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arxiv: 2604.20379 · v1 · submitted 2026-04-22 · ⚛️ physics.flu-dyn

Emergence of Transport Regimes from the Axial Field-Induced Interfacial Gradients in Uniform Surface Potential Nanopores

Pramodt Srinivasula , Doyel Pandey This is my paper

Pith reviewed 2026-05-09 23:47 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords nanoporeselectric double layerion selectivityionic current rectificationelectroosmotic flowasymmetry parameterelectrokineticssymmetry breaking
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The pith

Uniform surface potential in a nanopore couples with an axial driving field to create an axially nonuniform electric double layer that breaks symmetry and produces ion selectivity, current rectification, and non-canonical flow.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that a perfectly uniform wall potential does not remain uniform in its effect once an axial transmembrane field is applied. The field distorts the electric double layer along the pore length, creating an effective axial gradient in zeta potential even though the surface charge is constant. This single electrostatic mechanism produces ion selectivity, ionic current rectification, and unusual electroosmotic flow patterns, all controlled by one derived asymmetry parameter alpha. At alpha equals zero the double layer becomes antisymmetric, reversing selectivity and generating negative flow rectification together with internal vortices. A reader should care because the result reframes voltage-gated nanopore behavior as an intrinsic field-induced symmetry-breaking effect rather than a consequence of geometry or surface chemistry.

Core claim

A uniform surface potential inherently interacts with the axial driving field to generate a three-dimensional, axially nonuniform electric double layer (EDL). This field-induced EDL heterogeneity effectively mimics a linear axial variation in zeta potential, breaking translational symmetry within an otherwise uniform pore. As a result, the system exhibits coupled electrokinetic responses, including ion selectivity, ionic current rectification, and non-canonical electroosmotic flow, all governed by a single asymmetry parameter alpha derived from the EDL structure. Critical transitions occur at specific values of alpha; in particular, at alpha=0, the EDL becomes axially antisymmetric, leading,

What carries the argument

The asymmetry parameter alpha, extracted from the axial structure of the field-induced electric double layer, which quantifies the degree of translational symmetry breaking and controls the strength and direction of all observed electrokinetic responses.

If this is right

  • At alpha equals zero, ion selectivity reverses sign.
  • Ionic current rectification reaches significant values without any geometric or chemical asymmetry.
  • Electroosmotic flow exhibits negative rectification accompanied by steady internal vortices.
  • All transport regimes are tunable by a single parameter derived from the double-layer structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same field-induced mechanism may operate in any long, confined electrolyte system driven by an axial field, not only nanopores.
  • Voltage control of alpha could allow switching between different transport regimes in real time without changing pore geometry.
  • The predicted vortical structures at alpha equals zero provide a clear target for particle-image velocimetry experiments inside transparent nanopores.

Load-bearing premise

The surface potential stays perfectly uniform and the continuum Poisson-Nernst-Planck plus Navier-Stokes equations plus asymptotic analysis fully capture the physics without discrete-ion, roughness, or non-equilibrium double-layer effects.

What would settle it

Direct experimental measurement of negative electroosmotic flow rectification together with internal vortical structures inside a pore whose surface potential is verified to be axially uniform when alpha equals zero.

Figures

Figures reproduced from arXiv: 2604.20379 by Doyel Pandey, Pramodt Srinivasula.

Figure 1
Figure 1. Figure 1: (a) Physical and (b) mathematical model of a cylindrical nanopore of radius 𝑎, length 𝑙, connecting two identical reservoirs of dimension (𝑎𝑅 × 𝑙𝑅 ), filled with incom￾pressible, binary, monovalent electrolyte solution. An asym￾metric cylindrical coordinate system (𝑟, 𝑧) is considered with the origin placed at the junction of the nanopore and the bottom reservoir. The computational domain is highlighted by… view at source ↗
Figure 2
Figure 2. Figure 2: Validation of numerical method. (a) Comparison of 𝐼 − 𝑉 results of the present model using FSP condition (Eq. 5) with the experimental work of Tsutsui et al. [52]. (b) Axial velocity of the fluid at a cross-section of the nanopore of radius 50 nm away from the pore-reservoir junction. Blue solid line denotes the analytical electroosmotic velocity of an infinitely long cylindrical channel [26], and circular… view at source ↗
Figure 3
Figure 3. Figure 3: Non dimensional equivalent zeta potential along the axial direction of the nanochannel for (a) 𝜅𝑎 = 1.03 Eq. (28), (b) 𝜅𝑎 = 16.2 Eq. (31) and different values of 𝑉0 = ±25,±50, 0 mV. Other parameters are fixed at gate potential 𝑉𝐺 = −25 mV, nanochannel length 𝑙 = 1 𝜇m. potential 𝑉𝐺 within small buffer zone approximation, we obtain 𝜁eq(𝑧) = 𝑉𝐺 − 𝑉0 𝑧 𝑙 − ∑∞ 𝑛=1 𝑏𝑛 𝐼0 (𝛼𝑛𝑎) sin( 𝑛𝜋𝑧 𝑙 ) 1 − 1 𝐼0 (𝜅𝑎) . (28) D… view at source ↗
Figure 4
Figure 4. Figure 4: (a–e) Space charge density distributions within the nanopore at 𝑐0 = 1 mM for different transmembrane potentials 𝑉0 (corresponding 𝛼 values indicated). Left: fixed surface charge (FSC) with 𝜁 = −25 mV; right: fixed surface potential (FSP) with 𝑉𝐺 =−25 mV. Here pore length 𝑙= 1𝜇m and radius 𝑎= 50 nm. 𝑄𝑒 = 𝜀0 𝜀𝑟 𝜇 𝐸𝑧 𝜁𝑒𝑞(𝑧)𝜋𝑎2 ( 2𝐼𝑖 (𝜅𝑎) 𝜅𝑎𝐼0 (𝜅𝑎) − 1) (36) Further, using the two reservoir conditions, 𝑝(0)=𝑝… view at source ↗
Figure 5
Figure 5. Figure 5: Ionic selectivity. (a) Ionic selectivity (𝑆) as a function of transmembrane potential (𝑉0 ) for bulk concentrations 𝑐0 = 0.04, 1, and 10 mM, corresponding to 𝜅𝑎 ≈ 1, 5, and 16, respectively. Circular and triangular symbols denote fixed uniform surface potential (𝑉𝐺 = −25 mV) and fixed surface charge with uniform zeta potential (𝜁 = −25 mV) conditions, respectively. (b–e) Corresponding space charge density … view at source ↗
Figure 6
Figure 6. Figure 6: Ionic current rectification. (a) Ionic current 𝐼 (pA) as a function of transmembrane potential 𝑉0 (mV) for fixed surface potential (𝑉𝐺 = −25 mV, red circles) and fixed surface charge (of 𝜁 = −25 mV, blue triangles) conditions. Results are shown for bulk concentrations 𝑐0 = 0.0004, 0.04 mM (bottom panel) and 1, 10 mM (top panel), corresponding to 𝜅𝑎 ≈ 0.1, 1, 5, and 16, respectively. (b) Corresponding recti… view at source ↗
Figure 7
Figure 7. Figure 7: EOF rectification: (a,b) Average velocity (𝑢𝑎𝑣) verses applied external potential 𝑉0 at two different scenarios of (a) 𝜁 = −25 mV and (b) gate potential 𝑉𝐺 = −25 mV on the nanochannel wall. Here, four different values of the bulk concentration is considered as 𝑐0 = 0.0004, 0.04, 1, 10 mM, which corresponds to 𝜅𝑎≈ 0.1, 1, 5, 16, respectively. (d) Corresponding rectification factor 𝑅𝑓,𝐸𝑂𝐹 as a function of |𝑉… view at source ↗
Figure 8
Figure 8. Figure 8: Boundary conditions at each boundary of the computational domain shown in a representative crosssection of the axisymmetric geometry for the fixed surface potential operation. Identical boundary conditions are considered at the lateral and membrane contact boundaries of the top and bottom reservoir. boundaries and geometric singularities to balance accuracy and computational cost. Grid independence is veri… view at source ↗
read the original abstract

Gate-modulated nanopores have emerged as a promising platform for achieving ion selectivity and ionic current rectification (ICR) with the advantage of active field-based control. However, the mechanistic origin of these experimentally reported phenomena, arising from electrostatic coupling between the prescribed radial pore surface potential and the axial transmembrane electric field, remains insufficiently understood. Here, using coupled Poisson--Nernst--Planck and Navier--Stokes simulations supported by asymptotic analysis, we show that a uniform surface potential inherently interacts with the axial driving field to generate a three-dimensional, axially nonuniform electric double layer (EDL). This field-induced EDL heterogeneity effectively mimics a linear axial variation in zeta potential, breaking translational symmetry within an otherwise uniform pore. As a result, the system exhibits coupled electrokinetic responses, including ion selectivity, ionic current rectification, and non-canonical electroosmotic flow, all governed by a single asymmetry parameter $\alpha$ derived from the EDL structure. Critical transitions occur at specific values of $\alpha$; in particular, at $\alpha=0$, the EDL becomes axially antisymmetric, leading to reversal of ion selectivity, significant ICR and the emergence of a peculiar negative electroosmotic flow rectification accompanied by internal vortical structures. These findings establish the electrostatic mechanism for axial symmetry breaking as the underlying principle for transport in voltage-gated nanopores, enabling a unified framework for designing tunable electrokinetic functionalities beyond geometry- and chemistry-based strategies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that a uniform surface potential in a nanopore interacts with an axial transmembrane electric field to produce a three-dimensional, axially nonuniform electric double layer (EDL). This heterogeneity mimics a linear axial variation in effective zeta potential, breaking translational symmetry and giving rise to ion selectivity, ionic current rectification, and non-canonical electroosmotic flow. All these phenomena are governed by a single asymmetry parameter α derived from the EDL structure via coupled Poisson-Nernst-Planck and Navier-Stokes simulations supported by asymptotic analysis. Critical transitions occur at specific α values, notably reversal of selectivity and emergence of negative electroosmotic flow rectification with internal vortices at α = 0.

Significance. If the central derivation holds, the work supplies a unified electrostatic mechanism for axial symmetry breaking in otherwise uniform voltage-gated nanopores, explaining multiple transport regimes without invoking geometric or chemical asymmetry. The reduction to a single governing parameter α derived from the EDL structure is potentially powerful for device design. The combination of direct numerical simulation with asymptotic analysis is a methodological strength that could be extended to other electrokinetic systems.

major comments (2)
  1. [Methods (§2) and EDL analysis (§3)] The validity of the continuum PNP-NS description for the axially varying EDL is load-bearing for the quantitative value of α and the locations of the critical transitions (especially α = 0). When the Debye length is comparable to the pore radius or ion diameter, steric packing, hydration, and ion correlations modify the local charge density and therefore the effective axial gradient. The manuscript should explicitly delineate the parameter regime in which the continuum limit remains accurate or provide a supporting test (e.g., comparison against molecular dynamics) to confirm that the predicted transport regimes survive these corrections.
  2. [Asymptotic analysis (§4)] The asymptotic reduction that maps the three-dimensional EDL heterogeneity onto an effective one-dimensional model with linear zeta variation must be shown in detail. In particular, the steps leading to the definition of α should be presented so that it is clear the parameter is obtained directly from the EDL potential distribution rather than adjusted to match the observed transport curves.
minor comments (2)
  1. [Figures 2–5] Figure captions should explicitly state how α is extracted from the simulated EDL potential and indicate the range of α explored in each panel.
  2. [Introduction and notation] Notation for surface potential, zeta potential, and the axial field should be introduced consistently in the first section where they appear.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the work's significance and for the constructive major comments. We address each point below, indicating the revisions we will implement in the next version of the manuscript.

read point-by-point responses

  1. Referee: [Methods (§2) and EDL analysis (§3)] The validity of the continuum PNP-NS description for the axially varying EDL is load-bearing for the quantitative value of α and the locations of the critical transitions (especially α = 0). When the Debye length is comparable to the pore radius or ion diameter, steric packing, hydration, and ion correlations modify the local charge density and therefore the effective axial gradient. The manuscript should explicitly delineate the parameter regime in which the continuum limit remains accurate or provide a supporting test (e.g., comparison against molecular dynamics) to confirm that the predicted transport regimes survive these corrections.

    Authors: We agree that the continuum PNP-NS approximation has well-known limitations when λ_D approaches the pore radius a or hydrated ion size, where steric effects and correlations become important. In the regimes simulated here (λ_D/a ≲ 0.05 for typical 10–100 mM electrolytes and 10–50 nm pores), the model remains standard and has been benchmarked against experiments in the electrokinetics literature. We will add a dedicated paragraph in §2 (Methods) that explicitly delineates the validity window (λ_D/a < 0.1, moderate concentrations, no steric saturation) and cites supporting references. A direct MD comparison lies outside the present scope, but the axial symmetry-breaking mechanism is electrostatic in origin and expected to persist qualitatively. This addition will clarify the quantitative applicability of α and the critical transitions. revision: yes

  2. Referee: [Asymptotic analysis (§4)] The asymptotic reduction that maps the three-dimensional EDL heterogeneity onto an effective one-dimensional model with linear zeta variation must be shown in detail. In particular, the steps leading to the definition of α should be presented so that it is clear the parameter is obtained directly from the EDL potential distribution rather than adjusted to match the observed transport curves.

    Authors: We thank the referee for highlighting the need for greater transparency in the asymptotic reduction. In the revised manuscript we will expand §4 with a step-by-step derivation: (i) extraction of the local wall potential φ(a,z) from the 3D PNP solution, (ii) definition of the effective axial zeta profile ζ(z) = φ(a,z) − φ_bulk, (iii) decomposition into mean and linear-gradient components, and (iv) explicit construction of α as the normalized slope of that linear component. This procedure is performed directly on the computed EDL potential field before any transport calculations, confirming that α is not fitted to current or flow data. We will also add a short appendix containing the full asymptotic expansion for completeness. revision: yes

Circularity Check

0 steps flagged

No significant circularity; α emerges from EDL electrostatics rather than transport data

full rationale

The paper's derivation proceeds from coupled Poisson-Nernst-Planck + Navier-Stokes simulations plus asymptotic analysis of the 3D EDL formed by a uniform Dirichlet surface potential interacting with an imposed axial field. The asymmetry parameter α is extracted directly from the resulting axially varying EDL potential (or effective zeta) structure; the transport phenomena (selectivity, ICR, EOF) are then shown to be organized by this α. Because α is computed from the electrostatic solution and not fitted to or defined by the target current/velocity data, and because no self-citation chain or uniqueness theorem is invoked to close the argument, the chain does not reduce to its own inputs. The continuum model assumptions are stated explicitly and remain open to external falsification.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the continuum electrokinetic equations and the asymptotic reduction that isolates α; no new entities are postulated and no parameters are fitted to the final transport observables.

axioms (2)
  • domain assumption Continuum Poisson-Nernst-Planck and Navier-Stokes equations remain valid at the nanopore length scales considered
    Standard modeling assumption invoked for the coupled simulations
  • domain assumption The electric double layer reaches quasi-equilibrium on the timescale of the axial flow
    Required for the asymptotic analysis that extracts the effective axial zeta variation

pith-pipeline@v0.9.0 · 5564 in / 1335 out tokens · 39766 ms · 2026-05-09T23:47:33.989984+00:00 · methodology

discussion (0)

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