Academic literature on the topic 'Poisson-Nernst-Planck-Navier-Stokes equations'
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Journal articles on the topic "Poisson-Nernst-Planck-Navier-Stokes equations"
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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.
Conference papers on the topic "Poisson-Nernst-Planck-Navier-Stokes equations"
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Banerjee, A., and A. K. Nayak. "Electroosmotic Flow Separation in a Corrugated Micro-Channel: A Numerical Study." In ASME 2018 5th Joint US-European Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/fedsm2018-83026.
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A two dimensional numerical study is made on the electroosmotic flow separation and vortex formation in a symmetric wavy micro/nano channel filled with a Newtonian, incompressible electrolyte. Flow domain is modelled by two superimposed sinusoidal functions which is mapped into a simpler rectangular computational domain using a suitable coordinate transformation. The distributions of flow field and electric potential are obtained by solving a coupled set of nonlinear governing equations involving Poisson-Nernst-Planck equation and Navier-Stokes equation using finite volume method. Threshold value of the scaled wave amplitude for flow reversal is obtained for fixed Debye-Hückel parameter and solute strength where flow separation plays a vital role for micromixing which can be a major interest for many research problems of biological flows.
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Tang, G. Y., C. Yang, C. J. Chai, and H. Q. Gong. "Joule Heating Induced Thermal and Hydrodynamic Development in Microfluidic Electroosmotic Flow." In ASME 2004 2nd International Conference on Microchannels and Minichannels. ASMEDC, 2004. http://dx.doi.org/10.1115/icmm2004-2442.
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Joule heating is present in electrokinetically driven flow and mass transport in microfluidic systems. Specifically, in the cases of high applied voltages and concentrated buffer solutions, the thermal management may become a problem. In this study, a mathematical model is developed to describe the Joule heating and its effects on electroosmotic flow and mass species transport in microchannels. The proposed model includes the Poisson equation, the modified Navier-Stokes equation, and the conjugate energy equation (for the liquid solution and the capillary wall). Specifically, the ionic concentration distributions are modeled using (i) the general Nernst-Planck equation, and (ii) the simple Boltzmann distribution. These governing equations are coupled through temperature-dependent phenomenological thermal-physical coefficients, and hence they are numerically solved using a finite-volume based CFD technique. A comparison has been made for the results of the ionic concentration distributions and the electroosmotic flow velocity and temperature fields obtained from the Nernst-Planck equation and the Boltzmann equation. The time and spatial developments for both the electroosmotic flow fields and the Joule heating induced temperature fields are presented. In addition, sample species concentration is obtained by numerically solving the mass transport equation, taking into account of the temperature-dependent mass diffusivity and electrophoresis mobility. The results show that the presence of the Joule heating can result in significantly different electroosomotic flow and mass species transport characteristics.
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Chein, Reiyu, and Baogan Chung. "Electrokinetic Transport in Micro-Nanofluidic Systems With Sudden-Expansion and Contraction Cross Sections." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18120.
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In this study, electrokinetic transport in a micro-nanofluidic system is numerically investigated by solving the transient Poisson, Nernst-Planck, and Navier-Stokes equations simultaneously. The system considered is a nanochannel connected with two microchannels at its ends. Under various applied electric potential biases, the effect of concentration polarization on the fluid flow, induced pressure and electric current is examined. By comparing with the Donnan equilibrium condition and electroosmotic flow in microscale dimension, electric body force due to non-zero charge density is the mechanism for producing vortex flow and inducing positive pressure gradient in the anodic side of the system. The diffusive boundary layer thickness is reduced due to the stirring of the generated vortex flow and results in the over-limiting current when the applied electric potential bias is high.
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Wa¨lter, Bettina, and Peter Ehrhard. "Numerical Simulation of the Interplay of Electrical Double Layers, Electrode Reactions, and Pressure-Driven Flows in Microchannels." In ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62097.
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We investigate the influence of flow field and electrode reactions onto an electrical double layer (EDL), which is located in the immediate vicinity of the walls of a rectangular microchannel. The precise knowledge of the EDL appears to be important for many technical applications in microchannels of small width, since the electrokinetic effects, as electroosmosis or electrophoresis, in such cases depend on the detailed charge distribution. The mathematical model for the numerical treatment relies on a first–principle description of the EDL and the electrical forces caused by the electrical field between internal electrodes. Hence, the so–called Debye–Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the Navier–Stokes equations for the flow field, species transport equations, based on the Nernst–Planck equation, and a model for the electrode reactions, based on the Butler–Volmer equation. The simulations are time–dependent and two–dimensional (plane) in nature and employ a finite–volume method. It is discussed, e.g., how the thickness of the EDL expands at the stagnation point of a forced flow, as the velocity (or Reynolds number) is increased. Furthermore, the effect of electrode reactions on the ionic strength and, hence, on the EDL and the electroosmotic flow, are discussed.
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Zhou, Yi, Chun Yang, and Cunlu Zhao. "Thermal Effect on Electroosmotic Flow in a Slit Microchannel." In ASME 2013 11th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/icnmm2013-73055.
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Electroosmotic flow (EOF) in microfluidic systems is frequently subjected to thermal effect because of temperature-dependent material properties. Boltzmann equation is usually used to describe the ion distribution in EOF. This study will compare the ion distribution under the thermal effect with the Boltzmann distribution. Moreover, for thin electrical double layer (EDL), constant potential model always be used to simplify the calculation of EOF at constant charge. In this study, the thermal effects on EOF at both constant potential and constant charge are analyzed. In addition, as the surface charge density increases largely with higher temperature, in this study efforts are also made to address the thermal effect on EOF induced by the temperature-dependent charge density. In particular, a numerical model is presented for investigating the steady EOF under the thermal effect. The proposed model involves several coupled governing equations including the Nernst-Planck equations, the Poisson equation, the modified Navier-Stokes equations, and the energy equation. The simulation results show that the Boltzmann equation cannot fully describe the ionic concentration distributions under the large thermal effect when EDL overlap. Moreover, for thin EDL, the electroosmotic velocity under the thermal effect at constant potential is lower than that at constant charge, due to the negative electrothermal force at constant potential. Furthermore, it is revealed that the temperature-dependence of surface charge can significantly modify the characteristics of EOF.
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Wa¨lter, Bettina, and Peter Ehrhard. "Numerical Simulation of Fluid Flows and Mixing in Microchannels Induced by Internal Electrodes." In ASME 2009 7th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2009. http://dx.doi.org/10.1115/icnmm2009-82016.
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We investigate the influence of internal electrodes onto the flow field, governed by electroosmosis and electrophoresis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances, they can be operated at lower voltages and still ensure strong electrical field strength. Even at lower voltages, electrode reactions influence the species concentration fields, and the crucial question arises, whether at the electrodes all species can be kept in dissolution or whether some species are released in gaseous form. The position and charge of multiple internal electrodes is a further focus of our investigations: wall-tangential electrical field components are responsible for pumping, wall-normal electrical field components are responsible for mixing. Hence, an optimized position and charge of all electrodes will lead to an optimized electrical field, designed to fulfill the desired tasks of the modular microchannel. The mathematical model for the numerical treatment relies on a first-principle description of the EDL and the electrical forces caused by the electrical field between the internal electrodes. Hence, the so-called Debye-Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the continuity and Navier-Stokes equations for the flow field, species transport equations, based on the Nernst-Planck equation, and a charge transport equation. Further, a model for the electrode reactions, based on the Butler-Volmer equation, is in place. The simulations are time-dependent and two-dimensional in nature and employ a FVM.
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Hu, Guoqing. "Solute Transport in Nanochannels With Roughness-Like Structures." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18253.
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Newfound attention has been given to solute transport in nanochannels. Because the electric double layer (EDL) thickness is comparable to characteristic channel dimensions, nanochannels have been used to separate ionic species with a constant charge-to-size ratio (i.e., electrophoretic mobility) that otherwise cannot be separated in electroosmotic or pressure-driven flow along microchannels. In nanochannels, the electrical fields within the EDL cause transverse ion distributions and thus yield charge-dependent mean ion speeds in the flow. Surface roughness is usually inevitable during microfabrication of microchannels or nanochannels. Surface roughness is usually inevitable during the fabrication of nanochannels. In the present study, we develop a numerical model to investigate the transport of charged solutes in nanochannels with hundreds of roughness-like structures. The model is based on continuum theory that couples Navier-Stokes equations for flows, Poisson-Boltzmann equation for electrical fields, and Nernst-Planck equation for solute transports. Different operating conditions are considered and the solute transport patterns in rough channels are compared with those in smooth channels. Results indicate that solutes move slower in rough nanochannels than in smooth ones for both pressure-driven and electroosmotic flows. Moreover, solute separation can be significantly improved by surface roughness under certain circumstances.
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Chen, Yu-Feng, Ming-Chia Li, Wen-Jeng Chang, Chi-Chuan Wang, and C. P. Chen. "Electroosmotic Pumping Using Porous Anodic Alumina Membranes." In ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer. ASMEDC, 2008. http://dx.doi.org/10.1115/mnht2008-52137.
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This study demonstrated electroosmotic pumping with high flow rate per unit area at a rather low applied voltage through an alumina nano-porous membrane driven by Platinum mesh electrodes. The electrode was placed perpendicular to, and had direct contact with nano-channel inlet to reduce the electric voltage drop in the reservoir. The complete set of the Poisson-Nernst-Planck equations for electrical potential and ionic concentration, coupled with the Navier-Stokes equation were solved for the purpose of a full understanding of the ionic transport and flow characteristics of EOF in nano-fluidics capillaries. The measured flowrate versus electrolyte (KCl) concentration reveals that the flowrate is usually high in low concentration (10−5 M∼10−7 M) regime in which a maximum value also occurs. In addition, a remarkable surge of flow rate is observed when the concentration surpasses below 10−4 M. The maximum flowrate achieved from this study is 0.09 mL min−2V−1 cm−2 and the energy transfer efficiency is 0.43% at an operation voltage of 20V. The flowrates investigated in this study are comparable to other existing results whereas the corresponding operation voltage used this study is about one to two order lower than most existing results. Numerical results exhibit correct trends for nano flows involving strong overlap of electrical double layers. Comparisons of numerical and experimental results were made and discussed.
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Chiang, Chun-Lin, Che-Yen Lee, and Yu-shan Yeh. "Use Multiphysics Simulations and Resistive Pulse Sensing to Study the Effect of Metal and Non-Metal Nanoparticles in Different Salt Concentration." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69472.
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Wafer fabrication is a critical part of the semiconductor process when the finest linewidth with the improvement of technology continues to decline. The nanoparticles contained in the slurry or ultrapure water used for cleaning have a large influence on the manufacturing process. Therefore, semiconductor industry is hoping to find a viable method for on-line detection of the nanoparticles size and concentration. Resistive pulse sensing technology is one of the methods that may cover this question. There were a lot of reports showing that nanoparticles properties of materials differ significantly from their properties at nano length scales. So, we want to clear the translocation dynamic and ion current changes in measurement of metal nanoparticles or non-metal nanoparticles in different concentration electrolytes through the nanopore when resistive pulse sensing technology has been used. In this study, we try to use a finite element method that contains three governing equations to do multiphysics coupling simulations. The Navier-Stokes equation describes the laminar motion, the Nernst-Planck equation describes the ion transport, and the Poisson equation describes the potential distribution in the flow channel. Then, the reliability of the simulation results was verified by resistive pulse sensing test. The existing results showed that the lower the ion concentration the greater the effect of resistive pulse sensing was. We investigated the effect of resistive pulse sensing on different materials by both simulations and experiments. The results are discussed in this article.
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Bera, Subrata, and S. Bhattacharyya. "Effect of Charge Density on Electrokinetic Ions and Fluid Flow Through Polyelectrolyte Coated Nanopore." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69194.
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We have studied the electroosmotic flow (EOF) and its effect through a polyelectrolyte coated conical nanopore. The nanopore wall bears a uniform negative surface charge while charged density of the polyelectrolyte layer (PEL) bears positive charge. The degree of softness in the PEL is mainly affects the hydrodynamic field inside the nanopore while ionic current is not affected significantly by flow field. The characteristic of electrokinetic flow is based on the nonlinear Nernst-Planck equations for the ion transport coupled with the Brinkman extended Navier-Stokes equations for fluid flow and the Poisson equation for induced electric potential. The coupled set of governing non-linear equations for fluid flow and ionic species concentration are solved through a finite volume method on a staggered grid system. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field. This study investigated the importance of the bulk concentration of the electrolyte, the geometries of the nanopore and both the thickness and the charged density of PEL on the electrokinetic ion and fluid transport. The ratio of the cross-sectional average flow of the present model with plane cylindrical channel, decreases with the increase of the scaled charge density of PEL for both low and high ionic concentration cases when softness parameter and thickness of PEL are fixed. The average flow rate decreases with the increase of the PEL sealed charge density in both low and high ionic concentration cases for fixed PEL thickness. The increase of nanopore radius increases the cross sectional averaged flow for fixed scaled charged density and PEL thickness. The average flow rate decreases with the increase of the PEL thickness for fixed charged density of PEL. The critical value of scaled charge density of PEL is defined for which there is no flow through the nanopore. The average current density increases with the increase of applied electric field for different charged density of PEL. But there is no different of average current density for different charge density of PEL in high ionic concentration cases.