Charge Selectivity of an Ionic Transistor.

The charge selective properties of a long planar nanochannel with an embedded finite uniformly charged section in the middle are studied. The probability flux of a single test ion initially confined to the inlet reservoir is determined by integrating the Smoluchowski equation using a previously published series solution for the Debye-Hückel potential in this geometry. The charge selective properties are characterized by a dimensionless quantity that we call the "fractional blockage". We study how the fractional blockage depends on the dimensionless parameters that characterize the charge state and channel geometry. In the limit of strongly overlapped wall Debye layers, analytical expressions for the fractional blockage are presented that are found to be in good agreement with numerically computed values in the appropriate asymptotic regimes. These results may be helpful in the design of nanofluidic devices that have a variety of applications.

Anomalous diffusion in an electrolyte saturated paper matrix.

Diffusion of colored dye on water saturated paper substrates has been traditionally exploited with great skill by renowned water color artists. The same physics finds more recent practical applications in paper-based diagnostic devices deploying chemicals that react with a bodily fluid yielding colorimetric signals for disease detection. During spontaneous imbibition through the tortuous pathways of a porous electrolyte saturated paper matrix, a dye molecule undergoes diffusion in a complex network of pores. The advancing front forms a strongly correlated interface that propagates diffusively but with an enhanced effective diffusivity. We measure this effective diffusivity and show that it is several orders of magnitude greater than the free solution diffusivity and has a significant dependence on the solution pH and salt concentration in the background electrolyte. We attribute this to electrically mediated interfacial interactions between the ionic species in the liquid dye and spontaneous surface charges developed at porous interfaces, and introduce a simple theory to explain this phenomenon.

The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates.

Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed for strongly overlapped electrical double layers (EDL), accounting for the steric effect of ions and their expulsion from EDL edges into the surrounding solution. As a generalization of a study by Philipse et al. which does not account for these effects, an analytical expression is derived for the repulsion pressure in the limit of infinitely long plates with a zero-field assumption, which agrees closely with the corresponding numerical solution at low inter-plate separations. Our results show an augmented repulsive pressure for finite-sized ions at strong EDL overlaps. For plates with a finite lateral size, we demonstrate a further extended domain of low inter-plate gaps where the repulsion pressure increases with ion size due to a strong interplay between the steric interaction of ions and the EDL overspill phenomenon, considered earlier in a study by Ghosal & Sherwood limited to the linear Debye-Hückel regime (which cannot account for the steric effect of ions). This investigation on a simple model should enhance our understanding of the interaction between charged particles in electrophoresis, nanoscale self-assembly, active particles, and various other electrokinetic systems.

A numerical study of the selectivity of an isolated cylindrical or conical nanopore to a charged macro-ion.

The selectivity of a single nanopore in a uniformly charged solid membrane to a charged analyte ion is studied using numerical simulation. A continuum model is used where the ions are regarded as point particles and characterized by a continuously varying number density. The problem is described by the coupled equations for the electrostatic potential, ion-transport, and hydrodynamic flow, which are solved under appropriate boundary conditions using a finite volume method. The nanopore geometry is considered conical, the cylindrical pore being a special case where the cone angle is zero. The selectivity is characterized by a dimensionless parameter: the pore selectivity index. Results are presented showing how the pore selectivity index varies with the membrane surface charge and other parameters of the problem. The role of hydrodynamic flow on transport properties is examined and found to be consistent with theoretical results on electroosmotic flow through nanopores.

Solid-state nanopore hydrodynamics and transport.

The resistive pulse method based on measuring the ion current trace as a biomolecule passing through a nanopore has become an important tool in biotechnology for characterizing molecules. A detailed physical understanding of the translocation process is essential if one is to extract the relevant molecular properties from the current signal. In this Perspective, we review some recent progress in our understanding of hydrodynamic flow and transport through nanometer sized pores. We assume that the problems of interest can be addressed through the use of the continuum version of the equations of hydrodynamic and ion transport. Thus, our discussion is restricted to pores of diameter greater than about ten nanometers: such pores are usually synthetic. We address the fundamental nanopore hydrodynamics and ion transport mechanisms and review the wealth of observed phenomena due to these mechanisms. We also suggest future ionic circuits that can be synthesized from different ionic modules based on these phenomena and their applications.

Band Broadening Theories in Capillary Electrophoresis.

In capillary electrophoresis (CE), analytes are separated along the axis of a single microcapillary by virtue of their differential migration in an applied electric field. CE can also be performed in channels etched on solid substrates such as glass or PDMS and can be integrated into a microfluidic chip with a complex network of electric and fluidic circuits. The measure of quality of a CE instrument is resolution which is limited fundamentally by mixing due to various physical processes. The theoretical limit on the best separation that can be achieved is set by molecular diffusion, which is inevitable. The goal is to eliminate or minimize the other sources of dispersion by design. This chapter provides an overview of the various mechanisms of band broadening and the mathematical results that make it possible to estimate their relative contributions.

Asymmetric dynamics of DNA entering and exiting a strongly confining nanopore.

In nanopore sensing, changes in ionic current are used to analyse single molecules in solution. The translocation dynamics of polyelectrolytes is of particular interest given potential applications such as DNA sequencing. In this paper, we determine how the dynamics of voltage driven DNA translocation can be affected by the nanopore geometry and hence the available configurational space for the DNA. Using the inherent geometrical asymmetry of a conically shaped nanopore, we examine how DNA dynamics depends on the directionality of transport. The total translocation time of DNA when exiting the extended conical confinement is significantly larger compared to the configuration where the DNA enters the pore from the open reservoir. By using specially designed DNA molecules with positional markers, we demonstrate that the translocation velocity progressively increases as the DNA exits from confinement. We show that a hydrodynamic model can account for these observations.Translocation of a charged polymer through confined nanoenvironments is highly dependent on their geometrical parameters. Here, the authors investigate experimentally the translocation dynamics of DNA through conical nanopores and provide a quantitative model for the translocation into and out of confinement.

Repulsion Between Finite Charged Plates with Strongly Overlapped Electric Double Layers.

Screened Coulomb interactions between uniformly charged flat plates are considered at very small plate separations for which the Debye layers are strongly overlapped, in the limit of small electrical potentials. If the plates are of infinite length, the disjoining pressure between the plates decays as an inverse power of the plate separation. If the plates are of finite length, we show that screening Debye layer charges close to the edge of the plates are no longer constrained to stay between the plates, but instead spill out into the surrounding electrolyte. The resulting change in the disjoining pressure is calculated analytically: the force between the plates is reduced by this edge correction when the charge density is uniform over the surface of the plates, and is increased when the surface is at constant potential. A similar change in disjoining pressure due to loss of lateral confinement of the Debye layer charges should occur whenever the sizes of the interacting charged objects become small enough to approach the Debye scale. We investigate the effect here in the context of a two-dimensional model problem that is sufficiently simple to yield analytical results.

AC Electric Field-Induced Trapping of Microparticles in Pinched Microconfinements.

The trapping of charged microparticles under confinement in a converging-diverging microchannel, under a symmetric AC field of tunable frequency, is studied. We show that at low frequencies, the trapping characteristics stem from the competing effects of positive dielectrophoresis and the linear electrokinetic phenomena of electroosmosis and electrophoresis. It is found, somewhat unexpectedly, that electroosmosis and electrophoresis significantly affect the concentration profile of the trapped analyte, even for a symmetric AC field. However, at intermediate frequencies, the microparticle trapping mechanism is predominantly a consequence of positive dielectrophoresis. We substantiate our experimental results for the microparticle concentration distribution, along the converging-diverging microchannel, with a detailed theoretical analysis that takes into account all of the relevant frequency-dependent electrokinetic phenomena. This study should be useful in understanding the response of biological components such as cells to applied AC fields. Moreover, it will have potential applications in the design of efficient point-of-care diagnostic devices for detecting biomarkers and also possibly in some recent strategies in cancer therapy using AC fields.

A Landau-Squire nanojet.

Fluid jets are found in nature at all length scales from microscopic to cosmological. Here we report on an electroosmotically driven jet from a single glass nanopore about 75 nm in radius with a maximum flow rate ~15 pL/s. A novel anemometry technique allows us to map out the vorticity and velocity fields that show excellent agreement with the classical Landau-Squire solution of the Navier-Stokes equations for a point jet. We observe a phenomenon that we call flow rectification: an asymmetry in the flow rate with respect to voltage reversal. Such a nanojet could potentially find applications in micromanipulation, nanopatterning, and as a diode in microfluidic circuits.

Hydrodynamic flow in the vicinity of a nanopore induced by an applied voltage.

Continuum simulation is employed to study ion transport and fluid flow through a nanopore in a solid-state membrane under an applied potential drop. The results show the existence of concentration polarization layers on the surfaces of the membrane. The nonuniformity of the ionic distribution gives rise to an electric pressure that drives vortical motion in the fluid. There is also a net hydrodynamic flow through the nanopore due to an asymmetry induced by the membrane surface charge. The qualitative behavior is similar to that observed in a previous study using molecular dynamic simulations. The current-voltage characteristics show some nonlinear features but are not greatly affected by the hydrodynamic flow in the parameter regime studied. In the limit of thin Debye layers, the electric resistance of the system can be characterized using an equivalent circuit with lumped parameters. Generation of vorticity can be understood qualitatively from elementary considerations of the Maxwell stresses. However, the flow strength is a strongly nonlinear function of the applied field. Combination of electrophoretic and hydrodynamic effects can lead to ion selectivity in terms of valences and this could have some practical applications in separations.

DNA interactions in crowded nanopores.

The motion of DNA in crowded environments is a common theme in physics and biology. Examples include gel electrophoresis and the self-interaction of DNA within cells and viral capsids. Here we study the interaction of multiple DNA molecules within a nanopore by tethering the DNA to a bead held in a laser optical trap to produce a "molecular tug-of-war". We measure this tether force as a function of the number of DNA molecules in the pore and show that the force per molecule decreases with the number of molecules. A simple scaling argument based on a mean field theory of the hydrodynamic interactions between multiple DNA strands explains our observations. At high salt concentrations, when the Debye length approaches the size of the counterions, the force per molecule becomes essentially independent of the number of molecules. We attribute this to a sharp decrease in electroosmotic flow which makes the hydrodynamic interactions ineffective.

Ion transport through a graphene nanopore.

Molecular dynamics simulation is utilized to investigate the ionic transport of NaCl in solution through a graphene nanopore under an applied electric field. Results show the formation of concentration polarization layers in the vicinity of the graphene sheet. The nonuniformity of the ion distribution gives rise to an electric pressure which drives vortical motions in the fluid if the electric field is sufficiently strong to overcome the influence of viscosity and thermal fluctuations. The relative importance of hydrodynamic transport and thermal fluctuations in determining the pore conductivity is investigated. A second important effect that is observed is the mass transport of water through the nanopore, with an average velocity proportional to the applied voltage and independent of the pore diameter. The flux arises as a consequence of the asymmetry in the ion distribution which can be attributed to differing mobilities of the sodium and chlorine ions and to the polarity of water molecules. The accumulation of liquid molecules in the vicinity of the nanopore due to re-orientation of the water dipoles by the local electric field is seen to result in a local increase in the liquid density. Results confirm that the electric conductance is proportional to the nanopore diameter for the parameter regimes that we simulated. The occurrence of fluid vortices is found to result in an increase in the effective electrical conductance.

Strongly nonlinear waves in capillary electrophoresis.

In capillary electrophoresis, sample ions migrate along a microcapillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background. Under such conditions, the local migration velocity of sample ions becomes concentration-dependent, resulting in a nonlinear wave that exhibits shocklike features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers' equation [Ghosal and Chen, Bull. Math. Biol. 72, 2047 (2010)], which has an exact analytical solution for arbitrary initial condition. In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree with the weakly nonlinear theory presented earlier, but at high concentrations, the wave evolves in a way that is qualitatively different.

The nonlinear electromigration of analytes into confined spaces.

We consider the problem of electromigration of a sample ion (analyte) within a uniform background electrolyte when the confining channel undergoes a sudden contraction. One example of such a situation arises in microfluidics in the electrokinetic injection of the analyte into a micro-capillary from a reservoir of much larger size. Here, the sample concentration propagates as a wave driven by the electric field. The dynamics is governed by the Nerst-Planck-Poisson system of equations for ionic transport. A reduced one-dimensional nonlinear equation, describing the evolution of the sample concentration, is derived. We integrate this equation numerically to obtain the evolution of the wave shape and determine how the injected mass depends on the sample concentration in the reservoir. It is shown that due to the nonlinear coupling of the ionic concentrations and the electric field, the concentration of the injected sample could be substantially less than the concentration of the sample in the reservoir.

Studying DNA translocation in nanocapillaries using single molecule fluorescence.

We demonstrate simultaneous measurements of DNA translocation into glass nanopores using ionic current detection and fluorescent imaging. We verify the correspondence between the passage of a single DNA molecule through the nanopore and the accompanying characteristic ionic current blockage. By tracking the motion of individual DNA molecules in the nanocapillary perpendicular to the optical axis and using a model, we can extract an effective mobility constant for DNA in our geometry under high electric fields.

Capstan friction model for DNA ejection from bacteriophages.

Bacteriophages infect cells by attaching to the outer membrane and injecting their DNA into the cell. The phage DNA is then transcribed by the cell's transcription machinery. A number of physical mechanisms by which DNA can be translocated from the phage capsid into the cell have been identified. A fast ejection driven by the elastic and electrostatic potential energy of the compacted DNA within the viral capsid appears to be used by most phages, at least to initiate infection. In recent in vitro experiments, the speed of DNA translocation from a λ phage capsid has been measured as a function of ejected length over the entire duration of the event. Here, a mechanical model is proposed that is able to explain the observed dependence of exit velocity on ejected length, and that is also consistent with the accepted picture of the geometric arrangement of DNA within the viral capsid.

Electromigration dispersion in capillary electrophoresis.

In a previous paper (Ghosal and Chen in Bull. Math. Biol. 72:2047, 2010), it was shown that the evolution of the solute concentration in capillary electrophoresis is described by a nonlinear wave equation that reduced to Burger's equation if the nonlinearity was weak. It was assumed that only strong electrolytes (fully dissociated) were present. In the present paper, it is shown that the same governing equation also describes the situation where the electrolytic buffer consists of a single weak acid (or base). A simple approximate formula is derived for the dimensionless peak variance which is shown to agree well with published experimental data.

Does buckling instability of the pseudopodium limit how well an amoeba can climb?

The maximum force that a crawling cell can exert on a substrate is a quantity of interest in cell biomechanics. One way of quantifying this force is to allow the cell to crawl against a measurable and adjustable restraining force until the cell is no longer able to move in a direction opposite to the applied force. Fukui et al. (2000) reported on an experiment where amoeboid cells were imaged while they crawled against an artificial gravity field created by a centrifuge. An unexpected observation was that the net applied force on the amoeba did not seem to be the primary factor that limited its ability to climb. Instead, it appeared that the amoeba stalled when it was no longer able to support a pseudopodium against the applied gravity field. The high g-load bend the pseudopodium thereby preventing its attachment to the target point directly ahead of the cell. In this paper we further refine this idea by identifying the bending of the pseudopodium with the onset of elastic instability of a beam under its own weight. It is shown that the principal features of the experiment may be understood through this model and an estimate for the limiting g-load in reasonable accord with the experimental measurements is recovered.

Nonlinear waves in capillary electrophoresis.

Electrophoretic separation of a mixture of chemical species is a fundamental technique of great usefulness in biology, health care, and forensics. In capillary electrophoresis, the sample migrates in a microcapillary in the presence of a background electrolyte. When the ionic concentration of the sample is sufficiently high, the signal is known to exhibit features reminiscent of nonlinear waves including sharp concentration "shocks." In this paper, we consider a simplified model consisting of a single sample ion and a background electrolyte consisting of a single coion and a counterion in the absence of any processes that might change the ionization states of the constituents. If the ionic diffusivities are assumed to be the same for all constituents the concentration of sample ion is shown to obey a one dimensional advection diffusion equation with a concentration dependent advection velocity. If the analyte concentration is sufficiently low in a suitable nondimensional sense, Burgers' equation is recovered, and thus the time dependent problem is exactly solvable with arbitrary initial conditions. In the case of small diffusivity, either a leading edge or trailing edge shock is formed depending on the electrophoretic mobility of the sample ion relative to the background ions. Analytical formulas are presented for the shape, width, and migration velocity of the sample peak and it is shown that axial dispersion at long times may be characterized by an effective diffusivity that is exactly calculated. These results are consistent with known observations from physical and numerical simulation experiments.