Soft Nanochannel Research Articles

Combined electroosmotic and pressure driven flow through soft nanochannel grafted with partially ion-penetrable polyelectrolyte layers

ABSTRACT This study explores the coupled effects of pressure-driven and electroosmotic flows in a soft nanochannel filled with non-Newtonian ionised liquid, where the inner walls are coated with a polymer layer. The ion partitioning effect occurs due to the Born energy, arising from the dielectric permittivity difference between the polyelectrolyte medium and the ionised liquid. The model incorporates the nonlinear Poisson-Boltzmann equation, the modified Darcy-Brinkman equation in the polyelectrolyte layer (PEL), the Cauchy momentum equation in the electrolyte domains and the continuity equation for incompressible fluids. Using the Debye-Hückel approximation for analytical results, the study validates numerical findings. The study considers the no-slip boundary condition on the walls and examines the impact of volume charge density of PEL, bulk electrolyte concentration, non-Newtonian fluid rheology and polymer layer characteristics and applied pressure gradient on flow modulation and ionic transport in the nanochannel. We provide rigorous mathematical results showing how electrohydrodynamic factors like charged PEL, flow behaviour index, EDL thickness, ion partitioning parameters, Debye-Hückel parameter and softness parameters influence the strength of the potential and the total flow modulation. We illustrate ion selectivity in the soft nanochannel and the friction factor across its walls, considering ion partitioning effects.

The electrokinetic energy conversion and streaming potential analytical solutions of couple stress nanofluids in the circular polyelectrolyte-grafted nanochannel

The purpose of this study is to investigate the variation of streaming potential and EKEC efficiency of nanofluids with couple stress in the circular polyelectrolyte-grafted (PE-grafted) nanochannel under the combined effect of periodic pressure and magnetic field. The analytical solutions of the velocity field in the PEL region and electrolyte solution are obtained by solving the modified Navier-Stokes equation and the influence of several dimensionless parameters on the streaming potential and electrokinetic energy conversion (EKEC) efficiency are further discussed graphically. The results indicate that the streaming potential decreases with increasing Hartmann number and nanoparticle diameter within a certain parameter range. The dimensionless velocity shows an oscillating trend at different oscillating Reynolds numbers, and the oscillation is more pronounced at the interface between the PEL and the electrolyte solution. In addition, the EKEC efficiency of nanofluids in soft nanochannel is compared with that in a rigid one. It is shown that the EKEC efficiency is higher in PE-grafted nanochannel, and the couple stress plays an important role in improving the EKEC efficiency. We anticipate that these findings will help to reveal a novel understanding of energy conversion in the circular PE-grafted nanochannel.

Electroosmotic Flow Modulation and Enhanced Mixing through a Soft Nanochannel with Patterned Wall Charge and Hydrodynamic Slippage

Electroosmotic Flow Modulation and Enhanced Mixing through a Soft Nanochannel with Patterned Wall Charge and Hydrodynamic Slippage

Ionic Transport Behavior of Soft Nanochannels for Newtonian and Non-Newtonian Electrolytes

Ionic Transport Behavior of Soft Nanochannels for Newtonian and Non-Newtonian Electrolytes

Mitigating Joule heating in smart nanochannels: Evaluating the efficacy of AC vs. DC fields

This study delves into the profound implications of different electric field types, namely DC and AC with a sinusoidal waveform, on ion transport within intelligent soft nanochannels, aiming to mitigate Joule heating effects. The investigation considers temperature- and concentration-dependent properties and explores their impact on ionic selectivity, rectification factor, Joule heating, and viscosity dissipation in conical soft nanochannels. Operating in both co-current and counter-current modes, the study accounts for the nanochannel's coating with a dense and strongly negatively charged polyelectrolyte layer, addressing the ionic partitioning effect. Numerically solving the Poisson-Nernst-Planck, Navier-Stokes, and energy equations, the study reveals a significant alignment of Joule heating and viscosity dissipation with ionic current, emphasizing the influence of concentration and temperature ratios. Notably, the bidirectional AC field demonstrates a remarkable 85.51% and 71.72% reduction in Joule heating in co-current and counter-current modes, respectively, compared to DC. These findings highlight the significant impact of the AC field on thermal dynamics within nanochannels. In summary, our study offers essential insights into optimizing nanofluidic systems by effectively balancing ion transport efficiency and thermal effects across various electrical field scenarios. These findings directly address the critical challenge of managing Joule heating in intelligent nanochannels, which is essential for enhancing the performance of lab-on-a-chip devices in sensitive biomedical applications.

Electroosmotic flow modulation and dispersion of uncharged solutes in soft nanochannel.

We perform a systematic study on the modulation of electroosmotic flow (EOF), tuning the selectivity using electrolyte ions and hydrodynamic dispersion of the solute band across the soft nanochannel. The supporting walls of the channel are considered to be hydrophobic and bear non-zero surface charge. For such a channel, the inner side of the supporting rigid walls of the channel are coated with a soft polyelectrolyte layer (PEL). The inhomogeneous distribution of monomers and accompanying volume charge within the PEL is modelled via soft-step function. The dielectric permittivity of the PEL and electrolyte solution are in general different, which in turn leads to the ion partitioning effect. The impact of ion steric effects due to finite sized ions is further accounted through the modified ion activity coefficient. To model the EOF modulation considering the combined impact of the ion steric and ion partitioning effects as well as inhomogeneous distribution of monomers across the PEL, we adopt the modified Poisson-Boltzmann equation as the governing equation for electrostatic potential. The Debye-Bueche model is adopted to study the flow field across the PEL and the Stokes equation governs the EOF outside the PEL. In order to study the impact of the modulated EOF field on the dispersion of uncharged solution, we adopt three different models, i.e., a general 2D convective-diffusion model as well as cross-sectional averaged dispersion models due to Gill and late-time Taylor and Aris. Going beyond the widely employed Debye-Hückel approximation and uniform distribution of the monomer as well as accompanying volume charge, we find the results for the electric double layer (EDL) potential, EOF field and averaged throughput, by tuning the ion selectivity, etc., which is sufficient to analyze the transport of ionized liquid across the channel. The numerical results are supplemented with analytical results for the EDL potential as well as the EOF field under various limiting situations. Besides, we have further shown the impact of the modulated EOF field on the solute dispersion process. We have presented results that highlight the impact of parameters related to EOF field modulation, on solute dispersion governed by a convective-diffusive process, as well as obtaining the results for an effective dispersion coefficient. The dispersion models under the modulated EOF field adopted in the present study can thus be applied to study the dispersion process in engineered microdevices.

A numerical study supplemented with theoretical analysis on streaming potential in a soft nanochannel influenced by ion partitioning and mobile surface charge-dependent wall slip

We consider the pressure-driven flow of an electrolyte in a soft channel with a hydrophobic charged surface coated with a diffuse polyelectrolyte layer (PEL) with constant volumetric charge density. The objectives are to enhance the streaming potential and electrochemical energy conversion efficiency in the modulated soft channel as well as to examine the influence of surface charge mobility-dependent slip velocity on the electrokinetics. The laterally mobile adsorbed surface charge modifies the slip velocity condition, which is coupled with the induced streaming potential. The ion partitioning effect arises due to the step change in dielectric constant between the PEL and the electrolyte that modifies the distribution of ions, which is incorporated through the Born energy difference of ions. The nonlinear coupled set of equations governing the electrokinetics in a soft channel is solved numerically through a control volume approach. A simplified model based on the Debye–Hückel approximation under certain limiting conditions is also derived, which compares well with the present numerical model for a lower range of charge density and non-overlapping Debye layers. We find that a modulation of a nanochannel by coating a PEL of lower dielectric constant on hydrophobic charged walls can significantly enhance the streaming current and energy conversion efficiency. In contrast with existing studies, we find that the mobile surface charge can have a positive impact on the electrochemical energy conversion efficiency in a soft nanochannel. The mobility of the surface charge attenuates the streaming current in a PEL-free channel and can enhance the streaming current for a suitable choice of PEL volumetric charge density.

Engineering soft nanochannels in isoporous block copolymer nanofiltration membranes for ion separation

Membranes with high ion selectivity are important for the separation of ionic species at the Ångstrom scale. Here, we report on positively charged isoporous block copolymer (BCP) nanofiltration membranes with designed soft nanochannels. The isoporous BCP membranes were obtained from the combination of BCP self-assembly and non-solvent-induced phase separation. The well-defined soft nanochannels were engineered via a versatile post-modification approach using a combination of di- and monofunctional alkyl halide. The water permeance and effective pore size of the membranes were fine-tuned within the nanofiltration regime. Both single- and binary-salt retentions demonstrate the capability of separating mono-/divalent cations based on the ionic size difference in Ångstrom scale, charge, and energy to strip away the hydration shells. Especially the real selectivity from the binary-salt systems is > 2 times higher than the selectivity obtained from the single-salt systems, e.g., the real selectivity of K+/Mg2+ is up to 15 for the 10 mM binary-salt mixture with a mole ratio of 1:1. Such enhancement arises from the competition effect regarding energy barrier, size of hydrated ion, and diffusivity. The Na+/Mg2+ binary-salt system with simulating the salt concentration ratio of the seawater illustrates the potential of the resulting membranes to recover the valuable ionic species from water, e.g. Mg, classified as a “critical raw material” in Europe. The Na+/Mg2+ real selectivity is up to 42 with a permeance of 15 L m−2 h−1 MPa−1 at a salt concentration of 10 mM.

Impact of charged soft layers on electroosmosis of Maxwell fluids in soft nanochannels

In the present paper, we theoretically study the transient electroosmotic flow of general Maxwell fluids through the polyelectrolyte grafted nanochannel with a layered distribution of charges. By applying the method of Laplace transform, we semi-analytically obtain the transient electroosmotic flow from the Cauchy momentum equation and the Maxwell constitutive equation. For the nanochannels grafted with polyelectrolyte layers having different layered distributions of charges, we consider the influence of the dimensionless relaxation time, the dimensionless polyelectrolyte layer thickness, and the dimensionless drag coefficient on the transient electroosmotic flow. We present the results for some particular cases. First, we unravel that for the case of polyzwitterionic brush that the sum of positive and negative structural charges is zero, the total electroosmotic flow is non-zero. In particular, depending on charge distribution within the end part of polyelectrolyte layers, the direction of the electroosmotic flow can be reversed critically. Second, in order to quantitatively evaluate a reversal of electroosmotic flow for two polyelectrolyte layers of opposite signs, we introduce a critical number ks as the ratio between the layered charge densities of two polyelectrolyte layers. Increasing ks allows the electroosmotic flow to be reversed easily. We verify that adjusting charge distributions of the layer can intentionally control the direction of the flows as well as the strength of electroosmotic flow.

Viscoelectric effect on the chemiosmotic flow in charged soft nanochannels

The charged nanochannel surface and pH-sensitive grafted polyelectrolyte layer (PEL) play a critical role in the design of devices aimed at controlling nanofludic flow. They enable the manipulation of ionic transport by influencing the electric-double (EDL) layers that overlap. Additionally, the viscoelectric effect, amplified by a strong EDL electric field, may enhance the activation energy and viscosity of liquids. Motivated by this, we conducted a numerical investigation using a finite element method-based solver, COMSOL, to examine the effects of the viscoelectric effect on concentration-gradient-driven chemiosmotic flow in a charged soft nanochannel with grafted pH-sensitive polyelectrolyte layer on the inner wall surfaces. It is important to note that the nanochannel is positioned between two reservoirs with different pH values and bulk-ionic concentrations. The PEL is sensitive to protonic association–dissociation due to the presence of carboxylic and amine groups in monomeric units. In our study, we comprehensively demonstrate variations in key variables characterizing the underlying flow. These variations include changing the solute concentration in the left side reservoir within the range of 0.1–5 mol m−3, adjusting the pH of the right-side reservoir (pHR) within the range of 3–10, and varying the viscoelectric coefficient. The viscoelectric effect significantly raises viscosity near the wall due to the stronger EDL electric field generated at the left-side reservoir resulting from the higher solute concentration. On the other hand, viscosity tends to decrease with lower pHR values and remains unaffected by changes at higher pHR values. The average flow velocity shows an increasing–decreasing pattern as the concentration of the right-side reservoir is enhanced. Additionally, the decrease in flow velocity becomes noticeably more pronounced with higher solute concentrations in the right-side reservoir when accounting for the viscoelectric effect. The findings of the present study have practical implications for novel nanofluidic devices, frequently employed in various engineering applications to control flow.

Fine-tuning ionic transport through hybrid soft nanochannels: The role of polyelectrolyte charge density distribution

This study investigates a hybrid nanochannel consisting of two cylindrical and conical parts coated with a soft layer exhibiting either of four different spatial distribution functions: constant (type I), exponential (type II), sigmoidal (type III), and soft-step (type IV). The Poisson–Nernst–Planck and Navier–Stokes equations are numerically solved using the finite element method under steady-state conditions. The research focuses on the modification of behavior and enhancement of performance in nanochannels inspired by nature. Considering the spatial variation in charge density distribution and the limited understanding of ion transport mechanisms, this study highlights the importance of modeling tools in advancing this field. The findings contribute to the development of effective strategies for controlling and manipulating the behavior of charged nanochannels. The results demonstrate that changing the decay length from 0.2 to 1 at a concentration of 1 mM leads to an increase in the rectification factor for type II up to 6.129, i.e., 5.7 times. Furthermore, varying NPEL/NA from 25 to 100 mol m−3 at Vapp=+1 V results in ionic selectivity of 0.9072, 0.2009, 0.1543, and 0.9031 for functions of type I to type IV, respectively. These findings not only enhance our understanding of ion transport mechanisms in hybrid nanochannels but also suggest that manipulating the charge density of the soft layer enables the production of intelligent nanochannels with applications in separation, diagnostics, and sensing.

Electrokinetic Transport of Non-Newtonian Fluid through Soft Nanochannel with pH-Responsive and Partially Ion-Penetrable Polymer Layer

Electrokinetic Transport of Non-Newtonian Fluid through Soft Nanochannel with pH-Responsive and Partially Ion-Penetrable Polymer Layer

ELECTROKINETIC TRANSPORT OF NON-NEWTONIAN FLUID THROUGH SOFT NANOCHANNEL WITH PH-RESPONSIVE AND PARTIALLY ION-PENETRABLE POLYMER LAYER

The present article deals with the comprehensive parametric study on electroosmotic flow and transportation of ions through polymer grafted soft nanochannel containing non-Newtonian fluid. We consider the fully developed flow in a slit rectangular channel. The charged poly-electrolyte layer (PEL) carries a monovalent acidic ionizable group attached to a rigid wall. The ion partitioning effect is considered in our study, which arises from the difference in relative permittivity of the polyelectrolyte region and the bulk electrolyte. The non-linear Poisson−Boltzmann equation and the modified Cauchy momentum equation, which are coupled, are used to describe the mathematical model. The main objective of this analysis is to demonstrate the impact of bulk pH on the charge regulation of mono-ionic functional groups residing in PEL, the impact of flow behavior index and different electrohydrodynamic parameters, including EDL thickness, ion-partitioning parameter, the Debye−Hückel parameter, and softness parameters etc, on the overall flow modulation and selectivity parameter. This study is expected to constitute a significant step forward in the real-world continuum mathematical modelling of interfacial flow physics in the scenario of electrohydrodynamics in soft nanochannels.

Impact of Ion Partitioning Effect on the Electroosmotic Flow of Non-Newtonian Fluid and Ion Selectivity through Soft Nanochannel

Impact of Ion Partitioning Effect on the Electroosmotic Flow of Non-Newtonian Fluid and Ion Selectivity through Soft Nanochannel

Boost ionic selectivity by coating bullet-shaped nanochannels with dense polyelectrolyte brushes

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 80 mol/m3 and a bulk concentration of 20 mM, we demonstrate that the rectification factors for the bullet nanochannels, from 3.35 by ignoring the ion partitioning effect, can reach the values of 4.88 by considering the ion partitioning effect, respectively.

Importance of nanochannels shape on blue energy generation in soft nanochannels

Energy production is one of today's most pressing issues. Finding alternative energy sources has become one of the hottest research areas for scholars due to the limited use of fossil resources. Using water sources of different concentrations is one of the newest methods of energy production. Due to the energy of mixing fluids, two fluids of different concentrations on both sides of a nanochannel membrane can produce energy. Given the costs and restrictions of studying complex systems experimentally, simulation is required to investigate their behavior and determine the best states. As a result, using an energy production strategy, this work explores the effect of nanochannel shape on the ion transfer behavior. Asymmetric (bullet, trumpet, cigarette, hourglass, and hill) and symmetric (cylindrical) geometries were utilized. The effects of different geometries, soft layer density, and concentration ratio on energy production considering the effect of ion partitioning in soft surfaces was investigated. A finite element numerical computation approach was employed to solve the Poisson-Nernst-Planck and Navier-Stokes equations at steady-state. The best geometry at various concentration ratios to create the most performance were: cylindrical and cigarette for osmotic current, hourglass and trumpet for transmission number, hourglass and trumpet for diffusion potential, cylindrical for electrical conductivity, cylindrical and trumpet for power capacity, and hourglass and trumpet for energy conversion efficiency, respectively. In the case of considering the ion partitioning at a concentration ratio of CH/CL=1000for trumpet geometry, raising the soft layer's charge density from NPEL/NA=25to100mol/m3 boosted the maximum produced power by about 25 times, from 0.215pW to 5.35pW.

Influence of location junction on ion transfer behavior in conical nanopores with bipolar polyelectrolyte brushes

A bipolar ion diode consists of two positively and negatively charged surfaces that show the distribution of specific ions under different applied voltages. One of the most important electrokinetic phenomena occurring in bipolar nanopores is ionic current rectification (ICR). ICR in nanopores occur when, by applying a voltage to both ends of a nanochannel, the system exhibits non-linear current-voltage behavior or diode-like behavior, in other words, ionic current occurs in a specific direction. In modeling bipolar soft nanochannels, it is usually assumed that the properties of the soft layer and the electrolyte are the same, which is not true for soft layers with high charge densities. In the present work, the effect of sharp and wide aperture radius of nanochannels on ionic current rectification in bipolar nanochannels by coating polyelectrolytic layer with conical geometry in different values of soft layer lengths was studied. For this purpose, by adopting a numerical calculation approach Finite element, Poisson-Nernst-Planck and Navier-Stokes equations were solved for steady-state by considering different permeability values, diffusion coefficient, and dynamic viscosity for polyelectrolyte and electrolyte In general, it can be concluded that the bipolar conical nanopore has a higher ICR than the cylinder geometry with the same average radius If the junction is at the tip of the nanopore. For example, when the mole concentration was equal to c0=50mM, the ICR for the bipolar conical nanopore with a soft layer with an optimal junction at the tip of the nanopore reached 45, while in the bipolar cylindrical nanopore at best (the optimal junction in the middle of the nanopore) reached 25.

Nanofluidic Membranes to Address the Challenges of Salinity Gradient Energy Harvesting: Roles of Nanochannel Geometry and Bipolar Soft Layer.

Researchers are looking for new, clean, and accessible sources of energy due to rising global warming caused by the usage of fossil fuels and the irreversible harm that this does to the environment. Water salinity is one of the newest and most accessible renewable energy sources, which has sparked a lot of interest. Reverse electrodialysis (RED) has been utilized in the past to turn saline water into electricity. NRED, a reverse electrodialysis method utilizing nanofluidics, has gained popularity as nanoscale research advances. Developing and evaluating NRED systems is time-consuming and expensive due to the method's novelty; thus, modeling is required to identify the best locations for implementation and to comprehend its workings. In this work, we examined the influence of bipolar soft layer and nanochannel geometry on ion transfer and power production simultaneously. To achieve this, the two trumpet and cigarette geometries were coated with a bipolar soft layer so that both negative (type (I)) and positive (type (II)) charges could be positioned in the nanochannel's small aperture. After that, at steady state conditions, the Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations were solved concurrently. The findings revealed that altering the nanochannel coating from type (I) to type (II) alters the channel's selectivity from cations to anions. An approximately 22-fold improvement in energy conversion efficiency was achieved by raising the concentration ratio from 10 to 100 for the type (I) trumpet nanochannel. Type (I) cigarette geometry is advised for maximum power output at low and medium concentration ratios, whereas type (I) trumpet geometry is recommended for the maximum power production at high concentration ratios.

Effect of charge density distribution of polyelectrolyte layer on electroosmotic flow and ion selectivity in a conical soft nanochannel

Electroosmotic flow (EOF) and ion transport through a conical nanochannel coated with polyelectrolyte layer (PEL) are numerically investigated. The diffuse character is defined by an ununiform distribution of the polymer segment density. Soft step (Type I), exponential (Type II), and sigmoidal (Type III) functions were considered to describe the charge density distribution of PEL. A nonlinear model based on the Poisson-Nernst-Planck and the Navier–Stokes equations is used. The equations were solved using the finite element method. At applied voltages of ±1V, the electroosmotic velocity within diffuse soft nanochannels follows the order of uTypeI>uTypeII>uTypeIII. The soft step function leads to more ion selectivity. Considering a charge density of 100 mol/m3 and a salt concentration of 100 mM, we demonstrate that the rectification factors for the conical nanochannels, from 3 by considering the uniform PEL, can reach the value of 18 by considering the soft step function for PEL.

Ion partitioning and ion size effects on streaming field and energy conversion efficiency in a soft nanochannel

Ion partitioning and ion size effects on streaming field and energy conversion efficiency in a soft nanochannel