition in Aqueous Media." Key Engineering Materials 654 (July 2015): 23–28. http://dx.doi.org/10.4028/www.scientific.net/kem.654.23.
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The processing of ceramic thick and thin films, nano- and micro-scaled ceramic structures as well as bulk ceramics of high quality and precise dimensions under electrophoretic boundary conditions requires a full understanding of the dynamics of relevant interfacial mechanisms and interactions of colloidal phases at the nano- and micro-scale. Recent findings and latest insights on the importance of electrokinetic and electrohydrodynamic interfacial processes for membrane electrophoretic depositon in aqueous media are summarised. In this context, the paper addresses the fundamental importance of surficial charge heterogeneities, electric double layer instabilities, electrokinetically induced micro-vortex dynamics, as well as lateral and medial effective electrical field gradients. These phenomena are evaluated in terms of reasonable correlations and mechanistic coincidences of general EPD deposition principles. The experimental results are based on potentiometry, in-situ videomicroscopy, high-resolution as well as secondary electron microscopy. A numerical method for the simulation of the electrophoretic deposition process is suggested based on a multiphysical Finite Element approach given by Nernst-Planck, Poisson- and Navier-Stokes equations. The results of the simulations provide adequate agreement with experimental findings.
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Zhang, Kai, Lengjun Jiang, Zhihan Gao, Changxiu Zhai, Weiwei Yan, and Shuxing Wu. "Design and Numerical Study of Micropump Based on Induced Electroosmotic Flow." Journal of Nanotechnology 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/4018503.
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Induced charge electroosmotic flow is a new electric driving mode. Based on the Navier–Stokes equations and the Poisson–Nernst–Planck (PNP) ion transport equations, the finite volume method is adopted to calculate the equations and boundary conditions of the induced charge electroosmotic flow. In this paper, the formula of the induced zeta potential of the polarized solid surface is proposed, and a UDF program suitable for the simulation of the induced charge electroosmotic is prepared according to this theory. At the same time, on the basis of this theory, a cross micropump driven by induced charge electroosmotic flow is designed, and the voltage, electric potential, charge density, and streamline of the induced electroosmotic micropump are obtained. Studies have shown that when the cross-shaped micropump is energized, in the center of the induction electrode near the formation of a dense electric double layer, there exist four symmetrical vortices at the four corners, and they push the solution towards both outlets; it can be found that the average velocity of the solution in the cross-flow microfluidic pump is nonlinear with the applied electric field, which maybe helpful for the practical application of induced electroosmotic flow in the field of micropump.
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Mirbozorgi, S. A., H. Niazmand, and M. Renksizbulut. "Streaming Electric Potential in Pressure-Driven Flows Through Reservoir-Connected Microchannels." Journal of Fluids Engineering 129, no. 10 (May 16, 2007): 1346–57. http://dx.doi.org/10.1115/1.2776967.
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Electrical power generation employing pressure-driven flows is a fundamental problem in microfluidics. In the present work, analytical and numerical analyses are performed to study the interplaying effects of electrolyte motion with the associated electrical current in a flat microchannel with and without fluid reservoirs. The modified Navier–Stokes equations as well as a Poisson equation for the distribution of electric potential and the Nernst–Planck equations for the distribution of charge densities are solved for the steady flow of a Newtonian liquid. The results show that for a pressure-driven flow, an electric potential is induced due to the motion of charged particles, which increases linearly along the microchannel. This streaming potential generates an opposing conduction current in the core region of the channel as well as in the immediate vicinity of the walls, where the streaming current is negligible. The streaming potential varies in a nonlinear manner with the zeta potential at the walls such that a maximum potential exists at a certain zeta potential. The maximum potential is also observed to increase with both the applied pressure difference and the electric double layer thickness in the range studied. The presence of reservoirs adds significant complexity to this electrokinetic flow.
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Gross, Andreas, Arthur Morvezen, Pedro Castillo Gomez, Xuesong Xu, and Pei Xu. "Numerical Investigation of the Effect of Two-Dimensional Surface Waviness on the Current Density of Ion-Selective Membranes for Electrodialysis." Water 11, no. 7 (July 7, 2019): 1397. http://dx.doi.org/10.3390/w11071397.
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Ion-selective membranes are an important component of electrodialysis stacks for desalination. Manufacturing imperfections or slight inhomogeneity of the material can lead to minute membrane surface imperfections. Two-dimensional solutions of the coupled Poisson–Nernst–Planck and Navier–Stokes equations were sought for a perfectly smooth membrane and for membranes with well-defined small-amplitude harmonic surface roughness. The simulations were carried out with the validated rheoEFoam solver by Pimenta and Alves. In the overlimiting regime, the electric field is strong enough for an electrokinetic instability to occur. The instability leads to disturbance growth and the formation of electro-convection cells, which strongly increase the current density. The present simulations show that with an increasing ion concentration and applied voltage, the instability becomes stronger and the overlimiting regime is reached earlier. The limiting current density shows a noticeable dependence on the wavelength of the surface roughness. When the wavelength of the surface roughness is incommensurate with the wavelength of the naturally occurring instability, the limiting current density is increased. Since production membranes will always have some degree of surface roughness, this suggests that membrane surface treatments which favor certain wavelengths may have an effect on the overall membrane performance.
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Mai, Van-Phung, Wei-Hao Huang, and Ruey-Jen Yang. "Charge Regulation and pH Effects on Thermo-Osmotic Conversion." Nanomaterials 12, no. 16 (August 13, 2022): 2774. http://dx.doi.org/10.3390/nano12162774.
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Thermo-osmotic energy conversion using waste heat is one of the approaches to harvesting sustainable energy and reducing associated environmental impacts simultaneously. In principle, ions transport through a charged nanopore membrane under the effect of a thermal gradient, inducing a different voltage between two sides of the membrane. Recent publications mainly reported novel materials for enhancing the thermoelectric voltage in response to temperature difference, the so-called Seebeck coefficient. However, the effect of the surface charge distribution along nanopores on thermo-osmotic conversion has not been discussed yet. In this paper, a numerical simulation based on the Nernst–Planck–Poisson equations, Navier–Stokes equations, and heat transfer equations is carried out to consider the effect of surface charge-regulation density and pH of KCl solutions on the Seebeck coefficient. The results show that the highest ionic Seebeck coefficient of −0.64 mV/K is obtained at 10−4 M KCl solution and pH 9. The pH level and pore structure also reveal a strong effect on the thermo-osmotic performance. Moreover, the pH level at one reservoir is varied from 5 to 9, while the pH of 5 is fixed at the other reservoir to investigate the pH effect on the thermos-osmosis ion transport. The results confirm the feasibility that using the pH can enhance the thermo-osmotic conversion for harvesting osmotic power from low-grade heat energy.
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Li, Haijing, and Federico Toschi. "Plasma-induced catalysis: towards a numerical approach." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2175 (June 22, 2020): 20190396. http://dx.doi.org/10.1098/rsta.2019.0396.
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A lattice Boltzmann (LB) model is developed, validated and used to study simplified plasma/flow problems in complex geometries. This approach solves a combined set of equations, namely the Navier–Stokes equations for the momentum field, the advection–diffusion and the Nernst–Planck equations for electrokinetic and the Poisson equation for the electric field. This model allows us to study the dynamical interaction of the fluid/plasma density, velocity, concentration and electric field. In this work, we discuss several test cases for our numerical model and use it to study a simplified plasma fluid flowing and reacting inside a packed bed reactor. Inside the packed bed, electric breakdown reactions take place due to the electric field, making neutral species ionize. The presence of the packed beads can help enhance the reaction efficiency by locally increasing the electric field, and the size of packed beads and the pressure drop of the packed bed do influence the outflux. Hence trade-offs exist between reaction efficiency and packing porosity, the size of packing beads and the pressure drop of the packed bed. Our model may be used as a guidance to achieve higher reaction efficiencies by optimizing the relevant parameters. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.
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Uzdenova, Aminat. "2D Mathematical Modelling of Overlimiting Transfer Enhanced by Electroconvection in Flow-Through Electrodialysis Membrane Cells in Galvanodynamic Mode." Membranes 9, no. 3 (March 11, 2019): 39. http://dx.doi.org/10.3390/membranes9030039.
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Flow-through electrodialysis membrane cells are widely used in water purification and the processing of agricultural products (milk, wine, etc.). In the research and operating practice of such systems, a significant place is occupied by a galvanodynamic (or galvanostatic) mode. 2D mathematical modelling of ion transfer in the galvanodynamic mode requires solving the problem of setting the average current density equal to a certain value, while the current density distribution in the system is uneven. This article develops a 2D mathematical model of the overlimiting transfer enhanced by electroconvection in a flow-through electrodialysis cell in the galvanodynamic mode. The model is based on the system of Navier–Stokes, Nernst–Planck, Poisson equations and equations for the electric current stream function. To set the electric mode we use a boundary condition, relating the electric field strength and current density. This approach allows us to describe the formation of the extended space charge region and development of electroconvection at overlimiting currents. For the first time, chronopotentiograms and current–voltage characteristics of the membrane systems are calculated for the galvanodynamic mode taking into account the forced flow and development of electroconvection. The behaviors of the calculated chronopotentiograms and current–voltage characteristic coincide qualitatively with experimental data. The effects of the electrolyte concentration, forced flow velocity and channel size on the mass transfer at overlimiting currents are estimated.
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Kovalenko, Anna V., and Anna V. Ovsyannikova. "Mathematical modelling of salt ion transfer in the three-dimensional desalting channel of an electrodialysis apparatus." Journal of the Belarusian State University. Mathematics and Informatics, no. 2 (August 3, 2022): 70–81. http://dx.doi.org/10.33581/2520-6508-2022-2-70-81.
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A new 3D model of 1:1 salt ion transfer in the desalting channel of an electrodialysis apparatus is presented and investigated in this paper. For the first time a three-dimensional mathematical model of salt ion transfer in the desalting channel taking into account the electroconvection based on the system of Nernst – Planck, Poisson and Navier – Stokes equations with the electric force and the natural boundary conditions is proposed. To solve the boundary value problem, the finite element method is used in the cross-platform numerical analysis software COMSOL Multiphysics in combination with the method of successive approximations, when the electrochemical and hydrodynamic parts of the problem are solved one by one on the current layer. In turn, the electrochemical and hydrodynamic parts of the problem are solved by Newton’s method. As a result of numerical analysis, the fundamental regularities of salt ion transfer in a three-dimensional channel, the emergence and development of electroconvective vortices, including the discovery of new three-dimensional spiral forms of salt ions, are established for the first time. It is shown that electroconvective vortices exist in the form of clusters, within which vortex bifurcations can occur. Thus, the currently existing simplified view of the structure of electroconvective vortices is clarified and developed.
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Ma, Pengfei, Jianxiang Zheng, Danting Zhao, Wenjie Zhang, Gonghao Lu, Lingxin Lin, Zeyuan Zhao, Zijing Huang, and Liuxuan Cao. "The Selective Transport of Ions in Charged Nanopore with Combined Multi-Physics Fields." Materials 14, no. 22 (November 19, 2021): 7012. http://dx.doi.org/10.3390/ma14227012.
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The selective transport of ions in nanopores attracts broad interest due to their potential applications in chemical separation, ion filtration, seawater desalination, and energy conversion. The ion selectivity based on the ion dehydration and steric hindrance is still limited by the very similar diameter between different hydrated ions. The selectivity can only separate specific ion species, lacking a general separation effect. Herein, we report the highly ionic selective transport in charged nanopore through the combination of hydraulic pressure and electric field. Based on the coupled Poisson–Nernst–Planck (PNP) and Navier–Stokes (NS) equations, the calculation results suggest that the coupling of hydraulic pressure and electric field can significantly enhance the ion selectivity compared to the results under the single driven force of hydraulic pressure or electric field. Different from the material-property-based ion selective transport, this method endows the general separation effect between different kinds of ions. Through the appropriate combination of hydraulic pressure and electric field, an extremely high selectivity ratio can be achieved. Further in-depth analysis reveals the influence of nanopore diameter, surface charge density and ionic strength on the selectivity ratio. These findings provide a potential route for high-performance ionic selective transport and separation in nanofluidic systems.
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Karimzadeh, Mohammad, Mahdi Khatibi, and Seyed Nezameddin Ashrafizadeh. "Boost ionic selectivity by coating bullet-shaped nanochannels with dense polyelectrolyte brushes." Physics of Fluids 34, no. 12 (December 2022): 122008. http://dx.doi.org/10.1063/5.0130425.
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The influence of channel geometry on the ionic selectivity and ionic current rectification of soft nanochannels was numerically investigated. The nanochannels coated with polyelectrolyte layers (PELs) are termed as soft nanochannels. The asymmetric category of nanochannels, i.e., bullet-shaped, was considered in this study. When PEL is dense, the ionic partitioning effect cannot be ignored. To this end, through adopting a numerical approach using the finite element method, Poisson–Nernst–Planck and Navier–Stokes equations were solved at steady-state conditions by considering different values of permittivity, diffusivity, and dynamic viscosity for the PEL and the electrolyte. The results show that the PEL–electrolyte property difference leads to a significant improvement of the rectification behavior, especially at low and moderate salt concentrations. This not only highlights the importance of considering different properties for the PEL and the electrolyte but also implies that the rectification behavior of soft nanochannels/nanopores may be improved considerably by utilizing denser PELs. Considering a charge density of [Formula: see text] and a bulk concentration of [Formula: see text], we demonstrate that the rectification factors for the bullet nanochannels, from [Formula: see text] by ignoring the ion partitioning effect, can reach the values of [Formula: see text] by considering the ion partitioning effect, respectively.
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WEI, GUO-WEI. "MULTISCALE, MULTIPHYSICS AND MULTIDOMAIN MODELS I: BASIC THEORY." Journal of Theoretical and Computational Chemistry 12, no. 08 (December 2013): 1341006. http://dx.doi.org/10.1142/s021963361341006x.
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This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors, and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e. electrostatic) solvation, non-polar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics, and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace–Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson–Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst–Planck (NP) equations for the dynamics of charged solvent species, generalized Navier–Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent–solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent–solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.
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Chekanov, Vladimir, and Anna Kovalenko. "Experimental and Theoretical Study of an Autowave Process in a Magnetic Fluid." International Journal of Molecular Sciences 23, no. 3 (January 31, 2022): 1642. http://dx.doi.org/10.3390/ijms23031642.
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Magnetic fluid (MF) is a colloidal system consisting of ferromagnetic particles (magnetite) with a diameter of ~10 nm suspended in a dispersion medium of a carrier fluid (for example, kerosene). A distinctive feature of magnetic fluid is the fact that when an electric field is applied to it using two electrodes, thin layers consisting of close-packed particles of the dispersed phase are formed in the regions near the surface of both electrodes. These layers significantly affect the macroscopic properties of the colloidal system. In this work, the interpretation of the near-electrode layer is for the first time given as a new type of liquid membrane, in which the particles of the dispersed phase become charged with the opposite sign. On the basis of experimental studies, we propose a physicochemical mechanism of the autowave process in a cell with a magnetic fluid. It is based on the idea of oppositely recharging colloidal particles of magnetite in a liquid membrane. A mathematical model of an autowave process, which is described by a system of coupled partial differential equations of Nernst–Planck–Poisson and Navier–Stokes with appropriate boundary conditions, is proposed for the first time. One-dimensional, two-dimensional, and three-dimensional versions of the model are considered. The dependence of the frequency of concentration fluctuations on the stationary voltage between the electrodes was obtained, and the time of formation of a liquid membrane was estimated. Qualitative agreement between theoretical and experimental results has been established.
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Chatterjee, A., A. K. Nayak, and B. Weigand. "Effect of electromigration dispersion and non-Newtonian rheology of a charged solute in a microcapillary." Physics of Fluids 34, no. 11 (November 2022): 112011. http://dx.doi.org/10.1063/5.0110118.
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The present work is concerned with the electromigration interaction of non-Newtonian fluid in a rectangular micro-capillary under the influence of an external electric field to predict the spatiotemporal dynamics of the solute concentration due to an effective dispersion and migration velocity. The solute concentration is optimized by dispersion and a driving force exploiting the interplay between the sequential ionic distribution and the local electrical conductivity coupled with the characteristics of the fluid. The incompressible Navier–Stokes equation combined with the Poisson equation for the electric field is considered for the flow transport incorporated with the Nernst–Planck equation for the ion transport. The numerical computations are performed for the coupled electro-osmosis/electrophoresis migrated nonlinear equations by a control volume approach for effective dispersion. The analytical observation of electrical conductivity in the case of a planar uniformly charged substrate is found to be varied locally near the sample peak and majorly concentration dependent. The asymptotic analysis for the velocity is made by using the lubrication approximation. The solutal species calculation is made from an area averaged nonlinear advection diffusion equation incorporating the coupled momentum equation. It is observed that the Taylor–Aries dispersion effect is dependent on the flow behavior index of the power law fluid, the flow strength, and the local sample concentration. The study of the time regime and the flow strength dependent instantaneous dispersion has also been conducted.
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Shao, Sihong, and Tiezheng Qian. "A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces." Communications in Computational Physics 11, no. 3 (March 2012): 831–62. http://dx.doi.org/10.4208/cicp.071210.040511a.
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AbstractWe develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the On-sager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.
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Dezhkam, Rasool, Hoseyn A. Amiri, David J. Collins, and Morteza Miansari. "Continuous Submicron Particle Separation via Vortex-Enhanced Ionic Concentration Polarization: A Numerical Investigation." Micromachines 13, no. 12 (December 12, 2022): 2203. http://dx.doi.org/10.3390/mi13122203.
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Separation and isolation of suspended submicron particles is fundamental to a wide range of applications, including desalination, chemical processing, and medical diagnostics. Ion concentration polarization (ICP), an electrokinetic phenomenon in micro-nano interfaces, has gained attention due to its unique ability to manipulate molecules or particles in suspension and solution. Less well understood, though, is the ability of this phenomenon to generate circulatory fluid flow, and how this enables and enhances continuous particle capture. Here, we perform a comprehensive study of a low-voltage ICP, demonstrating a new electrokinetic method for extracting submicron particles via flow-enhanced particle redirection. To do so, a 2D-FEM model solves the Poisson–Nernst–Planck equation coupled with the Navier–Stokes and continuity equations. Four distinct operational modes (Allowed, Blocked, Captured, and Dodged) were recognized as a function of the particle’s charges and sizes, resulting in the capture or release from ICP-induced vortices, with the critical particle dimensions determined by appropriately tuning inlet flow rates (200–800 [µm/s]) and applied voltages (0–2.5 [V]). It is found that vortices are generated above a non-dimensional ICP-induced velocity of , which represents an equilibrium between ICP velocity and lateral flow velocity. It was also found that in the case of multi-target separation, the surface charge of the particle, rather than a particle’s size, is the primary determinant of particle trajectory. These findings contribute to a better understanding of ICP-based particle separation and isolation, as well as laying the foundations for the rational design and optimization of ICP-based sorting systems.
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Kovalenko, A., V. Gudza, M. Urtenov, and N. Chubyr. "Mathematical modeling of the influence of non-catalytic dissociation / recombination of water molecules in the desalination channel on electric convection." Journal of Physics: Conference Series 2131, no. 2 (December 1, 2021): 022109. http://dx.doi.org/10.1088/1742-6596/2131/2/022109.
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Abstract The article formulates a two-dimensional mathematical model of non-stationary transport of 1: 1 electrolyte in a potentiodynamic mode, taking into account electroconvection and non-catalytic dissociation / recombination reaction of water molecules in electromembrane systems, which are considered as the desalting channel of an electrodialysis device. The model is described by a system of coupled Navier-Stokes and Nernst-Planck-Poisson equations taking into account the electric force and physically justified boundary conditions. The article establishes the basic laws of mass transport, taking into account the dissociation / recombination of water molecules. It was shown for the first time that a double electric layer of hydrogen and hydroxyl ions arises in the recombination region. It is shown that between the region of recombination and quasi-equilibrium regions of space charge there are regions of electroneutrality and equilibrium with an almost linear distribution of concentrations. It was found that even under prelimiting, but close enough to the limiting current, modes, non-catalytic dissociation of water molecules in the quasi-equilibrium region of space charge occurs so intensely that the concentration of hydrogen and hydroxyl ions becomes comparable to the concentration of potassium and chlorine ions. At overlimiting current densities, due to the appearance of an extended space charge region and intense dissociation of water molecules in this region, as well as an increase in the electric double layer in the recombination region, the space charge and the dissociation / recombination reaction of water molecules significantly affect each other. In turn, this has a decisive effect on electroconvection and, accordingly, on the transport of salt ions.
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Li, Haijing, Herman J. H. Clercx, and Federico Toschi. "Lattice Boltzmann method investigation of a reactive electro-kinetic flow in porous media: towards a phenomenological model." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2208 (August 30, 2021): 20200398. http://dx.doi.org/10.1098/rsta.2020.0398.
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A model based on the Lattice Boltzmann method is developed to study the flow of reactive electro-kinetic fluids in porous media. The momentum, concentration and electric/potential fields are simulated via the Navier–Stokes, advection–diffusion/Nernst–Planck and Poisson equations, respectively. With this model, the total density and velocity fields, the concentration of reactants and reaction products, including neutral and ionized species, the electric potential and the interaction forces between the fields can be studied, and thus we provide an insight into the interplay between chemistry, flow and the geometry of the porous medium. The results show that the conversion efficiency of the reaction can be strongly influenced by the fluid velocity, reactant concentration and by porosity of the porous medium. The fluid velocity determines how long the reactants stay in the reaction areas, the reactant concentration controls the amount of the reaction material and with different dielectric constant, the porous medium can distort the electric field differently. All these factors make the reaction conversion efficiency display a non-trivial and non-monotonic behaviour as a function of the flow and reaction parameters. To better illustrate the dependence of the reaction conversion efficiency on the control parameters, based on the input from a number of numerical investigations, we developed a phenomenological model of the reactor. This model is capable of capturing the main features of the causal relationship between the performance of the reactor and the main test parameters. Using this model, one could optimize the choice of reaction and flow parameters in order to improve the performance of the reactor and achieve higher production rates. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.
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Kim, Jeonglae, Scott Davidson, and Ali Mani. "Characterization of Chaotic Electroconvection near Flat Inert Electrodes under Oscillatory Voltages." Micromachines 10, no. 3 (February 26, 2019): 161. http://dx.doi.org/10.3390/mi10030161.
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The onset of electroconvective instability in an aqueous binary electrolyte under external oscillatory electric fields at a single constant frequency is investigated in a 2D parallel flat electrode setup. Direct numerical simulations (DNS) of the Poisson–Nernst–Planck equations coupled with the Navier–Stokes equations at a low Reynolds number are carried out. Previous studies show that direct current (DC) electric field can create electroconvection near ion-selecting membranes in microfluidic devices. In this study, we show that electroconvection can be generated near flat inert electrodes when the applied electric field is oscillatory in time. A range of applied voltage, the oscillation frequency and the ratio of ionic diffusivities is examined to characterize the regime in which electroconvection takes place. Similar to electroconvection under DC voltages, AC electroconvection occurs at sufficiently high applied voltages in units of thermal volts and is characterized by transverse instabilities, physically manifested by an array of counter-rotating vortices near the electrode surfaces. The oscillating external electric field periodically generate and destroy such unsteady vortical structures. As the oscillation frequency is reduced to O ( 10 − 1 ) of the intrinsic resistor–capacitor (RC) frequency of electrolyte, electroconvective instability is considerably amplified. This is accompanied by severe depletion of ionic species outside the thin electric double layer and by vigorous convective transport involving a wide range of scales including those comparable to the distance L between the parallel electrodes. The underlying mechanisms are distinctly nonlinear and multi-dimensional. However, at higher frequencies of order of the RC frequency, the electrolyte response becomes linear, and the present DNS prediction closely resembles those explained by 1D asymptotic studies. Electroconvective instability supports increased electric current across the system. Increasing anion diffusivity results in stronger amplification of electroconvection over all oscillation frequencies examined in this study. Such asymmetry in ionic diffusivity, however, does not yield consistent changes in statistics and energy spectrum at all wall-normal locations and frequencies, implying more complex dynamics and different scaling for electrolytes with unequal diffusivities. Electric current is substantially amplified beyond the ohmic current at high oscillation frequencies. Also, it is found that anion diffusivity higher than cation has stronger impact on smaller-scale motions (≲ 0.1 L).
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Dietzel, Mathias, and Steffen Hardt. "Flow and streaming potential of an electrolyte in a channel with an axial temperature gradient." Journal of Fluid Mechanics 813 (January 27, 2017): 1060–111. http://dx.doi.org/10.1017/jfm.2016.844.
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The effect of an axial temperature gradient on the flow profile and the induced streaming potential of a pressure-driven symmetric electrolyte in a slit channel is investigated. Based on the non-isothermal Nernst–Planck equations, as well as the Poisson equation in the lubrication approximation, expressions for the ion distribution in the electric double layer (EDL) are derived. It is found that thermophoretic ion motion and a temperature-dependent electrophoretic ion mobility increase the local EDL thickness with temperature, whereas a temperature-dependent permittivity shrinks the EDL. Within the Debye–Hückel approximation, the Navier–Stokes equation with the corresponding electric body force terms is solved. Analytical expressions for the flow profile and the induced (streaming) field under non-isothermal conditions are derived. It is shown that for such a situation the induced electric field is the linear superposition of at least seven individual contributions. For very wide channels, only the thermoelectric field typically present in bulk electrolytes when subjected to a temperature gradient (Soret equilibrium) as well as the conventional pressure-induced streaming field are of importance. Counterintuitively, for the latter, while still being affected by the temperature dependence of the dielectric permittivity and local salt concentration, the temperature dependencies of the viscosity, Fickian diffusion coefficients and ion electromobilities exactly cancel each other. For narrow channels, five additional contributions become relevant, which – similar to the Soret voltage – do not vanish in the case that the externally applied pressure gradient is removed. The first is caused by selective thermo-electromigration driven by the interplay between the temperature-dependent electrophoretic ion mobility and the interaction of the ions with the surface wall charge. This non-advective effect is at its maximum under extreme confinement. For channels whose widths are of the same order as the EDL thickness, four thermoosmotic effects become significant. Besides the well-known thermoosmosis due to the temperature dependence of the dielectric permittivity in the (extended) Korteweg–Helmholtz force, it is demonstrated that – by contrast to isothermal conditions – a thermal gradient renders the ion cloud in the EDL out of mechanical equilibrium. In this context it is shown that a thermophoretic ion motion (i.e. the intrinsic Soret effect of the ions) and a temperature-dependent ion electromobility as well as a temperature-dependent permittivity not only cause an axial gradient of the EDL potential, but simultaneously lead to a pressure of thermal origin, which sets the fluid into an advective motion. Corresponding phenomena were not previously discussed in the literature and may be interpreted as an apparent, thermally induced slip velocity within the EDL. Subsequently, the ion advection affiliated with such thermoosmotic flow may induce a thermoelectric field of a similar order of magnitude to that caused by more conventional thermal effects.
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"An OpenFOAM-Integrated Numerical Solver for Electroconvective Flow." JST: Smart Systems and Devices 32, no. 2 (May 15, 2022): 74–81. http://dx.doi.org/10.51316/jst.158.ssad.2022.32.2.10.
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In this work, we developed a numerical solver, integrated it into the OpenFOAM platform, for modeling electroconvective flow. The solver deals with the system of Poisson-Nernst-Planck-Navier-Stokes equations. The finite volume schemes functioned in OpenFOAM were used for discretisation of the Poisson-Nernst-Planck equations. The Newton method was employed to solve the nonlinear Poisson-Nernst-Planck equations in a coupled manner. The validation shows the high accuracy of our solver. It is used to investigate ion conduction in the electrodialysis cell. The simulation results have allowed examining the flow’s profile, ion distribution in different regimes of the system. Especially, the mechanisms behind the vortex formation in the channel can be explained by these results. This solver developed on OpenFoam open-source code provides the research community with a valuable tool for the study of electrochemical problems.
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He, Mingyan, and Pengtao Sun. "Mixed Finite Element Method for Modified Poisson–Nernst–Planck/Navier–Stokes Equations." Journal of Scientific Computing 87, no. 3 (April 29, 2021). http://dx.doi.org/10.1007/s10915-021-01478-z.
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Wu, Fan. "Global regularity criterion for the dissipative systems modelling electrohydrodynamics involving the middle eigenvalue of the strain tensor." Proceedings of the Royal Society of Edinburgh: Section A Mathematics, September 21, 2021, 1–14. http://dx.doi.org/10.1017/prm.2021.56.
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In this paper, we study a dissipative systems modelling electrohydrodynamics in incompressible viscous fluids. The system consists of the Navier–Stokes equations coupled with a classical Poisson–Nernst–Planck equations. In the three-dimensional case, we establish a global regularity criteria in terms of the middle eigenvalue of the strain tensor in the framework of the anisotropic Lorentz spaces for local smooth solution. The proof relies on the identity for entropy growth introduced by Miller in the Arch. Ration. Mech. Anal. [16].
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Xiao, Weiliang, and Wenyu Kang. "Global large solutions to the Navier–Stokes–Nernst–Planck–Poisson equations in Fourier–Besov spaces." Applicable Analysis, May 14, 2022, 1–13. http://dx.doi.org/10.1080/00036811.2022.2075353.
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Marshall, Guillermo, Pablo Mocskos, and Martin Olivella. "A Growth Model For Ramified Electrochemical Deposition." MRS Proceedings 407 (1995). http://dx.doi.org/10.1557/proc-407-355.
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ABSTRACTWe introduce a macroscopic model for the description of growth pattern formation in ramified electrochemical deposition. The theoretical model is formulated as a 2D time-dependent problem consisting in the Nernst-Planck equations for the concentration of the solute (cations and anions), coupled to a Poisson equation for the electrostatic potential and the Navier-Stokes equations for the solvent, with a moving boundary. A dimensional analysis is performed and a new set of dimensionless numbers governing the flow regime is derived. A 2D discrete version of these equations in a DBM scheme with a random moving boundary constitutes the computational model. We present numerical results which show that our growth model, with a proper variation of the set of dimensionless numbers, gives a reasonable picture of the interplay of the electroconvective, migration and diffusive motion of the ions near the growing tips.
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Dreyer, Wolfgang, Pierre-Étienne Druet, Paul Gajewski, and Clemens Guhlke. "Analysis of improved Nernst–Planck–Poisson models of compressible isothermal electrolytes." Zeitschrift für angewandte Mathematik und Physik 71, no. 4 (July 2, 2020). http://dx.doi.org/10.1007/s00033-020-01341-5.
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Abstract We consider an improved Nernst–Planck–Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non-equilibrium. The elastic deformation of the medium, that induces an inherent coupling of mass and momentum transport, is taken into account. The model consists of convection–diffusion–reaction equations for the constituents of the mixture, of the Navier–Stokes equation for the barycentric velocity and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross-diffusion phenomena must occur, and the mobility matrix (Onsager matrix) has a non-trivial kernel. In this paper, we establish the existence of a global-in-time weak solution, allowing for a general structure of the mobility tensor and for chemical reactions with fast nonlinear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time.
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Tong, Leilei, and Zhong Tan. "Optimal decay rates of the solution for generalized Poisson–Nernst–Planck–Navier–Stokes equations in $${\mathbb {R}}^3$$." Zeitschrift für angewandte Mathematik und Physik 72, no. 6 (October 25, 2021). http://dx.doi.org/10.1007/s00033-021-01627-2.
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Pham, Van-Sang, and Duc-Anh Van. "Numerical Modeling for 3D Vortices Patterns of Electroconvective Flow Developing in Shear Flow ." Physics of Fluids, July 23, 2022. http://dx.doi.org/10.1063/5.0100731.
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In this study, using direct numerical modeling , we investigate the electroconvective flow developing on the surface of an ion-exchange membrane surface in the high applied voltage condition . The modeling is obtained by solving the system of Poisson-Nernst-Planck-Navier-Stokes equations in a direct and coupled manner on the OpenFOAM platform . We report simulation results proving the dependence of the flow's pattern on the applied voltage and the mechanism behind the formation of vortices at high electric fields. For the first time, the different types of vortices and the concurrent appearance of helical and unidirectional vortices are studied. The role of the vortices on the distribution of ions and the electric current is clarified to explain the over-limiting current phenomenon. This work contributes a useful OpenFOAM solver integration tool for modeling electrochemical problems.
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Bhattacharyya, S., and A. K. Nayak. "Combined Effect of Surface Roughness and Heterogeneity of Wall Potential on Electroosmosis in Microfluidic/Nanofuidic Channels." Journal of Fluids Engineering 132, no. 4 (April 1, 2010). http://dx.doi.org/10.1115/1.4001308.
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The motivation of the present study is to generate vortical flow by introducing channel wall roughness in the form of a wall mounted block that has a step-jump in ζ-potential on the upper face. The characteristics for the electrokinetic flow are obtained by numerically solving the Poisson equation, the Nernst–Planck equation, and the Navier–Stokes equations, simultaneously. A numerical method based on the pressure correction iterative algorithm (SIMPLE) is adopted to compute the flow field and mole fraction of the ions. The potential patch induces a strong recirculation vortex, which in turn generates a strong pressure gradient. The strength of the vortex, which appears adjacent to the potential patch, increases almost linearly with the increase in ζ-potential. The streamlines follow a tortuous path near the wall roughness. The average axial flow rate over the block is enhanced significantly. We found that the ionic distribution follow the equilibrium Boltzmann distribution away from the wall roughness. The solutions based on the Poisson–Boltzmann distribution and the Nernst–Planck model are different when the inertial effect is significant. The combined effects due to geometrical modulation of the channel wall and heterogeneity in ζ-potential is found to produce a stronger vortex, and hence a stronger mixing, compared with either of these. Increase in ζ-potential increases both the transport rate and mixing efficiency. A novelty of the present configuration is that the vortex forms above the obstacle even when the patch potential is negative.
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Ullah, Naqib, Rehan Ali Shah, Muhammad Sohail Khan, Aamir Khan, Mowffaq Oreijah, Kamel Guedri, and Ahmed M. Galal. "Electro-viscous effect of nanofluid flow over a rotating disk." International Journal of Modern Physics B, December 15, 2022. http://dx.doi.org/10.1142/s0217979223501382.
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In this research work, we investigate an unsteady flow over a rotating disk. We assign symbols to the selected dependent and independent quantities. Then all physical systems are modeled to mathematical form by applying physical laws for an ionized liquid flow over a rotating disk with nanoparticles from the set of Poisson Nernst–Planck model, Energy equation and Navier–Stokes equations. The set of partial differential equations along with the boundary conditions are transformed to a set of coupled ordinary differential equations for an electro-viscous flow of nanofluid over a rotating disk by using similarity transformations. The unknown physical quantities are investigated through Parametric Continuation Method (PCM). For physical purpose, physical quantities like flow behavior thermal properties, thermal variation, the distribution of ions in the fluid region, skin friction, are analyzed through graphical and tabulated results. As exact solutions are not possible for nonlinear ordinary differential equations (ODEs) system, therefore, such quantities are subjected to numerical calculation following Parametric Continuation Method (PCM) and validated the result through BVP4c package in Matlab.
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Bhattacharyya, S., and Naren Bag. "Enhanced Electroosmotic Flow Through a Nanochannel Patterned With Transverse Periodic Grooves." Journal of Fluids Engineering 139, no. 8 (May 18, 2017). http://dx.doi.org/10.1115/1.4036265.
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In this paper, we have analyzed an enhanced electroosmotic flow (EOF) by geometric modulation of the surface of a charged nanochannel. Otherwise, flat walls of the channel are modulated by embedding rectangular grooves placed perpendicular to the direction of the applied electric field in a periodic manner. The modulated channel is filled with a single electrolyte. The EOF within the modulated channel is determined by computing the Navier–Stokes–Nernst–Planck–Poisson equations for a wide range of Debye length. The objective of the present study is to achieve an enhanced EOF in the surface modulated channel. A significant enhancement in average EOF is found for a particular arrangement of grooves with the width of the grooves much higher than its depth and the Debye length is in the order of the channel height. However, the formation of vortex inside the narrow grooves can reduce the EOF when the groove depth is in the order of its width. Results are compared with the cases in which the grooves are replaced by superhydrophobic patches along which a zero shear stress condition is imposed.
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Marshall, G., P. Mocskos, F. Molina, and S. Dengra. "The Role of Coulombic Forces in Quasi-Two Dimensional Electrochemical Deposition." MRS Proceedings 451 (1996). http://dx.doi.org/10.1557/proc-451-147.
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ABSTRACTRecent work demonstrates the relevant influence of convection during growth pattern formation in thin-layer electrochemical deposition. Convection is driven mainly by coulombic forces due to local charges at the tip of the aggregation and by buoyancy forces due to concentration gradients. Here we study through physical experiments and numerical modeling the regime under which coulombic forces are important. In the experimental measurements fluid motion near the growing tips of the deposit is visualized with neutrally buoyant latex spheres and its speed measured with videomicroscope tracking techniques and image processing software. The numerical modeling consists in the solution of the 2D dimensionless Nernst-Planck equations for ion concentrations, the Poisson equation for the electric field and the Navier-Stokes equations for the fluid flow, and a stochastic growth rule for ion deposition. A new set of dimensionless numbers governing electroconvection dominated flows is introduced. Preliminary experimental measurements and numerical results indicate that in the electroconvection dominated regime coulombic forces increase with the applied voltage, and their influence over growth pattern formation can be assessed with the magnitude of the dimensionless electric Froude number. It is suggested that when this number decreases the deposit morphology changes from fractal to dense branching.
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Nandigana, Vishal V. R., and N. R. Aluru. "Nonlinear Electrokinetic Transport Under Combined ac and dc Fields in Micro/Nanofluidic Interface Devices." Journal of Fluids Engineering 135, no. 2 (February 1, 2013). http://dx.doi.org/10.1115/1.4023442.
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The integration of micro/nanofluidic devices led to many interesting phenomena and one of the most important and complex phenomenon among them is concentration polarization. In this paper, we report new physical insights in micro/nanofluidic interface devices on the application of ac and dc electric fields. By performing detailed numerical simulations based on the coupled Poisson, Nernst–Planck, and incompressible Navier–Stokes equations, we discuss electrokinetic transport and other hydrodynamic effects under the application of combined ac and dc electric fields for different nondimensional electrical double layer (EDL) thicknesses and nanochannel wall surface charge densities. We show that for a highly ion-selective nanochannel, the application of the combined ac/dc electric field, at amplitudes greater than the dc voltage and at a low Strouhal number, results in large dual concentration polarization regions (with unequal lengths) at both the micro/nanofluidic interfaces due to large and unequal voltage drops at these junctions. The highly nonlinear potential distribution gives rise to an electric field and body force that changes the electrokinetic fluid velocity from that obtained on the application of only a dc source.
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Dewangan, Mainendra Kumar, Uddipta Ghosh, Tanguy Le Borgne, and Yves Méheust. "Coupled electrohydrodynamic transport in rough fractures: a generalized lubrication theory." Journal of Fluid Mechanics 942 (May 17, 2022). http://dx.doi.org/10.1017/jfm.2022.306.
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Fractures provide pathways for fluids and solutes through crystalline rocks and low permeability materials, thus playing a key role in many subsurface processes and applications. In small aperture fractures, solute transport is strongly impacted by the coupling of electrical double layers at mineral–fluid interfaces to bulk ion transport. Yet, most models of flow and transport in fractures ignore these effects. Solving such coupled electrohydrodynamics in realistic three-dimensional (3-D) fracture geometries poses computational challenges which have so far limited our understanding of those electro-osmotic effects’ impact. Starting from the Poisson–Nernst–Planck–Navier–Stokes (PNPNS) equations and using a combination of rescaling, asymptotic analysis and the Leibniz rule, we derive a set of nonlinearly coupled conservation equations for the local fluxes of fluid mass, solute mass and electrical charges. Their solution yields the fluid pressure, solute concentration and electrical potential fields. The model is validated by comparing its predictions to the solutions of the PNPNS equations in 3-D rough fractures. Application of the model to realistic rough fracture geometries evidences several phenomena hitherto not reported in the literature, including: (i) a dependence of the permeability and electrical conductivity on the fracture walls’ charge density, (ii) local (sometimes global) flow reversal, and (iii) spatial heterogeneities in the concentration field without any imposed concentration gradient. This new theoretical framework will allow systematically addressing large statistics of fracture geometry realizations of given stochastic parameters, to infer the impact of the geometry and various hydrodynamic and electrical parameters on the coupled transport of fluid and ions in rough fractures.
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Riad, Adham, Behnam Khorshidi, and Mohtada Sadrzadeh. "Analysis of streaming potential flow and electroviscous effect in a shear-driven charged slit microchannel." Scientific Reports 10, no. 1 (October 27, 2020). http://dx.doi.org/10.1038/s41598-020-75531-6.
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Abstract Investigating the flow behavior in microfluidic systems has become of interest due to the need for precise control of the mass and momentum transport in microfluidic devices. In multilayered-flows, precise control of the flow behavior requires a more thorough understanding as it depends on multiple parameters. The following paper proposes a microfluidic system consisting of an aqueous solution between a moving plate and a stationary wall, where the moving plate mimics a charged oil–water interface. Analytical expressions are derived by solving the nonlinear Poisson–Boltzmann equation along with the simplified Navier–Stokes equation to describe the electrokinetic effects on the shear-driven flow of the aqueous electrolyte solution. The Debye–Huckel approximation is not employed in the derivation extending its compatibility to high interfacial zeta potential. Additionally, a numerical model is developed to predict the streaming potential flow created due to the shear-driven motion of the charged upper wall along with its associated electric double layer effect. The model utilizes the extended Nernst–Planck equations instead of the linearized Poisson–Boltzmann equation to accurately predict the axial variation in ion concentration along the microchannel. Results show that the interfacial zeta potential of the moving interface greatly impacts the velocity profile of the flow and can reverse its overall direction. The numerical results are validated by the analytical expressions, where both models predicted that flow could reverse its overall direction when the interfacial zeta potential of the oil–water is above a certain threshold value. Finally, this paper describes the electroviscous effect as well as the transient development of electrokinetic effects within the microchannel.
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Bhattacharyya, S., and Subrata Bera. "Nonlinear Electroosmosis Pressure-Driven Flow in a Wide Microchannel With Patchwise Surface Heterogeneity." Journal of Fluids Engineering 135, no. 2 (February 1, 2013). http://dx.doi.org/10.1115/1.4023446.
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In this paper, we have studied the electrokinetics and mixing driven by an imposed pressure gradient and electric field in a charged modulated microchannel. By performing detailed numerical simulations based on the coupled Poisson, Nernst–Planck, and incompressible Navier–Stokes equations, we discussed electrokinetic transport and other hydrodynamic effects under the application of combined pressure and dc electric fields for different values of electric double layer thickness and channel patch potential. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. Since electroosmotic flow depends on the magnitude and sign of wall potential, a vortex can be generated through adjusting the patch potential. The dependence of the vortical flow on imposed pressure gradient is investigated. Formation of vortex in electroosmotic flow has importance in producing solute dispersion. The circulation of vortex grows with the rise of patch potential, whereas the pressure-assisted electroosmotic flow produces a reduction in vortex size. However, the flow rate is substantially increased in pressure-assisted electroosmotic flow. Flow reversal and suppression of fluid transport is possible through an adverse pressure gradient. The ion distribution and electric field above the potential patch are distorted by the imposed pressure gradient. At higher values of the pressure gradient, the combined pressure electroosmotic-driven flow resembles the fully developed Poiseuille flow. Current density is found to increase with the rise of imposed pressure gradient.
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Monesi, Mahdiyeh, Mahdi Khatibi, and Ahmad Rahbar-Kelishami. "A simulation study of an electro-membrane extraction for enhancement of the ion transport via tailoring the electrostatic properties." Scientific Reports 12, no. 1 (July 16, 2022). http://dx.doi.org/10.1038/s41598-022-16482-y.
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AbstractMembrane technology with advantages such as reduced energy consumption due to no phase change, low volume and high mass transfer, high separation efficiency for solution solutions, straightforward design of membranes, and ease of use on industrial scales are different from other separation methods. There are various methods such as liquid–liquid extraction, adsorption, precipitation, and membrane processes to separate contaminants from an aqueous solution. The liquid membrane technique provides a practical and straightforward separation method for metal ions as an advanced solvent extraction technique. Stabilized liquid membranes require less solvent consumption, lower cost, and more effortless mass transfer due to their thinner thickness than other liquid membrane techniques. The influence of the electrostatic properties, derived from the electrical field, on the ionic transport rate and extraction recovery, in flat sheet supported liquid membrane (FSLM) and electro flat sheet supported liquid membrane (EFSLM) were numerically investigated. Both FSLM and EFSLM modes of operation, in terms of implementing electrostatic, were considered. Through adopting a numerical approach, Poisson-Nernst-Planck, and Navier–Stokes equations were solved at unsteady-state conditions by considering different values of permittivity, diffusivity, and viscosity for the presence of electrical force and stirrer, respectively. The most important result of this study is that under similar conditions, by increasing the applied voltage, the extraction recovery increased. For instance, at EFSLM mode, by increasing the applied voltage from $$10 $$ 10 to $$30 {\text{V}}$$ 30 V , the extraction recovery increased from $$53$$ 53 to $$98\%$$ 98 % . Furthermore, it was also observed that the presence of nanoparticles has significant effects on the performance of the SLM system.