Search results for: electroosmotic

Authors: Oscar Bautista, Jose Arcos

Abstract:

In this work, we conduct a theoretical analysis of an oscillatory electroosmotic flow in a parallel-plate microchannel taking into account slippage at the microchannel walls. The governing equations given by the Poisson-Boltzmann (with the Debye-Huckel approximation) and momentum equations are nondimensionalized from which four dimensionless parameters appear; a Reynolds angular number, the ratio between the zeta potentials of the microchannel walls, the electrokinetic parameter and the dimensionless slip length which measures the competition between the Navier slip length and the half height microchannel. The principal results indicate that the slippage has a strong influence on the magnitude of the oscillatory electroosmotic flow increasing the velocity magnitude up to 50% for the numerical values used in this work.

Keywords: electroosmotic flows, oscillatory flow, slippage, microchannel

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Authors: Jaime Muñoz, José Arcos, Oscar Bautista Federico Méndez

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The influence of a pulsatile electroosmotic flow (PEOF) at the rate of spread, or dispersivity, for a non-reactive solute released in a microcapillary with slippage at the boundary wall (modeled by the Navier-slip condition) is theoretically analyzed. Based on the flow velocity field developed under such conditions, the present study implements an analytical scheme of scaling known as the Theory of Homogenization, in order to obtain a mathematical expression for the dispersivity, valid at a large time scale where the initial transients have vanished and the solute spreads under the Taylor dispersion influence. Our results show the dispersivity is a function of a slip coefficient, the amplitude of the imposed electric field, the Debye length and the angular Reynolds number, highlighting the importance of the latter as an enhancement/detrimental factor on the dispersivity, which allows to promote the PEOF as a strong candidate for chemical species separation at lab-on-a-chip devices.

Keywords: dispersivity, microcapillary, Navier-slip condition, pulsatile electroosmotic flow, Taylor dispersion, Theory of Homogenization

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Authors: Naren Bag, S. Bhattacharyya, Partha P. Gopmandal

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In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Keywords: electric double layer, finite volume method, flow behavior index, mixed electroosmotic/pressure driven flow, non-Newtonian power-law fluids, numerical simulation

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Authors: Maher Z. Mohammed, Barry G. Clarke

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As an alternative to stone column in fine grained soils, it is possible to create stiffened columns of soils using electroosmosis (electroosmotic piles). This program of this research is to establish the effectiveness and efficiency of the process in different soils. The aim of this study is to assess the capability of electroosmosis treatment in a range of composite soils. The combined electroosmotic and preloading equipment developed by Nizar and Clarke (2013) was used with an octagonal array of anodes surrounding a single cathode in a nominal 250mm diameter 300mm deep cylinder of soil and 80mm anode to cathode distance. Copper coiled springs were used as electrodes to allow the soil to consolidate either due to an external vertical applied load or electroosmosis. The equipment was modified to allow the temperature to be monitored during the test. Electroosmotic tests were performed on China Clay Grade E kaolin and calcium bentonite (Bentonex CB) mixed with sand fraction C (BS 1881 part 131) at different ratios by weight; (0, 23, 33, 50 and 67%) subjected to applied voltages (5, 10, 15 and 20). The soil slurry was prepared by mixing the dry soil with water to 1.5 times the liquid limit of the soil mixture. The mineralogical and geotechnical properties of the tested soils were measured before the electroosmosis treatment began. In the electroosmosis cell tests, the settlement, expelled water, variation of electrical current and applied voltage, and the generated heat was monitored during the test time for 24 osmotic tests. Water content was measured at the end of each test. The electroosmotic tests are divided into three phases. In Phase 1, 15 kPa was applied to simulate a working platform and produce a uniform soil which had been deposited as a slurry. 50 kPa was used in Phase 3 to simulate a surcharge load. The electroosmotic treatment was only performed during Phase 2 where a constant voltage was applied through the electrodes in addition to the 15 kPa pressure. This phase was stopped when no further water was expelled from the cell, indicating the electroosmotic process had stopped due to either the degradation of the anode or the flow due to the hydraulic gradient exactly balanced the electroosmotic flow resulting in no flow. Control tests for each soil mixture were carried out to assess the behaviour of the soil samples subjected to only an increase of vertical pressure, which is 15kPa in Phase 1 and 50kPa in Phase 3. Analysis of the experimental results from this study showed a significant dewatering effect on the soil slurries. The water discharged by the electroosmotic treatment process decreased as the sand content increased. Soil temperature increased significantly when electrical power was applied and drops when applied DC power turned off or when the electrode degraded. The highest increase in temperature was found in pure clays at higher applied voltage after about 8 hours of electroosmosis test.

Keywords: electrokinetic treatment, electrical conductivity, electroosmotic consolidation, electroosmosis permeability ratio

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Authors: Virendra J. Majarikar, Harikrishnan N. Unni

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This paper sets to demonstrate a modeling of electrokinetic mixing employing electroosmotic stationary and time-dependent microchannel using alternate zeta patches on the lower surface of the micromixer in a lab on chip microfluidic device. Electroosmotic flow is amplified using different 2D and 3D model designs with alternate and geometric zeta potential values such as 25, 50, and 100 mV, respectively, to achieve high concentration mixing in the electrokinetically-driven microfluidic system. The enhancement of electrokinetic mixing is studied using Finite Element Modeling, and simulation workflow is accomplished with defined integral steps. It can be observed that the presence of alternate zeta patches can help inducing microvortex flows inside the channel, which in turn can improve mixing efficiency. Fluid flow and concentration fields are simulated by solving Navier-Stokes equation (implying Helmholtz-Smoluchowski slip velocity boundary condition) and Convection-Diffusion equation. The effect of the magnitude of zeta potential, the number of alternate zeta patches, etc. are analysed thoroughly. 2D simulation reveals that there is a cumulative increase in concentration mixing, whereas 3D simulation differs slightly with low zeta potential as that of the 2D model within the T-shaped micromixer for concentration 1 mol/m³ and 0 mol/m³, respectively. Moreover, 2D model results were compared with those of 3D to indicate the importance of the 3D model in a microfluidic design process.

Keywords: COMSOL Multiphysics®, electrokinetic, electroosmotic, microfluidics, zeta potential

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Authors: Rubén Bãnos, José Arcos, Oscar Bautista, Federico Méndez

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The Oscillatory electroosmotic flow (OEOF) in power law fluids through a microchannel is studied numerically. A time-dependent external electric field (AC) is suddenly imposed at the ends of the microchannel which induces the fluid motion. The continuity and momentum equations in the x and y direction for the flow field were simplified in the limit of the lubrication approximation theory (LAT), and then solved using a numerical scheme. The solution of the electric potential is based on the Debye-H¨uckel approximation which suggest that the surface potential is small,say, smaller than 0.025V and for a symmetric (z : z) electrolyte. Our results suggest that the velocity profiles across the channel-width are controlled by the following dimensionless parameters: the angular Reynolds number, Reω, the electrokinetic parameter, ¯κ, defined as the ratio of the characteristic length scale to the Debye length, the parameter λ which represents the ratio of the Helmholtz-Smoluchowski velocity to the characteristic length scale and the flow behavior index, n. Also, the results reveal that the velocity profiles become more and more non-uniform across the channel-width as the Reω and ¯κ are increased, so oscillatory OEOF can be really useful in micro-fluidic devices such as micro-mixers.

Keywords: low zeta potentials, non-newtonian, oscillatory electroosmotic flow, power-law model

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Authors: Ainul Haque, Ameeye Kumar Nayak

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Flow enhancement and species transport in a slit hydrophobic microchannel is studied for non-Newtonian fluids with the externally imposed electric field and pressure gradient. The incompressible Poisson-Nernst-Plank equations and the Navier-Stokes equations are approximated by lubrication theory to quantify the flow structure due to hydrophobic and hydrophilic surfaces. The analytical quantification of velocity and pressure of electroosmotic flow (EOF) is made with the numerical results due to the staggered grid based finite volume method for flow governing equations. The resistance force due to fluid friction and shear force along the surface are decreased by the hydrophobicity, enables the faster movement of fluid particles. The resulting flow enhancement factor Ef is increased with the low viscous fluid and provides maximum species transport. Also, the analytical comparison of EOF with pressure driven EOF justifies the flow enhancement due to hydrophobicity and shear impact on flow variation.

Keywords: electroosmotic flow, hydrophobic surface, power-law fluid, shear effect

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Authors: Partha P. Gopmandal, Somnath Bhattacharyya, Naren Bag

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In this article, we have studied the effect of pH-regulated surface charge on the electroosmotic flow (EOF) through nanochannel filled with binary symmetric electrolyte solution. The channel wall possesses either an acidic or a basic functional group. Going beyond the widely employed Debye-Huckel linearization, we develop a mathematical model based on Nernst-Planck equation for the charged species, Poisson equation for the induced potential, Stokes equation for fluid flow. A finite volume based numerical algorithm is adopted to study the effect of key parameters on the EOF. We have computed the coupled governing equations through the finite volume method and our results found to be in good agreement with the analytical solution obtained from the corresponding linear model based on low surface charge condition or strong electrolyte solution. The influence of the surface charge density, reaction constant of the functional groups, bulk pH, and concentration of the electrolyte solution on the overall flow rate is studied extensively. We find the effect of surface charge diminishes with the increase in electrolyte concentration. In addition for strong electrolyte, the surface charge becomes independent of pH due to complete dissociation of the functional groups.

Keywords: electroosmosis, finite volume method, functional group, surface charge

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Authors: Carlos Teodoro, Oscar Bautista

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In this work, we analyze theoretically the mass transport in a time-periodic electroosmotic flow through a parallel flat plate microchannel under different periodic functions of the applied external electric field. The microchannel connects two reservoirs having different constant concentrations of an electro-neutral solute, and the zeta potential of the microchannel walls are assumed to be uniform. The governing equations that allow determining the mass transport in the microchannel are given by the Poisson-Boltzmann equation, the modified Navier-Stokes equations, where the Debye-Hückel approximation is considered (the zeta potential is less than 25 mV), and the species conservation. These equations are nondimensionalized and four dimensionless parameters appear which control the mass transport phenomenon. In this sense, these parameters are an angular Reynolds, the Schmidt and the Péclet numbers, and an electrokinetic parameter representing the ratio of the half-height of the microchannel to the Debye length. To solve the mathematical model, first, the electric potential is determined from the Poisson-Boltzmann equation, which allows determining the electric force for various periodic functions of the external electric field expressed as Fourier series. In particular, three different excitation wave forms of the external electric field are assumed, a) sawteeth, b) step, and c) a periodic irregular functions. The periodic electric forces are substituted in the modified Navier-Stokes equations, and the hydrodynamic field is derived for each case of the electric force. From the obtained velocity fields, the species conservation equation is solved and the concentration fields are found. Numerical calculations were done by considering several binary systems where two dilute species are transported in the presence of a carrier. It is observed that there are different angular frequencies of the imposed external electric signal where the total mass transport of each species is the same, independently of the molecular diffusion coefficient. These frequencies are called crossover frequencies and are obtained graphically at the intersection when the total mass transport is plotted against the imposed frequency. The crossover frequencies are different depending on the Schmidt number, the electrokinetic parameter, the angular Reynolds number, and on the type of signal of the external electric field. It is demonstrated that the mass transport through the microchannel is strongly dependent on the modulation frequency of the applied particular alternating electric field. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.

Keywords: electroosmotic flow, mass transport, oscillatory flow, species separation

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Authors: Alper T. Celebi, Ali Beskok

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Electroosmotic (EO) slip flows in nanochannels are investigated using non-equilibrium molecular dynamics (MD) simulations, and the results are compared with analytical solution of Poisson-Boltzmann and Stokes (PB-S) equations with slip contribution. The ultimate objective of this study is to show that well-known continuum flow model can accurately predict the EO velocity profiles in nanochannels using the slip lengths and apparent viscosities obtained from force-driven flow simulations performed at various liquid-wall interaction strengths. EO flow of aqueous NaCl solution in silicon nanochannels are simulated under realistic electrochemical conditions within the validity region of Poisson-Boltzmann theory. A physical surface charge density is determined for nanochannels based on dissociations of silanol functional groups on channel surfaces at known salt concentration, temperature and local pH. First, we present results of density profiles and ion distributions by equilibrium MD simulations, ensuring that the desired thermodynamic state and ionic conditions are satisfied. Next, force-driven nanochannel flow simulations are performed to predict the apparent viscosity of ionic solution between charged surfaces and slip lengths. Parabolic velocity profiles obtained from force-driven flow simulations are fitted to a second-order polynomial equation, where viscosity and slip lengths are quantified by comparing the coefficients of the fitted equation with continuum flow model. Presence of charged surface increases the viscosity of ionic solution while the velocity-slip at wall decreases. Afterwards, EO flow simulations are carried out under uniform electric field for different liquid-wall interaction strengths. Velocity profiles present finite slips near walls, followed with a conventional viscous flow profile in the electrical double layer that reaches a bulk flow region in the center of the channel. The EO flow enhances with increased slip at the walls, which depends on wall-liquid interaction strength and the surface charge. MD velocity profiles are compared with the predictions from analytical solutions of the slip modified PB-S equation, where the slip length and apparent viscosity values are obtained from force-driven flow simulations in charged silicon nano-channels. Our MD results show good agreements with the analytical solutions at various slip conditions, verifying the validity of PB-S equation in nanochannels as small as 3.5 nm. In addition, the continuum model normalizes slip length with the Debye length instead of the channel height, which implies that enhancement in EO flows is independent of the channel height. Further MD simulations performed at different channel heights also shows that the flow enhancement due to slip is independent of the channel height. This is important because slip enhanced EO flow is observable even in micro-channels experiments by using a hydrophobic channel with large slip and high conductivity solutions with small Debye length. The present study provides an advanced understanding of EO flows in nanochannels. Correct characterization of nanoscale EO slip flow is crucial to discover the extent of well-known continuum models, which is required for various applications spanning from ion separation to drug delivery and bio-fluidic analysis.

Keywords: electroosmotic flow, molecular dynamics, slip length, velocity-slip

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Authors: Yun-Hsiang Wang, Huai-Yi Chen, Kin Fong Lei

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Deoxyribonucleic acid (DNA) hybridization is a common technique used in genetic assay widely. However, the hybridization ratio and rate are usually limited by the diffusion effect. Here, microfluidic electrode platform producing electroosmosis generated by alternating current signal has been proposed to enhance the hybridization ratio and rate. The electrode was made of aurum fabricated by microfabrication technique. Thiol-modified oligo probe was immobilized on the electrode for specific capture of target, which is modified by fluorescent tag. Alternative electroosmosis can induce local microfluidic vortexes to accelerate DNA hybridization. This study provides a strategy to enhance the rate of DNA hybridization in the genetic assay.

Keywords: DNA hybridization, electroosmosis, electrical enhancement, hybridization ratio

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Authors: Bahram Talebjedi, Emily Earl, Mina Hoorfar

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One of the issues that arises with microscale lab-on-a-chip technology is that the laminar flow within the microchannels limits the mixing of fluids. To combat this, micromixers have been introduced as a means to try and incorporate turbulence into the flow to better aid the mixing process. This study presents an electroosmotic micromixer that balances vortex generation and degeneration with the inlet flow velocity to greatly increase the mixing efficiency. A comprehensive parametric study was performed to evaluate the role of the relevant parameters on the mixing efficiency. It was observed that the suggested micromixer is perfectly suited for biological applications due to its low pressure drop (below 10 Pa) and low shear rate. The proposed micromixer with optimized working parameters is able to attain a mixing efficiency of 95% in a span of 0.5 seconds using a frequency of 10 Hz, a voltage of 0.7 V, and an inlet velocity of 0.366 mm/s.

Keywords: microfluidics, active mixer, pulsed AC electroosmosis flow, micromixer

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Authors: Reza Hadjiaghaie Vafaie, Aysan Madanpasandi, Behrooz Zare Desari, Seyedmohammad Mousavi

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High lamination in microchannel is one of the main challenges in on-chip components like micro total analyzer systems and lab-on-a-chips. Electro-osmotic force is highly effective in chip-scale. This research proposes a microfluidic-based micropump for low ionic strength solutions. Narrow microchannels are designed to generate an efficient electroosmotic flow near the walls. Microelectrodes are embedded in the lateral sides and actuated by low electric potential to generate pumping effect inside the channel. Based on the simulation study, the fluid velocity increases by increasing the electric potential amplitude. We achieve a net flow velocity of 100 µm/s, by applying +/- 2 V to the electrode structures. Our proposed low voltage design is of interest in conventional lab-on-a-chip applications.

Keywords: integration, electrokinetic, on-chip, fluid pumping, microfluidic

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Authors: Yana Posmitnaya, Galina Rudnitskaya, Tatyana Lukashenko, Anton Bukatin, Anatoly Evstrapov

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An important area of biological and medical research is the study of genetic mutations and polymorphisms that can alter gene function and cause inherited diseases and other diseases. The following methods to analyse DNA fragments are used: capillary electrophoresis and electrophoresis on microfluidic chip (MFC), mass spectrometry with electrophoresis on MFC, hybridization assay on microarray. Electrophoresis on MFC allows to analyse small volumes of samples with high speed and throughput. A soft lithography in polydimethylsiloxane (PDMS) was chosen for operative fabrication of MFCs. A master-form from silicon and photoresist SU-8 2025 (MicroChem Corp.) was created for the formation of micro-sized structures in PDMS. A universal topology which combines T-injector and simple cross was selected for the electrophoretic separation of the sample. Glass K8 and PDMS Sylgard® 184 (Dow Corning Corp.) were used for fabrication of MFCs. Electroosmotic flow (EOF) plays an important role in the electrophoretic separation of the sample. Therefore, the estimate of the quantity of EOF and the ways of its regulation are of interest for the development of the new methods of the electrophoretic separation of biomolecules. The following methods of surface modification were chosen to change EOF: high-frequency (13.56 MHz) plasma treatment in oxygen and argon at low pressure (1 mbar); 1% aqueous solution of polyvinyl alcohol; 3% aqueous solution of Kolliphor® P 188 (Sigma-Aldrich Corp.). The electroosmotic mobility was evaluated by the method of Huang X. et al., wherein the borate buffer was used. The influence of physical and chemical methods of treatment on the wetting properties of the PDMS surface was controlled by the sessile drop method. The most effective way of surface modification of MFCs, from the standpoint of obtaining the smallest value of the contact angle and the smallest value of the EOF, was the processing with aqueous solution of Kolliphor® P 188. This method of modification has been selected for the treatment of channels of MFCs, which are used for the separation of mixture of oligonucleotides fluorescently labeled with the length of chain with 10, 20, 30, 40 and 50 nucleotides. Electrophoresis was performed on the device MFAS-01 (IAI RAS, Russia) at the separation voltage of 1500 V. 6% solution of polydimethylacrylamide with the addition of 7M carbamide was used as the separation medium. The separation time of components of the mixture was determined from electropherograms. The time for untreated MFC was ~275 s, and for the ones treated with solution of Kolliphor® P 188 – ~ 220 s. Research of physical-chemical methods of surface modification of MFCs allowed to choose the most effective way for reducing EOF – the modification with aqueous solution of Kolliphor® P 188. In this case, the separation time of the mixture of oligonucleotides decreased about 20%. The further optimization of method of modification of channels of MFCs will allow decreasing the separation time of sample and increasing the throughput of analysis.

Keywords: electrophoresis, microfluidic chip, modification, nucleic acid, polydimethylsiloxane, soft lithography

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Authors: Dilin Chen, Kang Luo, Jian Wu, Chun Yang, Hongliang Yi

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Electrically driven flows (EDF) systems play an important role in fuel cells, electrochemistry, bioseparation technology, fluid pumping, and microswimmers. The core scientific problem is multifield coupling, the further development of which depends on the exploration of nonlinear instabilities, force competing mechanisms, and energy budgets. In our study, two categories of electrostatic force-dominated phenomena, induced charge electrosmosis (ICEO) and ion conduction pumping are investigated while considering polymer rheological characteristics and heat gradients. With finite volume methods, the thermal modulation strategy of ICEO under the thermal buoyancy force is numerically analyzed, and the electroelastic instability turn associated with polymer addition is extended. The results reveal that the thermal buoyancy forces are sufficient to create typical thermogravitational convection in competition with electroconvective modes. Electroelastic instability tends to be promoted by weak electrical forces, and polymers effectively alter the unstable transition routes. Our letter paves the way for improved mixing and heat transmission in microdevices, as well as insights into the non-Newtonian nature of electrohydrodynamic dynamics.

Keywords: non-Newtonian fluid, electroosmotic flow, electrohydrodynamic, viscoelastic liquids, heat transfer

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Authors: Brian Wartell, Michel Boufadel

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Contaminants such as polycyclic aromatic hydrocarbons (PAHs) are compounds present in crude and petroleum oils and are known to be toxic and often carcinogenic. Therefore, a major effort is placed on tracking their subsurface soil concentrations following an oil spill. The PAHs can persist for years in the subsurface especially if there is a lack of oxygen. Both aerobic and anaerobic biodegradation of PAHs encounter the difficulties of both nutrient transport and bioavailability (proximal access) to the organisms of the contaminants. A technology, known as electrokinetics (EK or EK-BIO for ‘electrokinetic bioremediation’) has been found to transport efficiently nutrients or other chemicals in the subsurface. Experiments were conducted to demonstrate migration patterns in both sands and clay for both ionic and nonionic compounds and aerobic biodegradation studies were conducted with soil spiked with Polycyclic Aromatic Hydrocarbons yielding interesting results. In one set of experiment, Self-designed electrokinetic setups were constructed to examine the differences in electromigration and electroosmotic rates. Anionic and non-ionic dyes were used to visualize these phenomena, respectively. In another experiment, a silt-clay soil was spiked with three low-molecular-weight compounds (fluorene, phenanthrene, fluoranthene) and placed within self-designed electrokinetic setups and monitored for aerobic degradation. Plans for additional studies are in progress including the transport of peroxide through anaerobic sands.

Keywords: bioavailability, bioremediation, electrokinetics, subsurface transport

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Authors: Somnath Bhattacharyya

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The mobile adsorbed surface charge on hydrophobic surfaces can modify the velocity slip condition as well as create a Marangoni stress at the interface. The functionalized hydrophobic walls of micro/nanopores, e.g., graphene nanochannels, may possess physio-sorbed ions. The lateral mobility of the physisorbed absorbed ions creates a friction force as well as an electric force, leading to a modification in the velocity slip condition at the hydrophobic surface. In addition, the non-uniform distribution of these surface ions creates a surface tension gradient, leading to a Marangoni stress. The impact of the mobile surface charge on streaming potential and electrochemical energy conversion efficiency in a pressure-driven flow of ionized liquid through the nanopore is addressed. Also, enhanced electro-osmotic flow through the hydrophobic nanochannel is also analyzed. The mean-filed electrokinetic model is modified to take into account the short-range non-electrostatic steric interactions and the long-range Coulomb correlations. The steric interaction is modeled by considering the ions as charged hard spheres of finite radius suspended in the electrolyte medium. The electrochemical potential is modified by including the volume exclusion effect, which is modeled based on the BMCSL equation of state. The electrostatic correlation is accounted for in the ionic self-energy. The extremal of the self-energy leads to a fourth-order Poisson equation for the electric field. The ion transport is governed by the modified Nernst-Planck equation, which includes the ion steric interactions; born force arises due to the spatial variation of the dielectric permittivity and the dielectrophoretic force on the hydrated ions. This ion transport equation is coupled with the Navier-Stokes equation describing the flow of the ionized fluid and the 3fourth-order Poisson equation for the electric field. We numerically solve the coupled set of nonlinear governing equations along with the prescribed boundary conditions by adopting a control volume approach over a staggered grid arrangement. In the staggered grid arrangements, velocity components are stored on the midpoint of the cell faces to which they are normal, whereas the remaining scalar variables are stored at the center of each cell. The convection and electromigration terms are discretized at each interface of the control volumes using the total variation diminishing (TVD) approach to capture the strong convection resulting from the highly enhanced fluid flow due to the modified model. In order to link pressure to the continuity equation, we adopt a pressure correction-based iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm, in which the discretized continuity equation is converted to a Poisson equation involving pressure correction terms. Our results show that the physisorbed ions on a hydrophobic surface create an enhanced slip velocity when streaming potential, which enhances the convection current. However, the electroosmotic flow attenuates due to the mobile surface ions.

Keywords: microfluidics, electroosmosis, streaming potential, electrostatic correlation, finite sized ions

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