Driving force for hydraulic and pervaporative transport in homogeneous membranes

Experiments were designed to demonstrate that the chemical potential gradient required for liquid transport through swollen network polymer membranes manifests itself as a concentration gradient and that the rate of transport is independent of how this gradient is established. The fluxes of various liquids through a crosslinked rubber membrane were measured in hydraulic and pervaporation modes of permeation. The pressure applied downstream in the latter act simply to fix the activity of the liquid in the downstream membrane surface. The experiments show the flux is a unique function of this activity, and it does not matter how it is established. Sorption data were used to convert these results into a plot of flux versus concentration differential across the membrane which was analyzed by Fick's law using a model for the concentration dependence of the diffusion coefficient. Measured ceiling fluxes for pervaporation for a number of liquids were found to be the same as those estimated from hydraulic permeation data. A simple mathematical representation for an ideal system is used as a pedagogical device to demonstrate the conclusions.     

Transport of a liquid water and methanol mixture through carbon nanotubes under a chemical potential gradient

In this work, we report a dual-control-volume grand canonical molecular dynamics simulation study of the transport of a water and methanol mixture under a fixed concentration gradient through nanotubes of various diameters and surface chemistries. Methanol and water are selected as fluid molecules since water represents a strongly polar molecule while methanol is intermediate between nonpolar and strongly polar molecules. Carboxyl acid (-COOH) groups are anchored onto the inner wall of a carbon nanotube to alter the hydrophobic surface into a hydrophilic one. Results show that the transport of the mixture through hydrophilic tubes is faster than through hydrophobic nanotubes although the diffusion of the mixture is slower inside hydrophilic than hydrophobic pores due to a hydrogen network. Thus, the transport of the liquid mixture through the nanotubes is controlled by the pore entrance effect for which hydrogen bonding plays an important role.     

Molecular transport in nanopores: a theoretical perspective

Molecular transport in nanopores plays a central role in many emerging nanotechnologies for gas separation and storage, as well as in nanofluidics. Theories of the transport provide an understanding of the mechanisms that influence the transport and their interplay, and can lead to tractable models that can be used to advance these nanotechnologies through process analysis and optimisation. We review some of the most influential theories of fluid transport in small pores and confined spaces. Starting from the century old Knudsen formulation, the dusty gas model and several other related approaches that share a common point of departure in the Maxwell-Stefan diffusion equations are discussed. In particular, the conceptual basis of the models and the validity of the assumptions and simplifications necessary to obtain their final results are analysed. It is shown that the effect of adsorption is frequently either neglected, or treated on an ad hoc basis, such as through the division of the pore flux into gas-phase and surface diffusion contributions. Furthermore, while it is commonplace to assume that cross-sectional pressure is uniform, it is demonstrated that this violates the Gibbs-Duhem relation and that it is the chemical potential that essentially remains constant in the cross-section, as near-equilibrium density profiles are preserved even during transport. The Dusty Gas model and Maxwell-Stefan model for surface diffusion are analysed, and their strengths and weaknesses discussed, illustrating the use of conflicting choices of frames of reference in the former case, and the importance of assigning appropriate values for the binary diffusivity in the latter case. The oscillator model, developed in this laboratory, which is exact in the low density limit under diffuse reflection conditions, is shown to represent an advance on the classical Knudsen formula, although the latter frequently appears as a fundamental part of many transport models. The distributed friction model, also developed in this laboratory for the study of multi-component transport at any Knudsen number is discussed and compared with previous approaches. Finally, the outlook for theory and future research needs are discussed.     

Template-synthesized nanotubes for chemical separations and analysis

We have developed a new class of synthetic membranes that consist of a porous polymeric support that contains an ensemble of gold nanotubes that span the thickness of the support membrane. The support is a commercially-available microporous polycarbonate filter with cylindrical nanoscopic pores. The gold nanotubes are prepared by electroless deposition of Au onto the pore walls, that is, the pores acts as templates for the nanotubes. We have shown that by controlling the Au deposition time, Au nanotubes that have effective inside diameters of molecular dimensions (<1 nm) can be prepared. These nanotube membranes can be used to cleanly separate small molecules on the basis of molecular size. Furthermore, use of these membranes as a novel electrochemical sensor is also discussed. This new sensing scheme involves applying a constant potential across the Au nanotube membrane and measuring the drop in the transmembrane current upon the addition of the analyte. This paper reviews our recent progress on size-based based transport selectivity and sensor applications in this new class of membranes.     

Template synthesized gold nanotube membranes for chemical separations and sensing

We have developed a new class of synthetic membranes that consist of a porous polymeric support that contains an ensemble of gold nanotubes that span the thickness of the support membrane. The support is a commercially-available microporous polycarbonate filter with cylindrical nanoscopic pores. The gold nanotubes are prepared via electroless deposition of Au onto the pore walls; i.e., the pores acts as templates for the nanotubes. We have shown that by controlling the Au deposition time, Au nanotubes that have effective inside diameters of molecular dimensions (< 1 nm) can be prepared. These membranes are a new class of molecular sieves and can be used to separate both small molecules and proteins on the basis of molecular size. In addition, the use of these membranes in new approaches to electrochemical sensing is reviewed here. In this case, a current is forced through the nanotubes, and analyte molecules present in a contacting solution phase modulate the value of this transmembrane current.     

Molecular sieving and sensing with gold nanotube membranes

We have developed a new class of synthetic membranes that consist of a porous polymeric support that contains an ensemble of gold nanotubes that span the thickness of the support membrane. The support is a commercially available microporous polycarbonate filter with cylindrical nanoscopic pores. The gold nanotubes are prepared via electroless deposition of Au onto the pore walls; i.e., the pores act as templates for the nanotubes. We have shown that by controlling the Au deposition time, Au nanotubes that have effective inside diameters of molecular dimensions (<1 nm) can be prepared. These nanotube membranes can be used to cleanly separate small molecules on the basis of molecular size. Furthermore, use of these membranes as a novel electrochemical sensor is also discussed. This new sensing scheme involves applying a constant potential across the Au nanotube membrane and measuring the drop in the transmembrane current upon the addition of the analyte. This paper reviews our recent progress on size-based transport selectivity and sensor applications in this new class of membranes.     

Electrohydrodynamic transport of non‐symmetric electrolyte through porous wall of a microtube

Transport of salt through the wall of porous microtube is relevant in various physiological microcirculation systems. Transport phenomena based modeling of such system is undertaken in the present study considering a combined driving force consisting of pressure gradient and external electric field. Transport of salt is modeled in two domains, in the flow conduit and in the pores of porous wall of the microtube. The solute transport in the microtube is presented by convective‐diffusive mass balance and it is solved using integral method under the framework of boundary layer analysis. The wall of the microtube is considered to be consisting of series of straight parallel cylindrical pores with charged inner surface. The solute transport through the pores is considered to be composed of diffusive, convective and electric potential gradient governed by Nernst‐Planck equation. Transport in the microtube and pores is coupled through the osmotic pressure model for the solvent and Donnan equilibrium distribution for the solute. The simulated results agree remarkably well with the experimental data conducted by in‐house experimental set up. The charge density of the porous wall is estimated through the minimization of errors involved between the experimental and simulated data for different operating conditions.     

Transient phoretic migration of a permselective colloidal particle

We quantify the phoretic migration of a spherical cation-permselective colloidal particle immersed in a binary electrolyte under a time-dependent electric field. We invoke the thin-Debye-layer approximation, where the size of ionic Debye layer enveloping the particle is much smaller than the particle radius. The imposed electric field generates ion concentration gradients, or concentration polarization, in the bulk (electroneutral) electrolyte outside the Debye layer. The bulk ion concentration polarization--and consequently the particle's phoretic velocity--evolves on the time scale for ion diffusion around the particle, which can be on the order of milliseconds for typical colloidal dimensions. Notably, concentration polarization arises here solely due to the permselectivity of the particle; it does not require non-uniform ionic transport in the Debye layer (i.e., surface conduction). Thus, the phoretic transport of a permselective particle is significantly different to that of a inert, dielectric particle, since surface conduction is necessary to achieve bulk concentration polarization in the (more commonly studied) latter case. Calculations are presented for a permselective particle under oscillatory (ac) and suddenly applied electric fields. In the former case, the particle velocity possesses frequency-dependent components in phase and out of phase with the driving field; in the latter case, the particle approaches its terminal velocity with a long-time (algebraic) tail.     

Electroosmotic transport of immiscible binary system with a layer of non‐conducting fluid under interfacial slip: The role applied pressure gradient

We investigate the transport of immiscible binary fluid layers, constituted by one conducting (top layer fluid) and another non‐conducting (bottom layer fluid) fluids in a microfluidic channel under the combined influences of an applied pressure gradient and imposed electric field. We solve the transport equation governing the flow dynamics analytically and obtain the closed‐form expressions of the velocity fields. We bring out the alteration in the flow dynamics, mainly attributable to the non‐linear interaction between interfacial slip and the electrical double layer effect over small scales as modulated by the applied pressure gradient. In particular, we show the augmentation in the net volume transport rate through the channel, emerging from an intricate competition among electrical forcing, applied pressure gradient and the viscous resistance as modulated by the interfacial slip. We believe that the results of this study may be of immense consequence for the design of various microfluidic devises, which are often used for the manipulation of two immiscible fluids in different biomedical/biochemical processes.     

Structural and mathematical models for pressure-dependent electrodiffusion of an electrolyte through heterogeneous ion-exchange membranes: Pressure-dependent electrodiffusion of NaOH through the MA-41 anion-exchange membrane

Structural and mathematical models are proposed for describing electrolyte transport through heterogeneous anion-exchange membranes under conditions of pressure-dependent electrodiffusion. The idea that mesopores and macropores are present in the membrane provides the basis for the structural model. The Nernst-Planck equations with a convective term are used to describe ion transport in the solution filling the pores. Results of the solution to the mathematical problem and the experimental investigations demonstrate the possibility of decreasing the transport numbers of sodium ions through an anion-exchange membrane by applying a pressure gradient in the same direction as the electrolyte diffusion flux in the membrane.     

Numerical modeling of Joule heating-induced temperature gradient focusing in microfluidic channels

Temperature gradient focusing (TGF) is a recently developed technique for spatially focusing and separating ionic analytes in microchannels. The temperature gradient required for TGF can be generated either by an imposed temperature gradient or by Joule heating resulting from an applied electric field that also drives the flow. In this study, a comprehensive numerical model describing the Joule heating induced temperature development and TGF is developed. The model consists of a set of governing equations including the Poisson-Boltzmann equation, the Laplace equation, the Navier-Stokes equations, the energy equations and the mass transport equation. As the thermophysical and electrical properties including the liquid dielectric constant, viscosity, and electric conductivity are temperature-dependent, these governing equations are coupled, and therefore the coupled governing equations are solved numerically by using a CFD-based numerical method. The numerical simulations agree well with the experimental results, suggesting the valid mathematical model presented in this study.     

Modeling Disjoining Pressures in Submicrometer Liquid-Filled Cylindrical Geometries

This work develops models for calculating the disjoining pressures of a cylindrical fluid "plug", specifically in submicrometer cylindrical pores. This modeling produces closed-form, cylindrical-pore disjoining pressures for London/van der Waals and solute/pore-wall adsorption interactions, which are the slit-pore models with the characteristic pore size replaced by the radius and multiplied by 6, resulting in a 48-fold or more increase in magnitude. In addition, this work contains a numerical solution for electrostatic interactions. The result of the numerical solution was a 9-fold increase in the modeled disjoining pressure compared to that in the slit-pore model. The cylindrical models may apply to the chemical coating of the interior walls of cylindrical pores or to the thermodynamics within droplets after the breakup of a fluid coating a surface. However, the application used as the base case in this paper is the extension of transport and thermodynamic laws for porous media, previously developed with capillary pressure models, to fully saturated porous media with submicrometer-sized pores. As such, the models could apply to mass transport in ultrafiltration, nanofiltration, and reverse-osmosis membranes. Copyright 2001 Academic Press.     

Oscillating Poiseuille flow in photo-aligned liquid crystal cells

We present an experimental study of thin liquid crystal (LC) layers under the action of a harmonically varied pressure gradient. Optical measurements were performed to register the linear oscillations of a nematic director related to homeotropic and homeoplanar (hybrid) initial states. In the latter case one of the inner surfaces of the rectangular channels was treated by ultraviolet light to provide a relatively weak planar anchoring. The optical response of hybrid and homeotropic LC cells under an oscillating pressure gradient was investigated in relation to on the amplitude and frequency of the pressure gradient. A hydrodynamic model is developed taking into account the LC polar anchoring strength and the surface viscosity responsible for a fast LC surface dynamics. Our estimates show that the thickness of the boundary layer corresponding to the surface viscosity does not exceed 10^-6 m, and further experiments are needed with thinner LC cells and higher frequency oscillations to achieve a more precise value. An oscillating Poiseuille flow in the hybrid cell was found to be useful for characterizing elastic and viscous properties of a weakly anchoring LC surface layer in a fast surface dynamic process.     

Oscillating Poiseuille flow in photo‐aligned liquid crystal cells

We present an experimental study of thin liquid crystal (LC) layers under the action of a harmonically varied pressure gradient. Optical measurements were performed to register the linear oscillations of a nematic director related to homeotropic and homeoplanar (hybrid) initial states. In the latter case one of the inner surfaces of the rectangular channels was treated by ultraviolet light to provide a relatively weak planar anchoring. The optical response of hybrid and homeotropic LC cells under an oscillating pressure gradient was investigated in relation to on the amplitude and frequency of the pressure gradient. A hydrodynamic model is developed taking into account the LC polar anchoring strength and the surface viscosity responsible for a fast LC surface dynamics. Our estimates show that the thickness of the boundary layer corresponding to the surface viscosity does not exceed 10^?6 m, and further experiments are needed with thinner LC cells and higher frequency oscillations to achieve a more precise value. An oscillating Poiseuille flow in the hybrid cell was found to be useful for characterizing elastic and viscous properties of a weakly anchoring LC surface layer in a fast surface dynamic process.     

Diffusioosmotic flows in slit nanochannels

Diffusioosmotic flows of electrolyte solutions in slit nanochannels with homogeneous surface charges induced by electrolyte concentration gradients in the absence of externally applied pressure gradients and potential differences are investigated theoretically. A continuum mathematical model consisting of the strongly coupled Nernst-Planck equations for the ionic species' concentrations, the Poisson equation for the electric potential in the electrolyte solution, and the Navier-Stokes equations for the flow field is numerically solved simultaneously. The induced diffusioosmotic flow through the nanochannel is computed as functions of the externally imposed concentration gradient, the concentration of the electrolyte solution, and the surface charge density along the walls of the nanochannel. With the externally applied electrolyte concentration gradient, a strongly spatially dependent electric field and pressure gradient are induced within the nanochannel that, in turn, generate a spatially dependent diffusioosmotic flow. The diffusioosmotic flow is opposite to the applied concentration gradient for a relatively low bulk electrolyte concentration. However, the electrolyte solution flows from one end of the nanochannel with a higher electrolyte concentration to the other end with a lower electrolyte concentration when the bulk electrolyte concentration is relatively high. There is an optimal concentration gradient under which the flow rate attains the maximum. The induced flow is enhanced with the increase in the fixed surface charge along the wall of the nanochannel for a relatively low bulk electrolyte concentration.     

Diffusiophoresis of an Elongated Cylindrical Nanoparticle along the Axis of a Nanopore

The translation of a charged, elongated cylindrical nanoparticle along the axis of a nanopore driven by an imposed axial salt concentration gradient is investigated using a continuum theory, which consists of the ionic mass conservation equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the modified Stokes equations for the hydrodynamic field. The diffusiophoretic motion is driven by the induced electrophoresis and chemiphoresis. The former is driven by the generated overall electric field arising from the difference in the ionic diffusivities and the double layer polarization, while the latter is generated by the induced osmotic pressure gradient around the charged particle. The induced diffusiophoretic motion is investigated as functions of the imposed salt concentration gradient, the ratio of the particle’s radius to the double layer thickness, the cylinder’s aspect ratio (length/radius), the ratio of the nanopore size to the particle size, the surface charge densities of the nanoparticle and the nanopore, and the type of the salt used. The induced diffusiophoretic motion of a nanorod in an uncharged nanopore is mainly governed by the induced electrophoresis, driven by the induced electric field arising from the double layer polarization. The induced particle motion is driven by the induced electroosmotic flow, if the charges of the nanorod and nanopore wall have the same sign.     

Concentration-dependent self-diffusion of liquids in nanopores: a nuclear magnetic resonance study

Nuclear magnetic resonance has been applied to study the details of molecular motion of low-molecular-weight polar and nonpolar organic liquids in nanoporous silicon crystals of straight cylindrical pore morphology at different pore loadings. Effective self-diffusion coefficients as obtained using the pulsed field gradient nuclear magnetic resonance method were found to pass through a maximum with increasing concentration for all liquids under study. Taking account of a concentration-dependent coexistence of capillary condensed, adsorbed and gaseous phases a generalized model for the effective self-diffusion coefficient was developed and shown to satisfactorily explain the experimental results. An explicit use of the adsorption isotherm properties within the model extends its applicability to the mesoporous range and highlights the role of surface interaction for the transport of molecules in small pores. The problem of surface diffusion and diffusion of multilayered molecules is also addressed.     

Single-file water in nanopores

Water molecules confined to pores with sub-nanometre diameters form single-file hydrogen-bonded chains. In such nanoscale confinement, water has unusual physical properties that are exploited in biology and hold promise for a wide range of biomimetic and nanotechnological applications. The latter can be realized by carbon and boron nitride nanotubes which confine water in a relatively non-specific way and lend themselves to the study of intrinsic properties of single-file water. As a consequence of strong water-water hydrogen bonds, many characteristics of single-file water are conserved in biological and synthetic pores despite differences in their atomistic structures. Charge transport and orientational order in water chains depend sensitively on and are mainly determined by electrostatic effects. Thus, mimicking functions of biological pores with apolar pores and corresponding external fields gives insight into the structure-function relation of biological pores and allows the development of technical applications beyond the molecular devices found in living systems. In this Perspective, we revisit results for single-file water in apolar pores, and examine the similarities and the differences between these simple systems and water in more complex pores.     

Disorder-induced exciton localization and violation of optical selection rules in supramolecular nanotubes

Using numerical simulations, we study the effect of disorder on the optical properties of cylindrical aggregates of molecules with strong excitation transfer interactions. The exciton states and the energy transport properties of such molecular nanotubes attract considerable interest for application in artificial light-harvesting systems and energy transport wires. In the absence of disorder, such nanotubes exhibit two optical absorption peaks, resulting from three super-radiant exciton states, one polarized along the axis of the cylinder, the other two (degenerate) polarized perpendicular to this axis. These selection rules, imposed by the cylindrical symmetry, break down in the presence of disorder in the molecular transition energies, due to the fact that the exciton states localize and no longer wrap completely around the tube. We show that the important parameter is the ratio of the exciton localization length and the tube's circumference. When this ratio decreases, the distribution of polarization angles of the exciton states changes from a two-peak structure (at zero and ninety degrees) to a single peak determined by the orientation of individual molecules within the tube. This is also reflected in a qualitative change of the absorption spectrum. The latter agrees with recent experimental findings.