Pith. sign in

REVIEW 2 major objections 5 minor 51 references

Transient osmotic flows in a microfluidic channel: measurements of solute permeability and reflection coefficients of hydrogel membranes

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A single transient osmotic flow in a dead-end microchannel yields both the reflection coefficient and the solute permeability of a membrane from one exponential fit.

desk verdict A genuinely useful microfluidic method for extracting sigma and LD from transient osmotic flows, with a sloppy but non-fatal validation of the linearization assumption for sucrose. read the letter →

arxiv 2506.06186 v1 pith:A3JA5J6K submitted 2025-06-06 cond-mat.soft

Julien Renaudeau , Pierre Lidon , Jean-Baptiste Salmon This is my paper
classification cond-mat.soft
keywords forwardosmosisreflectioncoefficientsolutepermeabilityhydrogelmembranemicrofluidicsKedem-Katchalskyequationsmolecularweightcut-offtransientosmoticflow
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 a single transient measurement in a microfluidic chip determines both fundamental transport coefficients of a membrane: the solute permeability $\mathcal{L}_D$ and the reflection coefficient $\sigma$. In the proposed dead-end geometry, forward osmosis drives water into a channel, while solute leaking through the membrane gradually kills the osmotic driving force, so the entrance volume flux decays as a pure exponential. The initial amplitude of that decay gives $\sigma$ and the decay rate gives $\mathcal{L}_D$. The authors verify the idea on photo-crosslinked PEGDA hydrogel membranes, finding $\sigma \simeq 0.8$ for sucrose, $\sigma$ near 1 for dextran (10 kg/mol), and a molecular-weight cut-off near 1 kg/mol. If reliable, the method turns a cheap microfluidic flow-decay movie into a complete in situ membrane characterization.

What carries the argument

The central object is the dead-end microchannel separated along its length from a solute reservoir by the membrane. The argument runs on the linearized Kedem-Katchalsky equations, simplified by two smallness conditions: the advective solute flux is negligible ($\mathrm{Pe} = \sigma \mathcal{L}_p R T C_0/\mathcal{L}_D \ll 1$) and the membrane resistance dominates over transverse diffusion in the channel ($R = w\mathcal{L}_D/D_s \ll 1$). Under those assumptions the channel concentration is spatially uniform and obeys $dC/dt = (\mathcal{L}_D/w)(C_0 - C)$, which forces the exponential volume-flux law. A shear-flow criterion (eq. 9) additionally guarantees that no concentration boundary layer forms in the reservoir; the membrane area $h \times L$ and channel width $w$ enter the amplitude $V_0 = (L/w)\mathcal{L}_p R T C_0$, so an independent hydraulic-permeability measurement is needed to set the scale.

What would settle it

A decisive check is to repeat the transient-osmosis experiment for the same membrane and solute at several reservoir concentrations $C_0$: the model predicts fitted $\sigma$ and $\mathcal{L}_D$ independent of $C_0$, so any drift with concentration would show the linearization has broken. A second check is to compare the $\mathcal{L}_D$ from the flow decay against an independent no-flow permeation measurement on the same membrane.

Watch

Extended reading notes

Core claim

The central discovery is that the transient osmotic flow in a dead-end microchannel obeys $$V_i = \$\sigma$ V_0 \exp(-\mathcal{L}_D t / w),$$ where $V_0$ is the flow an ideal semi-permeable membrane would drive, $w$ is the channel width, and $t$ is time after the solute reservoir is switched on. Because the exponential amplitude is $\sigma V_0$ and the decay rate is $\mathcal{L}_D/w$, a single time series of the entrance volume flux separates the two Kedem-Katchalsky parameters that are usually measured in different apparatuses. The solute concentration in the channel rises as $C_0(1 - \exp(-\mathcal{L}_D t/w))$, so the same exponential governs solute accumulation. For PEGDA hydrogel membranes the deduced $\sigma$ rises from near zero for NaCl toward 1 with increasing solute molecular weight, and the deduced $\mathcal{L}_D$ values map onto independently measured $kD_m$ permeation data, supporting the model and giving a molecular-weight cut-off around 1 kg/mol.

Load-bearing premise

The load-bearing requirement is that solute carried by the osmotic flow through the membrane is negligible relative to diffusive leakage, quantified by a Péclet number much smaller than one; the paper's own sucrose fit gives about 0.75, so for that solute the requirement is only marginally met.

Editorial extensions

If this is right

  • Membrane characterization can be done in situ, on membranes photo-crosslinked inside a chip, without clamping them into a separate diffusion or osmosis cell.
  • One exponential fit to $V_i(t)$ returns both $\sigma$ and $\mathcal{L}_D$; no separate solute-flux measurement is required, and the solute permeability can be converted to $kD_m$ through the membrane thickness.
  • The same decay rate governs solute accumulation, so the method self-checks against independent permeation measurements such as the methylene blue filling curves.
  • Applying the model to solutes of increasing molecular weight gives an estimate of the membrane's molecular-weight cut-off directly from the point where $\sigma(M_w) \simeq 1$.
  • If the dead-end channel is closed instead of open, the same physics predicts a hydrostatic-pressure relaxation with the same time constant, offering a pressure-based variant that needs no particle tracking.

Reading between the lines

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

  • The method should transfer to any membrane that can be integrated in a chip and to any solute with an osmotic signal, provided the Péclet number stays well below one; solutes near or above that limit would need the full nonlinear Kedem-Katchalsky equations.
  • Because the exponential fit couples $\sigma$ and $\mathcal{L}_D$, an independent measurement of $\mathcal{L}_D$ (for example from a no-flow permeation experiment) could be used to fix one parameter and let the fit isolate $\sigma$, tightening the molecular-weight cut-off estimate.
  • For solutes with small $\sigma$, such as NaCl, the initial osmotic flow is weak, so raising $C_0$ to amplify the signal also raises the Péclet number; this trade-off sets a practical window of solutes for which the linearized extraction is trustworthy.
  • The bracketing of $\sigma \to 0$ for NaCl and $\sigma \simeq 1$ for dextran suggests the cut-off scale could be compared with independent estimates of the hydrogel mesh size, for example from poro-elastic or swelling measurements.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper proposes a microfluidic configuration for measuring, in situ, the solute permeability L_D and reflection coefficient σ of an embedded membrane. In a dead-end microchannel separated from a solute reservoir by the membrane, forward osmosis drives a transient volume flux; the authors derive from the Kedem–Katchalsky equations that the entrance flux decays exponentially as Vi = σ V0 exp(−L_D t / w), so the initial amplitude and decay rate yield σ and L_D. They implement the method with PEGDA hydrogel membranes photo-crosslinked in a chip, measure L_p independently, and report σ and L_D for NaCl, sucrose, PEG-400, PEG-1000, and dextran, obtaining σ ≈ 0.8 for sucrose, σ near 1 for the larger solutes, and a molecular-weight cut-off near 1 kg/mol. They also compare the resulting kD_m values with independent no-flow permeation measurements.

Significance. The method addresses a real gap: in situ characterization of both σ and L_D for membranes integrated in microfluidic chips. The derivation from Kedem–Katchalsky is elementary and explicit, and the central exponential prediction is not obtained by fitting and then re-used; the extracted kD_m values are checked against independent no-flow permeation data, which is a strong validation strategy. The method is experimentally simple and likely to be useful for hydrogel and other integrated membranes. However, as detailed below, the paper's validity check for the linearization is not quantitatively correct for the sucrose case, and the magnitude of the resulting systematic error is not assessed; this does not invalidate the approach but requires re-analysis before publication.

major comments (2)
  1. [Section IV D and Eq. (3)] The condition for neglecting the advective term in Eq. (2) is not Pe = σL_p RTC_0/L_D ≪ 1 but rather (1−σ)σL_pRT⟨C⟩/L_D ≪ 1, i.e., O((1−σ)Pe) with ⟨C⟩ ≤ C_0. For the sucrose fit, σ ≈ 0.8 and Pe ≈ 0.75, so the actual advective-to-diffusive ratio is in the range 0.075–0.15, depending on the definition of ⟨C⟩. The statement in Sec. IV D that Pe = 0.75 'confirms' Eq. (3) is therefore not supported, and the systematic error in the exponential decay rate—and hence in the fitted L_D and σ—is left unquantified. The authors should either fit the full Kedem–Katchalsky solute flux including the advective term, or provide a quantitative estimate of the bias and state whether the reported values are corrected.
  2. [Section II A, Eqs. (1), (2), (6)] The model applies the linear Kedem–Katchalsky relations to the entire transient, including the initial state C=0, for which ∆C = C_0 and the stated condition ∆C ≪ ⟨C⟩ is strongly violated. The exponential solution (6)–(8) therefore relies on an unstated extrapolation of the constant-coefficient linear form to O(1) concentration ratios. The agreement of the osmotic kD_m values with independent no-flow measurements provides empirical support for this extrapolation, but the authors should state this limitation explicitly and, ideally, assess the sensitivity of σ and L_D to the treatment of ⟨C⟩.
minor comments (5)
  1. [Section II A, Eq. (5)] The overbar notation \bar{C} for the longitudinally averaged concentration is introduced but not used in the displayed equations; using \bar{C} in Eqs. (5)–(7) would clarify the distinction from the local field C(x,t).
  2. [Fig. 6] The text reports a power-law fit with α ≈ 2.3 but does not state whether the fit uses only the Nguyen data or all displayed points, nor its goodness-of-fit; please specify the fitted dataset and provide a quantitative measure of agreement.
  3. [Fig. 11b] No error bars or confidence intervals are shown for the reflection coefficient σ, although it is the primary quantity of interest in this figure; please add uncertainty estimates or explain why they are omitted.
  4. [Section II B] The Pedley condition (9) is stated for an ideal semi-permeable membrane with J_v = L_pRTC_0; for later use with partially reflecting solutes, the appropriate scale should be σL_pRTC_0, and this should be stated to avoid ambiguity.
  5. [Section IV C] The empirical fit (15) is described as differing from a virial expansion; please clarify that a and b are purely empirical parameters in the concentrated regime and are not intended to represent a virial expansion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transient-osmotic-flow result is derived from the Kedem-Katchalsky equations and checked against independent no-flow permeation measurements.

full rationale

Equation (8) is obtained by integrating the Kedem-Katchalsky eqs. (1)-(2) under the explicit linearization assumptions (3)-(4), not by assuming the exponential form and then re-labeling it as a prediction. The fitted quantities sigma and LD are the intended estimands of the inverse problem, and the measured decay curves are compared with the model rather than generated by the model itself. Independent support is provided by the no-flow permeation experiment with methylene blue (Fig. 7, yielding kDm approximately 1.5e-11 m^2/s) and by comparison with the prior permeation dataset of Nguyen et al., which is an external experimental dataset rather than a restatement of the osmotic-flow fit. The self-citations supply protocols, prior permeability values, and context, but the central derivation does not reduce to them. The statement in Sec. IV D that Pe about 0.75 'confirms' assumption (3) is a validity concern because 0.75 is not much smaller than 1, but this is a correctness issue, not a circularity: it does not make eqn (8) equivalent to its inputs by construction. No circular step of the enumerated kinds is exhibited.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced; the method is a measurement scheme using standard membrane transport coefficients. The only fitted outputs are the two transport coefficients sigma and LD, and the independent permeation cross-checks reduce the risk of circularity.

free parameters (2)
  • sigma (reflection coefficient) = Around 0.8 for sucrose; values shown in Fig. 11b
    Fitted as the normalized initial amplitude Vi(t=0)/V0 in eqn (8). This is the quantity the method aims to measure, not a hidden tuning parameter.
  • LD (solute permeability) = Around 0.25 um/s for sucrose; others from Fig. 11a fits
    Fitted from the exponential decay time of Vi(t) via LD = w/tau. Cross-checked against independent no-flow permeation measurements.
assumptions (6)
  • domain assumption Kedem-Katchalsky linear flux equations (1)-(2) with constant Lp, LD, sigma and van't Hoff osmotic pressure.
    Defines the meaning of sigma and LD; used throughout Sec. II and in the fits.
  • domain assumption Advective solute flux in eqn (2) is negligible, i.e. Pe = sigma Lp R T C0 / LD << 1 (eqn 3).
    Required for the linear solute balance leading to eqns (5)-(8); the sucrose fit gives Pe around 0.75, so this condition is only marginally satisfied.
  • domain assumption Membrane-limited solute transfer, R = w LD / Ds << 1 (eqn 4), giving uniform transverse concentration.
    Used to reduce transport to a 1D dead-end mass balance; reported R around 0.12 for sucrose and around 0.2 for methylene blue.
  • domain assumption No external concentration polarization in the reservoir, Pedley condition beta << 1, Qosm << Q, and delta << h, w.
    Justifies C(y=0+) = C0 along the membrane; experimental beta values are between 0.01 and 0.24.
  • domain assumption Forward osmosis dominates, delta P and delta Posm << delta Pi.
    Required so that eqn (1) reduces to Jv approximately Lp sigma delta Pi; checked for each solute in Sec. IV.
  • domain assumption Perfect dead-end channel with zero solute flux on all boundaries except the membrane.
    Used to derive eqn (5); the paper notes a small long-time leakage into the closed outlet dead volume (ratio 0.35), causing the observed discrepancy at long times.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Transient osmotic flows in a microfluidic channel: measurements of solute permeability and reflection coefficients of hydrogel membranes." pith.science (2026). https://pith.science/paper/A3JA5J6K

@misc{pith2026250606186,
  author       = {Pith},
  title        = {Pith review of: Transient osmotic flows in a microfluidic channel: measurements of solute permeability and reflection coefficients of hydrogel membranes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A3JA5J6K}},
  note         = {Machine review of arXiv:2506.06186}
}
abstract

We first highlight theoretically a microfluidic configuration that allows to measure two fundamental parameters describing mass transport through a membrane: the solute permeability coefficient $\mathcal{L}_D$, and the associated reflection coefficient $\sigma$. This configuration exploits the high confinement of microfluidic geometries to relate these two coefficients to the dynamics of a transient flow induced by forward osmosis through a membrane embedded in a chip. We then applied this methodology to hydrogel membranes photo-crosslinked in a microchannel with \textit{in situ} measurements of osmotically-induced flows. These experiments enable us to estimate $\mathcal{L}_D$ and $\sigma$ and their dependence on the molecular weight of the solute under consideration, ultimately leading to a precise estimate of the molecular weight cut-off of these hydrogel membranes.

Figures

Figures reproduced from arXiv: 2506.06186 by the authors.

Figure 1
Figure 1. FIG. 1. Geometry of the model. A dead-end microfluidic channel [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Sketch of the configuration studied by Pedley [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Microfluidic PEGDA chip with integrated hydrogel mem [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Membrane hydraulic permeability. (a) Local volume flux [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. Characterization of membrane hydraulic permeability [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Characterization of membrane solute permeability. (a) A [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Steady osmotically-induced flows. (a) Volume flux [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Osmotic flows induced by forward osmosis. A concentra [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Transient osmotically-induced flow. Entrance volume flux [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Transient osmotically-induced flows. (a) Normalized os [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages

  1. [1]

    author author R. W. \ Baker ,\ @noop title Membrane Technology and Applications \ ( publisher John Wiley & Sons, Ltd ,\ address Chichester, UK ,\ year 2012 ) NoStop

    work page 2012

  2. [2]

    author author M. A. \ Shannon , author P. W. \ Bohn , author M. Elimelech , author J. G. \ Georgiadis , author B. J. \ Marinas , \ and\ author A. M. \ Mayes ,\ title title Science and technology for water purification in the coming decades , \ @noop journal journal Nature \ volume 452 ,\ pages 301 ( year 2008 ) NoStop

    work page 2008

  3. [3]

    \ Wang , author D

    author author P.-C. \ Wang , author D. L. \ Devoe , \ and\ author C. S. \ Lee ,\ title title Integration of polymeric membranes with microfluidic networks for bioanalytical applications , \ @noop journal journal Electrophoresis \ volume 22 ,\ pages 3857 ( year 2001 ) NoStop

    work page 2001

  4. [4]

    Chen \ and\ author J

    author author X. Chen \ and\ author J. Shen ,\ title title Review of membranes in microfluidics , \ @noop journal journal J Chem Technol Biotechnol \ volume 92 ,\ pages 271 ( year 2017 ) NoStop

    work page 2017

  5. [5]

    , author R

    author author de Jong J. , author R. G. H. \ Lammertink , \ and\ author M. Wessling ,\ title title Membranes and microfluidics: a review , \ @noop journal journal Lab Chip \ volume 6 ,\ pages 1125 ( year 2006 ) NoStop

    work page 2006

  6. [6]

    Bacchin , author J

    author author P. Bacchin , author J. Leng , \ and\ author J. B. \ Salmon ,\ title title Microfluidic Evaporation, Pervaporation, and Osmosis: From Passive Pumping to Solute Concentration , \ @noop journal journal Chem. Rev. \ volume 122 ,\ pages 6938 ( year 2022 ) NoStop

    work page 2022

  7. [7]

    Kaufman , author R

    author author Y. Kaufman , author R. Kasher , author R. G. \ Lammertink , \ and\ author V. Freger ,\ title title Microfluidic NF/RO separation: Cell design, performance and application , \ @noop journal journal J. Membr. Sci. \ volume 396 ,\ pages 67 ( year 2012 ) NoStop

    work page 2012

  8. [8]

    Jajack , author I

    author author A. Jajack , author I. Stamper , author E. Gomez , author M. Brothers , author G. Begtrup , \ and\ author J. Heikenfeld ,\ title title Continuous, quantifiable, and simple osmotic preconcentration and sensing within microfluidic devices , \ @noop journal journal PloS ONE \ volume 14 ,\ pages e0210286 ( year 2019 ) NoStop

    work page 2019

Show all 51 references
  1. [9]

    Song , author A

    author author S. Song , author A. K. \ Singh , author T. J. \ Shepodd , \ and\ author B. J. \ Kirby ,\ title title Microchip dialysis of proteins using in situ photopatterned nanoporous polymer membranes , \ @noop journal journal Anal. Chem. \ volume 76 ,\ pages 2367 ( year 20...

    2004

  2. [10]

    Junius , author S

    author author N. Junius , author S. Jaho , author Y. Sallaz-Damaz , author F. Borel , author J.-B. \ Salmon , \ and\ author M. Budayova-Spano ,\ title title A microfluidic device for both on-chip dialysis protein crystallization and: In situ X-ray diffraction , \ @noop journal...

    2020

  3. [11]

    author author Y. C. \ Su \ and\ author L. Lin ,\ title title A water-powered micro drug delivery system , \ @noop journal journal J. Microelectromech. Syst. \ volume 13 ,\ pages 75 ( year 2004 ) NoStop

    2004

  4. [12]

    Shay , author M

    author author T. Shay , author M. D. \ Dickey , \ and\ author O. D. \ Velev ,\ title title Hydrogel-enabled osmotic pumping for microfluidics: Towards wearable human-device interfaces , \ @noop journal journal Lab Chip \ volume 17 ,\ pages 710 ( year 2017 ) NoStop

    2017

  5. [13]

    author author C. H. \ Chuang \ and\ author Y. Y. \ Chiang ,\ title title Bio-o-pump: a novel portable microfluidic device driven by osmotic pressure , \ @noop journal journal Sens. Actuators, B \ volume 284 ,\ pages 736 ( year 2019 ) NoStop

    2019

  6. [14]

    author author K. H. \ Jensen , author J. Lee , author T. Bohr , \ and\ author H. Bruus ,\ title title Osmotically driven flows in microchannels separated by a semipermeable membrane , \ @noop journal journal Lab Chip \ volume 9 ,\ pages 2093 ( year 2009 ) NoStop

    2009

  7. [15]

    Wang , author D

    author author J. Wang , author D. S. \ Dlamini , author A. K. \ Mishra , author M. T. M. \ Pendergast , author M. C. \ Wong , author B. B. \ Mamba , author V. Freger , author A. R. \ Verliefde , \ and\ author E. M. \ Hoek ,\ title title A critical review of transport through o...

    2014

  8. [16]

    author author V. H. \ Hegde , author M. F. \ Doherty , \ and\ author T. M. \ Squires ,\ title title A two-phase model that unifies and extends the classical models of membrane transport , \ @noop journal journal Science \ volume 377 ,\ pages 186 ( year 2022 ) NoStop

    2022

  9. [17]

    Kedem \ and\ author A

    author author O. Kedem \ and\ author A. Katchalsky ,\ title title Thermodynamic analysis of the permeability of biological membranes to non-electrolytes , \ @noop journal journal Biochim. Biophys. Acta \ volume 27 ,\ pages 229 ( year 1958 ) NoStop

    1958

  10. [18]

    Kedem \ and\ author A

    author author O. Kedem \ and\ author A. Katchalsky ,\ title title A physical interpretation of the phenomenological coefficients of membrane permeability , \ @noop journal journal J. Gen. Physiol. \ volume 45 ,\ pages 143 ( year 1961 ) NoStop

    1961

  11. [19]

    Marbach , author H

    author author S. Marbach , author H. Yoshida , \ and\ author L. Bocquet ,\ title title Osmotic and diffusio-osmotic flow generation at high solute concentration. I. Mechanical approaches , \ @noop journal journal J. Chem. Phys. \ volume 146 ,\ pages 194701 ( year 2017 ) NoStop

    2017

  12. [20]

    author author G. S. \ Manning ,\ title title Binary Diffusion and Bulk Flow through a Potential-Energy Profile: A Kinetic Basis for the Thermodynamic Equations of Flow through Membranes , \ @noop journal journal J. Chem. Phys. \ volume 49 ,\ pages 2668 ( year 1968 ) NoStop

    1968

  13. [21]

    Marbach \ and\ author L

    author author S. Marbach \ and\ author L. Bocquet ,\ title title Osmosis, from molecular insights to large-scale applications , \ @noop journal journal Chem. Soc. Rev. \ volume 48 ,\ pages 3102 ( year 2019 ) NoStop

    2019

  14. [22]

    author author J. S. \ Schultz , author R. Valentine , \ and\ author C. Y. \ Choi ,\ title title Reflection coefficients of homopore membranes: effect of molecular size and configuration. \ @noop journal journal J. Gen. Physiol. \ volume 73 ,\ pages 49 ( year 1979 ) NoStop

    1979

  15. [23]

    Dainty \ and\ author B

    author author J. Dainty \ and\ author B. Ginzburg ,\ title title The reflection of coefficient of plant cell membranes for certain solutes , \ @noop journal journal Biochim. Biophys. Acta \ volume 79 ,\ pages 129 ( year 1964 ) NoStop

    1964

  16. [24]

    Opong \ and\ author A

    author author W. Opong \ and\ author A. L. \ Zydney ,\ title title Effect of membrane structure and protein concentration on the osmotic reflection coefficient , \ @noop journal journal J. Membr. Sci. \ volume 72 ,\ pages 277 ( year 1992 ) NoStop

    1992

  17. [25]

    Matsuyama , author M

    author author H. Matsuyama , author M. Teramoto , \ and\ author H. Urano ,\ title title Analysis of solute diffusion in poly(vinyl alcohol) hydrogel membrane , \ @noop journal journal J. Membr. Sci. \ volume 126 ,\ pages 151 ( year 1997 ) NoStop

    1997

  18. [26]

    Li , author L

    author author L. Li , author L. Schulte , author L. D. \ Clausen , author K. M. \ Hansen , author G. E. \ Jonsson , \ and\ author S. Ndoni ,\ title title Gyroid Nanoporous Membranes with Tunable Permeability , \ @noop journal journal ACS Nano \ volume 5 ,\ pages 7754 ( year 20...

    2011

  19. [27]

    Pusch ,\ title title Examination methods for the physicochemical properties of synthetic membranes , \ @noop journal journal Pure & Appl

    author author W. Pusch ,\ title title Examination methods for the physicochemical properties of synthetic membranes , \ @noop journal journal Pure & Appl. Chem., \ volume 58 ,\ pages 1669 ( year 1986 ) NoStop

    1986

  20. [28]

    Kim , author J

    author author H. Kim , author J. Kim , author E.-G. \ Kim , author A. J. \ Heinz , author S. Kwon , \ and\ author H. Chun ,\ title title Optofluidic in situ maskless lithography of charge selective nanoporous hydrogel for DNA preconcentration , \ @noop journal journal Biomicro...

    2010

  21. [29]

    Kim \ and\ author T

    author author M. Kim \ and\ author T. Kim ,\ title title Integration of nanoporous membranes into microfluidic devices: Electrokinetic bio-sample pre-concentration , \ @noop journal journal Analyst \ volume 138 ,\ pages 6007 ( year 2013 ) NoStop

    2013

  22. [30]

    author author I. H. \ Shin , author K. J. \ Kim , author J. Kim , author H. C. \ Kim , \ and\ author H. Chun ,\ title title Cation-selective electropreconcentration , \ @noop journal journal Lab Chip \ volume 14 ,\ pages 1811 ( year 2014 ) NoStop

    2014

  23. [31]

    author author G. C. \ Randall , author K. M. \ Schultz , \ and\ author P. S. \ Doyle ,\ title title Methods to electrophoretically stretch DNA: microcontractions, gels, and hybrid gel-microcontraction devices , \ @noop journal journal Lab Chip \ volume 6 ,\ pages 516 ( year 20...

    2006

  24. [32]

    Gumuscu , author A

    author author B. Gumuscu , author A. S. \ Haase , author A. M. \ Benneker , author M. A. \ Hempenius , author A. van den Berg , author R. G. \ Lammertink , \ and\ author J. C. \ Eijkel ,\ title title Desalination by Electrodialysis Using a Stack of Patterned Ion-Selective Hydr...

    2016

  25. [33]

    author author J. S. \ Paustian , author R. N. \ Azevedo , author S. T. B. \ Lundin , author M. J. \ Gilkey , \ and\ author T. M. \ Squires ,\ title title Microfluidic microdialysis: spatiotemporal control over solution microenvironments using integrated hydrogel membrane micro...

    2013

  26. [34]

    author author J. S. \ Paustian , author C. D. \ Angulo , author R. Nery-Azevedo , author N. Shi , author A. I. \ Abdel-Fattah , \ and\ author T. M. \ Squires ,\ title title Direct measurements of colloidal solvophoresis under imposed solvent and solute gradients , \ @noop jour...

    2015

  27. [35]

    Gu , author V

    author author Y. Gu , author V. Hegde , \ and\ author K. J. M. \ Bishop ,\ title title Measurement and mitigation of free convection in microfluidic gradient generators , \ @noop journal journal Lab Chip \ volume 18 ,\ pages 3371 ( year 2018 ) NoStop

    2018

  28. [36]

    Decock , author M

    author author J. Decock , author M. Schlenk , \ and\ author J.-B. \ Salmon ,\ title title In-situ photo-patterning of pressure-resistant hydrogel membranes with controlled permeabilities in PEGDA microfluidic channels , \ @noop journal journal Lab Chip \ volume 18 ,\ pages 107...

    2018

  29. [37]

    author author H. T. \ Nguyen , author M. Massino , author C. Keita , \ and\ author J.-B. \ Salmon ,\ title title Microfluidic dialysis using photo-patterned hydrogel membranes in PDMS chips , \ @noop journal journal Lab Chip \ volume 20 ,\ pages 2383 ( year 2020 ) NoStop

    2020

  30. [38]

    Keita , author Y

    author author C. Keita , author Y. Hallez , \ and\ author J.-B. \ Salmon ,\ title title Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient , \ @noop journal journal Phys. Rev. E \ volume 104 ,\ p...

    2021

  31. [39]

    author author T. J. \ Pedley ,\ title title The interaction between stirring and osmosis. Part 2 , \ @noop journal journal J. Fluid Mech. \ volume 107 ,\ pages 281 ( year 1981 ) NoStop

    1981

  32. [40]

    Cath , author A

    author author T. Cath , author A. Childress , \ and\ author M. Elimelech ,\ title title Forward osmosis: Principles, applications, and recent developments , \ @noop journal journal J. Membr. Sci. \ volume 281 ,\ pages 70 ( year 2006 ) NoStop

    2006

  33. [41]

    Jiao , author C

    author author Y. Jiao , author C. Zhao , author Y. Kang , \ and\ author C. Yang ,\ title title Microfluidics-based fundamental characterization of external concentration polarization in forward osmosis , \ @noop journal journal Microfluid. Nanofluid. \ volume 23 ,\ pages 36 ( ...

    2019

  34. [42]

    The Matlab particle tracking code repository

    @noop note See https://site.physics.georgetown.edu/matlab/ for “The Matlab particle tracking code repository.” NoStop

  35. [43]

    Bruus ,\ @noop title Theoretical Microfluidics \ ( publisher Oxford Master Series in Physics ,\ year 2007 ) NoStop

    author author H. Bruus ,\ @noop title Theoretical Microfluidics \ ( publisher Oxford Master Series in Physics ,\ year 2007 ) NoStop

    2007

  36. [44]

    Kotsmar , author T

    author author C. Kotsmar , author T. Sells , author N. Taylor , author D. E. \ Liu , author J. M. \ Prausnitz , \ and\ author C. J. \ Radke ,\ title title Aqueous Solute Partitioning and Mesh Size in HEMA/MAA Hydrogels , \ @noop journal journal Macromolecules \ volume 45 ,\ pa...

    2012

  37. [45]

    author author A. A. \ Selifonov , author O. G. \ Shapoval , author A. N. \ Mikerov , \ and\ author V. V. \ Tuchin ,\ title title Determination of the Diffusion Coefficient of Methylene Blue Solutions in Dentin of a Human Tooth using Reflectance Spectroscopy and Their Antibacte...

    2019

  38. [46]

    author author C. E. \ Ioan , author T. Aberle , \ and\ author W. Burchard ,\ title title Structure Properties of Dextran. 2. Dilute Solution , \ @noop journal journal Macromolecules \ volume 33 ,\ pages 5730 ( year 2000 ) NoStop

    2000

  39. [47]

    Noda , author N

    author author I. Noda , author N. Kato , author T. Kitano , \ and\ author M. Nagasawa ,\ title title Thermodynamic properties of moderately concentrated solutions of linear polymers , \ @noop journal journal Macromolecules \ volume 14 ,\ pages 668 ( year 1981 ) NoStop

    1981

  40. [48]

    author author J. A. \ Cohen , author R. Podgornik , author P. L. \ Hansen , \ and\ author V. A. \ Parsegian ,\ title title A phenomenological one-parameter equation of state for osmotic pressures of PEG and other neutral flexible polymers in good solvents , \ @noop journal jou...

    2009

  41. [49]

    Comtet , author K

    author author J. Comtet , author K. H. \ Jensen , author R. Turgeon , author A. D. \ Stroock , \ and\ author A. E. \ Hosoi ,\ title title Passive phloem loading and long-distance transport in a synthetic tree-on-a-chip , \ @noop journal journal Nat. Plants \ volume 3 ,\ pages ...

    2017

  42. [50]

    Starzak \ and\ author S

    author author M. Starzak \ and\ author S. D. \ Peacock ,\ title title Water activity coefficient in aqueous solutions of sucrose -a comprehensive data analysis , \ @noop journal journal Zuckerind. \ volume 122 ,\ pages 380 ( year 1997 ) NoStop

    1997

  43. [51]

    author author K. H. \ Jensen , author K. Berg-S rensen , author H. Bruus , author N. M. \ Holbrook , author J. Liesche , author A. Schulz , author M. A. \ Zwieniecki , \ and\ author T. Bohr ,\ title title Sap flow and sugar transport in plants , \ @noop journal journal Rev. Mo...

    2016

Pith tools

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