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REVIEW 3 major objections 7 minor 59 references

pH-Dependent Zeta Potential Induces Diffusiophoretic Focusing in an Acid-Base Reaction

T0 review · 3 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Particles focus into a steady band in an acid-base channel only when their surface charge depends on pH.

desk verdict A useful analytical account of diffusiophoretic focusing in acid-base systems, but the claim that pH-dependent zeta is necessary is under-tested against salt-dependent zeta. read the letter →

arxiv 2506.05731 v1 pith:T5L5MGVN submitted 2025-06-06 cond-mat.soft physics.chem-ph

Ethan Coleman , Ankur Gupta This is my paper
classification cond-mat.softphysics.chem-ph PACS 47.57.-s47.61.-k
keywords diffusiophoresiszetapotentialpHgradientcolloidalfocusingmulti-iontransportNernst-Planckacid-basereactionmicrofluidics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that in a microchannel with hydrochloric acid on one side and sodium hydroxide on the other, plus sodium chloride salt, suspended particles can gather into a stationary band by reversing their diffusiophoretic direction mid-channel. The reversal is possible only if the particle's zeta potential changes with pH; a constant zeta potential would make particles defocus instead. The authors derive analytical inequalities that give the range of salt concentrations producing a focusing band and whether the band sits exactly at the acid-base reaction front or off it. A sympathetic reader would care because this provides a design rule for concentrating colloids in microfluidic and biological settings using simple acid-base gradients.

What carries the argument

The model combines a steady-state multi-ion Nernst-Planck description of Na$^+$, Cl$^-$, H$^+$, and OH$^-$ with the standard low-potential diffusiophoretic velocity $U = (\varepsilon/\mu)[E\zeta + (\partial \log I/\partial x)\zeta^2/8]$. The pH-dependence of the surface charge enters as a linear interpolation of zeta potential between $-49$ mV at pH 4 and $-61$ mV at pH 10 (Eq. 1d). Under an instantaneous acid-base reaction, the channel splits into acidic and basic three-ion regions, and the velocity decomposes into contributions from HCl and NaCl (acidic side) or NaOH and NaCl (basic side), giving closed-form mobility expressions (Eq. 2). Requiring $U>0$ on the left and $U<0$ on the right yields the two inequalities in Eq. (3) that define the focusing window.

What would settle it

Run the same acid-base channel with particles whose zeta potential is measured to be flat across pH 4 to 10; the model predicts no focusing at any salt concentration, so observing a focusing band would contradict the mechanism, while measuring the band's salt window for particles with a known non-linear zeta-potential curve would test the quantitative prediction of Eq. (3).

Watch

Extended reading notes

Core claim

The central discovery is that pH-dependent zeta potential, not the salt gradient alone, is the switch that makes diffusiophoretic focusing happen in the HCl/NaOH/NaCl system. When salt is added, it drives particles leftward, opposing the rightward acid/base-driven motion. Because the zeta potential is more negative on the basic side, the salt-induced velocity is amplified there, so the basic side reverses direction first; with a constant zeta potential the acidic side would reverse first and particles would defocus. The paper derives semi-analytic conditions (Eq. 3) that predict the salt range for focusing, and distinguishes on-front and off-front focusing using dimensionless groups $\xi_a$ and $\xi_b$ based on the zeta potential and ionic fluxes.

Load-bearing premise

The zeta potential is modeled as a linear function of pH, pinned to two measured values (-49 mV at pH 4 and -61 mV at pH 10), and the paper states the results do not hold for particles with non-linear pH dependence.

Editorial extensions

If this is right

  • For particles with a known linear $\zeta(pH)$, Eq. (3) gives the exact salt concentrations at which a focusing band forms and where it sits, enabling predictive design of microfluidic concentrators.
  • The model reproduces all four experimental regimes from prior work: pH-dominated motion, focusing, pseudo-focusing, and salt-dominated motion, so the framework can be used to interpret experiments.
  • Weak acids and bases, which produce smaller pH jumps, are predicted to yield a narrower range of salt concentrations for focusing.
  • The three-ion mobility expressions in Eq. (2) extend the binary-electrolyte result to any system with a common ion, so they can be reused for electrochemical and membrane transport problems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If zeta potential depends nonlinearly on pH, the same mechanism might create more than one zero-velocity point and hence multiple or drifting bands; the linear assumption in the paper would need to be relaxed to test this.
  • The mechanism should apply to any surface-charge-regulated particle, including protein aggregates or lipid vesicles in biological pH gradients, suggesting that acid-base fronts in cells and pores could self-organize colloidal matter into layers.
  • A direct experimental test would be to measure the focusing salt window for particles with deliberately flattened zeta potential versus pH; the paper's Eq. (3) predicts the window should vanish, a distinctive signature of the mechanism.
  • The analytical conditions could be inverted: instead of predicting focusing from a known $\zeta(pH)$, one could measure the focusing window experimentally to infer the particle's zeta-potential sensitivity to pH.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. The paper develops a steady-state multi-ion diffusiophoresis model for a one-dimensional HCl/NaOH/NaCl channel in which particles can reverse their diffusiophoretic velocity and focus into a band. The authors argue that a pH-dependent zeta potential is necessary for this focusing, identify on-front versus off-front focusing and a pseudo-focusing regime, and derive analytical inequalities, Eq. (3), for the salt-concentration range that allows focusing. They compare the model qualitatively with the experiments of Shi et al. and report a uniform 2.5 mM shift in salt concentration.

Significance. If established, the proposed mechanism would explain a puzzling experimental observation and provide design rules for diffusiophoretic focusing in acid-base systems, with potential applications in microfluidics and biophysical transport. The paper contributes a three-ion analytical framework and a phase diagram in the zeta-variation versus salt-concentration plane. However, the central claim of necessity is not fully isolated from competing ionic-strength effects on zeta, and the key analytical derivation is relegated to unavailable Supplemental Material. These issues currently limit the strength of the theoretical conclusions.

major comments (3)
  1. [Eq. (1d) and Fig. 3] The central claim that pH-dependent zeta potential is necessary for focusing is not isolated from the possibility of ionic-strength-dependent zeta. The model imposes zeta as a function of pH only, Eq. (1d), and never tests a counterfactual in which zeta depends on local salt concentration. In this geometry, NaCl is present only at x=0, so the ionic strength varies strongly across the channel, and for typical polystyrene particles |zeta| increases as salt concentration decreases. That dependence would produce the same spatial asymmetry the paper attributes to pH: a larger |zeta| on the low-salt/basic side, which can make the salt-induced velocity more negative there and cause a positive-to-negative velocity switch even with no pH dependence of zeta. The paper cites ref. [28] on concentration-dependent zeta but does not incorporate or test such a model. The phase diagram in Fig. 3 varies Delta-zeta while holding the pH-only functional form fixed, so it cannot distinguish pH-dependence from ionic-strength-dependence; a model or bound with zeta = zeta(ionic strength) is needed to support the word 'necessary' in the abstract and conclusions.
  2. [Eq. (2) and Eq. (3)] The derivation of the analytical focusing conditions is not present in the manuscript. The text states that 'the solution in the acidic and basic side become [52]' and that details are in the Supplemental Material, but the supplement is not available with this arXiv version. Eq. (3) is used to draw the phase diagram and is the main quantitative design rule, so the derivation of Eqs. (2) and (3) must be included or the supplement must be made available for review. As written, the central inequalities cannot be checked by the reader.
  3. [Fig. 2 and discussion near 'self-consistent with our model'] The comparison with the experiments of Shi et al. has a systematic salt-concentration offset of 2.5 mM, and the model requires cs > c0 for focusing while experiments focus at cs = c0 = 0.5 mM. The manuscript attributes the offset to the low-potential assumption without quantitative support, stating only that the assumption 'may artificially lead to decreased sensitivity.' This discrepancy is at the boundary of the predicted focusing regime and could be a symptom of the missing ionic-strength dependence of zeta. The qualitative agreement is therefore weaker than claimed, and the offset needs an explanation or a model extension that abridges the gap.
minor comments (7)
  1. [Eq. (1e)] There is a typo in 'low potential limit limit' which should read 'low potential limit.'
  2. [Fig. 3 caption] The word 'psuedofocusing' should be 'pseudo-focusing.'
  3. [Eq. (1d) paragraph] The sentence 'we set zeta a to be the zeta potential at pH=4.5 ad zeta b to be the zeta potential at pH=9.5' contains a typo: 'ad' should be 'and.'
  4. [Setup description and Fig. 1, Sec. 1] The boundary condition for NaCl at x=L is not stated. The text specifies [NaCl]=cs at x=0 but does not say whether the right reservoir contains no NaCl; this should be clarified for reproducibility.
  5. [Eq. (1d) and Fig. 3] The linear zeta model is anchored at pH=4 and pH=10, while the phase diagram uses pH=3.3 and pH=10.7 at the channel ends. The relationship between these two sets of anchor points should be explained to avoid apparent inconsistency.
  6. [Eq. (3)] The expressions for xi_a and xi_b would be clearer with parentheses, e.g., xi_a = (8 + zeta~_a)/(8 - zeta~_a), to avoid ambiguity in the printed ratio.
  7. [Discussion near Eq. (1d)] The authors acknowledge that the results are sensitive to pH and will not hold for nonlinear pH-dependence; this limitation should be stated more prominently, for example in the abstract or conclusions, because it qualifies the universality of the main claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the model is self-contained and compares to external data without fitting ζ to the focusing observation.

full rationale

The paper's derivation chain is self-contained: ion concentration profiles follow from the steady-state Nernst-Planck equations with electroneutrality and zero current (Eq. 1a-1c); the diffusiophoretic velocity is computed from the standard multi-ion expression (Eq. 1e) taken from ref. [48], a published derivation used as a known physical law. The only material input specific to the system is the linear ζ(pH) relation (Eq. 1d), pinned to two externally measured values from refs. [13,44]; it is not fitted to the focusing observations. The focusing criterion is derived within the same model (Eq. 3) and overlaid on the model's own phase diagram; this is an analytical consistency check, not an independent empirical prediction, and it does not reduce to its inputs because it derives from the model equations rather than being imposed. The comparison with Shi et al. [44] is external and qualitative, and the observed salt-concentration shift is acknowledged rather than fitted away. Self-citations (refs. [48,51]) are to standard diffusiophoresis/Nernst-Planck expressions, not to an author-specific uniqueness theorem, and no load-bearing claim depends solely on an unpublished or circular prior result. The alternative confound that ζ may also depend on ionic strength is a modeling-assumption robustness concern, not a circularity.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests mainly on the assumed linear pH dependence of zeta, the steady-state and instantaneous-reaction assumptions, and the low-potential form of the diffusiophoretic velocity. No new physical entities are introduced. The free parameters are the zeta anchors and the pseudo-focusing threshold.

free parameters (3)
  • zeta_acid_linear_anchor = -49 mV at pH 4
    Anchor for the linear pH-zeta relation (Eq. 1d), taken from literature values in refs [13,44]. The magnitude and slope control the predicted focusing range.
  • zeta_base_linear_anchor = -61 mV at pH 10
    Second anchor for the linear pH-zeta interpolation, from prior experiments. It is an input, not fitted to the focusing data.
  • pseudofocusing_threshold = U_min/U_max < 1e-2
    Ad hoc threshold defining the pseudo-focusing regime in the phase diagram. It does not affect the central focusing condition but is used to classify regimes.
assumptions (6)
  • domain assumption The concentration field is at steady state and particles respond to these steady gradients without altering them.
    Used throughout, including the statement 'we focus on the scenario when the concentration is at a steady state and the particles respond to the steady gradients' (near Fig. 2). Ignores feedback of particle motion on ion distribution.
  • domain assumption The acid-base reaction is instantaneous in the analytical two-region model, giving ca_OH = 0 and cb_H = 0.
    Used in the analytical section to split the channel into acidic and basic sides. A finite-rate reaction would blur the front and could weaken the focusing conditions.
  • domain assumption The diffusiophoretic velocity formula Eq. (1e) is valid in the low-potential limit (|tilde zeta| <= 4).
    The model uses Eq. (1e) from ref [48]; the authors acknowledge accuracy for |tilde zeta| <= 4, which holds for their potentials but limits quantitative accuracy.
  • ad hoc to paper Zeta potential varies linearly with pH (Eq. 1d).
    A simplification anchored at two measured points, introduced specifically for this work. The authors state results will not hold for non-linear pH dependence.
  • domain assumption The reaction front is treated as a sharp interface with a pH jump from about 4 to about 10, and on/off-front focusing is determined by assuming the front spans pH 4.5 to 9.5.
    Used to compute dashed lines in Fig. 3. The range pH 4.5 to 9.5 is chosen from titration behavior, not from direct measurement.
  • domain assumption Uniform initial particle distribution and dilute particles, so particles do not interact.
    Assumed in the Langevin trajectory simulations and the qualitative model; interactions among particles are ignored.

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Cite this review

Pith. "Pith review of pH-Dependent Zeta Potential Induces Diffusiophoretic Focusing in an Acid-Base Reaction." pith.science (2026). https://pith.science/paper/T5L5MGVN

@misc{pith2026250605731,
  author       = {Pith},
  title        = {Pith review of: pH-Dependent Zeta Potential Induces Diffusiophoretic Focusing in an Acid-Base Reaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T5L5MGVN}},
  note         = {Machine review of arXiv:2506.05731}
}
read the original abstract

Diffusiophoresis of charged particles in the presence of electrolytes has been extensively studied in the literature. However, in these setups, particles typically move in a single direction, either up or down the electrolyte gradient. Here, we theoretically investigate the conditions under which a particle can reverse its diffusiophoretic direction within the same setup, leading to the formation of a focusing band under steady-state concentration gradients. Using multi-ion diffusiophoresis calculations, we simulate particle transport in an acid-based reaction system where salt is added alongside the acid. For a range of salt concentrations, particles focus within the channel. Our analysis reveals that a pH-dependent zeta potential is necessary for this focusing to occur, and determines where the particles focus, i.e., on or off the acid-base reaction front. We report qualitative agreement with prior experimental observations and derive analytical conditions governing particle focusing, highlighting the delicate balance between concentration gradients and zeta potential variations. The work elucidates the crucial physics of pH-dependent zeta potential and opens new avenues for exploring diffusiophoresis in acid-base systems, with implications for microfluidic design and biophysical transport processes.

Figures

Figures reproduced from arXiv: 2506.05731 by the authors.

Figure 1
Figure 1. FIG. 1. Overview of the setup and qualitative descrip [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Comparison of model results with experimental obser [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

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Works this paper leans on

59 extracted references · 54 canonical work pages

  1. [44]

    N. Shi, R. Nery-Azevedo, A. I. Abdel-Fattah, and T. M. Squires, Diffusiophoretic focusing of suspended colloids, Physical Review Letters 117, 258001 (2016)

    work page 2016

  2. [52]

    If U switches di- rection from positive to negative as we move from left to right, we refer to it as focusing

    and U as a function of ∆ ζ and cs. If U switches di- rection from positive to negative as we move from left to right, we refer to it as focusing. We define ˜δ = 1 − xf /xr such that when δ = 0, we observe on-front focusing and when δ ̸= 0, we observe off-front focusing. In addition, we define ˜U = Umin/Umax such that if ˜U < 10−2, we refer to the conditio...

    work page

  3. [28]

    Akdeniz, J

    B. Akdeniz, J. A. Wood, and R. G. Lammertink, Diffu- siophoresis and diffusio-osmosis into a dead-end channel: Role of the concentration-dependence of zeta potential, Langmuir 39, 2322 (2023)

    work page 2023

  4. [1]

    Palacci, S

    J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Science 339, 936 (2013)

    work page 2013

  5. [2]

    Aubret, M

    A. Aubret, M. Youssef, S. Sacanna, and J. Palacci, Tar- geted assembly and synchronization of self-spinning mi- crogears, Nature Physics 14, 1114 (2018)

    2018

  6. [3]

    B. M. Alessio and A. Gupta, Diffusiophoresis-enhanced turing patterns, Science Advances 9, eadj2457 (2023)

    work page 2023

  7. [4]

    S. Shin, P. B. Warren, and H. A. Stone, Cleaning by sur- factant gradients: Particulate removal from porous mate- rials and the significance of rinsing in laundry detergency, Physical Review Applied 9, 034012 (2018)

    work page 2018

  8. [5]

    S. Shin, O. Shardt, P. B. Warren, and H. A. Stone, Mem- braneless water filtration using CO2, Nature Communi- cations 8, 15181 (2017)

    work page 2017

Show all 59 references
  1. [6]

    Ab´ ecassis, C

    B. Ab´ ecassis, C. Cottin-Bizonne, C. Ybert, A. Ajdari, and L. Bocquet, Boosting migration of large particles by solute contrasts, Nature Materials 7, 785 (2008)

    2008

  2. [7]

    Prieve, J

    D. Prieve, J. Anderson, J. Ebel, and M. Lowell, Motion of a particle generated by chemical gradients. Part 2. electrolytes, Journal of Fluid Mechanics 148, 247 (1984)

    1984

  3. [8]

    J. L. Anderson, Colloid transport by interfacial forces, Annual Review of Fluid Mechanics 21, 61 (1989)

    1989

  4. [9]

    H. J. Keh and Y. K. Wei, Diffusiophoretic mobility of spherical particles at low potential and arbitrary double- layer thickness, Langmuir 16, 5289 (2000)

    2000

  5. [10]

    Velegol, A

    D. Velegol, A. Garg, R. Guha, A. Kar, and M. Kumar, Origins of concentration gradients for diffusiophoresis, Soft Matter 12, 4686 (2016)

    2016

  6. [11]

    Ganguly, S

    A. Ganguly, S. Roychowdhury, and A. Gupta, Uni- fied mobility expressions for externally driven and self- phoretic propulsion of particles, Journal of Fluid Mechan- ics 994, A2 (2024)

    2024

  7. [12]

    Chiang and D

    T.-Y. Chiang and D. Velegol, Multi-ion diffusiophoresis, Journal of Colloid and Interface Science 424, 120 (2014)

    2014

  8. [13]

    S. Shim, J. K. Nunes, G. Chen, and H. A. Stone, Dif- fusiophoresis in the presence of a ph gradient, Physical Review Fluids 7, 110513 (2022)

    2022

  9. [14]

    Ganguly, B

    A. Ganguly, B. M. Alessio, and A. Gupta, Diffusiophore- sis: A novel transport mechanism-fundamentals, appli- cations, and future opportunities, Frontiers in Sensors 4, 1322906 (2023)

    2023

  10. [15]

    Shim, Diffusiophoresis, diffusioosmosis, and microflu- idics: Surface-flow-driven phenomena in the presence of flow, Chemical Reviews 122, 6986 (2022)

    S. Shim, Diffusiophoresis, diffusioosmosis, and microflu- idics: Surface-flow-driven phenomena in the presence of flow, Chemical Reviews 122, 6986 (2022)

    2022

  11. [16]

    J. T. Ault and S. Shin, Physicochemical hydrodynamics of particle diffusiophoresis driven by chemical gradients, Annual Review of Fluid Mechanics 57 (2024)

    2024

  12. [17]

    H. J. Keh, Diffusiophoresis of charged particles and dif- fusioosmosis of electrolyte solutions, Current Opinion in Colloid & Interface Science 24, 13 (2016)

    2016

  13. [18]

    Kar, T.-Y

    A. Kar, T.-Y. Chiang, I. Ortiz Rivera, A. Sen, and D. Velegol, Enhanced transport into and out of dead-end pores, ACS Nano 9, 746 (2015)

    2015

  14. [19]

    B. M. Alessio, S. Shim, E. Mintah, A. Gupta, and H. A. Stone, Diffusiophoresis and diffusioosmosis in tan- dem: Two-dimensional particle motion in the presence of multiple electrolytes, Physical Review Fluids 6, 054201 (2021)

    2021

  15. [20]

    B. M. Alessio, S. Shim, A. Gupta, and H. A. Stone, Diffusioosmosis-driven dispersion of colloids: A Taylor dispersion analysis with experimental validation, Journal of Fluid Mechanics 942, A23 (2022)

    2022

  16. [21]

    J. T. Ault, P. B. Warren, S. Shin, and H. A. Stone, Diffu- siophoresis in one-dimensional solute gradients, Soft Mat- ter 13, 9015 (2017)

    2017

  17. [22]

    J. L. Wilson, S. Shim, Y. E. Yu, A. Gupta, and H. A. Stone, Diffusiophoresis in multivalent electrolytes, Lang- muir 36, 7014 (2020)

    2020

  18. [23]

    Gupta, S

    A. Gupta, S. Shim, and H. A. Stone, Diffusiophoresis: from dilute to concentrated electrolytes, Soft Matter 16, 6975 (2020)

    2020

  19. [24]

    Singh, G

    N. Singh, G. T. Vladisavljevi´ c, F. Nadal, C. Cottin- Bizonne, C. Pirat, and G. Bolognesi, Reversible trapping of colloids in microgrooved channels via diffusiophoresis under steady-state solute gradients, Physical Review Let- ters 125, 248002 (2020). 6

    2020

  20. [25]

    Singh, G

    N. Singh, G. T. Vladisavljevic, F. Nadal, C. Cottin- Bizonne, C. Pirat, and G. Bolognesi, Enhanced accumu- lation of colloidal particles in microgrooved channels via diffusiophoresis and steady-state electrolyte flows, Lang- muir 38, 14053 (2022)

    2022

  21. [26]

    S. Shin, E. Um, B. Sabass, J. T. Ault, M. Rahimi, P. B. Warren, and H. A. Stone, Size-dependent control of col- loid transport via solute gradients in dead-end channels, Proceedings of the National Academy of Sciences 113, 257 (2016)

    2016

  22. [27]

    S. Shin, J. T. Ault, J. Feng, P. B. Warren, and H. A. Stone, Low-cost zeta potentiometry using solute gradi- ents, Advanced Materials 29, 1701516 (2017)

    2017

  23. [29]

    S. Shin, J. T. Ault, P. B. Warren, and H. A. Stone, Accu- mulation of colloidal particles in flow junctions induced by fluid flow and diffusiophoresis, Physical Review X 7, 041038 (2017)

    2017

  24. [30]

    Liu and A

    H. Liu and A. A. Pahlavan, Diffusioosmotic reversal of colloidal focusing direction in a microfluidic T-junction, Physical Review Letters 134, 098201 (2025)

    2025

  25. [31]

    Chakra, N

    A. Chakra, N. Singh, G. T. Vladisavljevic, F. Nadal, C. Cottin-Bizonne, C. Pirat, and G. Bolognesi, Continu- ous manipulation and characterization of colloidal beads and liposomes via diffusiophoresis in single-and double- junction microchannels, ACS Nano 17, 14644 (2023)

    2023

  26. [32]

    Chakra, C

    A. Chakra, C. Puijk, G. T. Vladisavljevi´ c, C. Cottin- Bizonne, C. Pirat, and G. Bolognesi, Surface chemistry- based continuous separation of colloidal particles via dif- fusiophoresis and diffusioosmosis, Journal of Colloid and Interface Science 693, 137577 (2025)

    2025

  27. [33]

    Palacci, B

    J. Palacci, B. Ab´ ecassis, C. Cottin-Bizonne, C. Ybert, and L. Bocquet, Colloidal motility and pattern formation under rectified diffusiophoresis, Physical Review Letters 104, 138302 (2010)

    2010

  28. [34]

    Palacci, C

    J. Palacci, C. Cottin-Bizonne, C. Ybert, and L. Bocquet, Osmotic traps for colloids and macromolecules based on logarithmic sensing in salt taxis, Soft Matter 8, 980 (2012)

    2012

  29. [35]

    Banerjee and T

    A. Banerjee and T. M. Squires, Long-range, selective, on- demand suspension interactions: Combining and trigger- ing soluto-inertial beacons, Science Advances5, eaax1893 (2019)

    2019

  30. [36]

    R. R. Raj, C. W. Shields, and A. Gupta, Two- dimensional diffusiophoretic colloidal banding: Optimiz- ing the spatial and temporal design of solute sinks and sources, Soft Matter 19, 892 (2023)

    2023

  31. [37]

    H. Tan, A. Banerjee, N. Shi, X. Tang, A. Abdel-Fattah, and T. M. Squires, A two-step strategy for delivering particles to targets hidden within microfabricated porous media, Science Advances 7, eabh0638 (2021)

    2021

  32. [38]

    Jotkar, I

    M. Jotkar, I. Ben-Noah, J. J. Hidalgo, and M. Dentz, Diffusiophoresis of colloids in partially-saturated porous media, Advances in Water Resources193, 104828 (2024)

    2024

  33. [39]

    Alipour, Y

    M. Alipour, Y. Li, H. Liu, and A. A. Pahlavan, Diffu- siophoretic transport of colloids in porous media, arXiv preprint arXiv:2411.14712 (2024)

    2024 arXiv

  34. [40]

    P. B. Warren, Non-faradaic electric currents in the nernst-planck equations and nonlocal diffusiophoresis of suspended colloids in crossed salt gradients, Physical Re- view Letters 124, 248004 (2020)

    2020

  35. [41]

    action-at-a-distance

    I. Williams, P. B. Warren, R. P. Sear, and J. L. Keddie, Colloidal diffusiophoresis in crossed electrolyte gradients: Experimental demonstration of an “action-at-a-distance” effect predicted by the Nernst-Planck equations, Physical Review Fluids 9, 014201 (2024)

    2024

  36. [42]

    Sambamoorthy and H

    S. Sambamoorthy and H. C. Chu, Diffusiophoresis in porous media saturated with a mixture of electrolytes, Nanoscale Advances 7, 2057 (2025)

    2025

  37. [43]

    Sambamoorthy and H

    S. Sambamoorthy and H. C. Chu, Diffusiophoresis of a spherical particle in porous media, Soft Matter 19, 1131 (2023)

    2023

  38. [45]

    F. M. M¨ oller, F. Kriegel, M. Kieß, V. Sojo, and D. Braun, Steep ph gradients and directed colloid transport in a microfluidic alkaline hydrothermal pore, Angewandte Chemie International Edition 56, 2340 (2017)

    2017

  39. [46]

    M. Seo, S. Park, D. Lee, H. Lee, and S. J. Kim, Contin- uous and spontaneous nanoparticle separation by diffu- siophoresis, Lab on a Chip 20, 4118 (2020)

    2020

  40. [47]

    H. Lee, J. Kim, J. Yang, S. W. Seo, and S. J. Kim, Diffu- siophoretic exclusion of colloidal particles for continuous water purification, Lab on a Chip 18, 1713 (2018)

    2018

  41. [48]

    Gupta, B

    A. Gupta, B. Rallabandi, and H. A. Stone, Diffusio- phoretic and diffusioosmotic velocities for mixtures of valence-asymmetric electrolytes, Physical Review Fluids 4, 043702 (2019)

    2019

  42. [49]

    Florea, S

    D. Florea, S. Musa, J. M. Huyghe, and H. M. Wyss, Long-range repulsion of colloids driven by ion ex- change and diffusiophoresis, Proceedings of the National Academy of Sciences 111, 6554 (2014)

    2014

  43. [50]

    N. A. Timmerhuis and R. G. Lammertink, Diffusio- phoretic movements of polystyrene particles in a h- shaped channel for inorganic salts, carboxylic acids, and organic salts, Langmuir 38, 12140 (2022)

    2022

  44. [51]

    Gupta, S

    A. Gupta, S. Shim, L. Issah, C. McKenzie, and H. A. Stone, Diffusion of multiple electrolytes cannot be treated independently: Model predictions with experimental val- idation, Soft Matter 15, 9965 (2019)

    2019

  45. [53]

    See Supplemental Material at URL-will-be-inserted-by- publisher for details of the theoretical formulation

  46. [54]

    B. W. Ninham and V. A. Parsegian, Electrostatic po- tential between surfaces bearing ionizable groups in ionic equilibrium with physiologic saline solution, Journal of Theoretical Biology 31, 405 (1971)

    1971

  47. [55]

    W. M. Deen, Analysis of Transport Phenomena(Oxford University Press, New York, 2012)

    2012

  48. [56]

    Hafner and M

    G. Hafner and M. Muller, Reaction-driven diffusiophore- sis of liquid condensates: Potential mechanisms for intra- cellular organization, ACS Nano 18, 16530 (2024)

    2024

  49. [57]

    K. Wang, S. Leville, B. Behdani, and C. A. S. Batista, Long-range transport and directed assembly of charged colloids under aperiodic electrodiffusiophoresis, Soft Mat- ter 18, 5949 (2022)

    2022

  50. [58]

    K. Wang, B. Behdani, and C. A. Silvera Batista, Visual- ization of concentration gradients and colloidal dynamics under electrodiffusiophoresis, Langmuir 38, 5663 (2022)

    2022

  51. [59]

    Jarvey, F

    N. Jarvey, F. Henrique, and A. Gupta, Asymmetric rec- tified electric and concentration fields in multicomponent electrolytes with surface reactions, Soft Matter 19, 6032 (2023)

    2023

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Reviewed August 7, 2026 · model on record in the stance chip above.