Rivalry of diffusion, external field and gravity in micro-convection of magnetic colloids

Andrejs C\=ebers; Guntars Kitenbergs

REVIEW 4 major objections 5 minor 23 references

Rivalry of diffusion, external field and gravity in micro-convection of magnetic colloids

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Gravity, not the magnetic field, inflates micro-convection mixing rates

desk verdict Likely-important gravitational artifact claim, but the paper's own critical-field verification contradicts it and needs a real answer, not a parenthetical caveat. read the letter →

arxiv 1908.05011 v2 pith:UUUBFQWY submitted 2019-08-14 cond-mat.soft physics.flu-dyn

Guntars Kitenbergs , Andrejs Cēbers This is my paper · ORCID

classification cond-mat.softphysics.flu-dyn PACS 47.61.-k47.20.-k75.50.Mm

keywords colloidsmicro-convectiongravityeffectsmicrofluidicsmagneticnanoparticleseffectivediffusionRayleighnumber

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

The paper targets a discrepancy from earlier magnetic micro-convection experiments: the effective diffusion coefficient measured at a magnetic/non-magnetic fluid interface was two orders of magnitude larger than the true diffusion of the nanoparticles. The authors propose that the extra smearing is not a magnetic enhancement but a gravitational artifact: the magnetic fluid is slightly denser, and inside a thin channel this small density difference drives a slow convective roll that smears the interface in a way that looks diffusive. They build a model controlled by a single gravitational Rayleigh number, verify it numerically and experimentally across three channel thicknesses, and show that when this gravity-driven contribution is removed, the earlier Brinkman model of magnetic micro-convection still holds.

What carries the argument

The central object is the gravitational Rayleigh number $Ra_g = \Delta\rho\, g\, h^3 / (8 D \eta)$, built from the density mismatch $\Delta\rho$, channel thickness $h$, diffusion coefficient $D$, and viscosity $\eta$. The argument runs through a Stokes-flow model in the $x$–$z$ plane with a concentration-dependent gravity force and a convection–diffusion equation (Eqs. 2–3); solutions are thickness-averaged to mimic microscope images, and the slope of the concentration profile at the interface yields an effective diffusion coefficient via $1/\bigl(4\pi(\partial c/\partial x)^2\bigr) = D t$. This machinery converts a three-way rivalry (diffusion, magnetic field, gravity) into a single dimensionless number whose size decides whether gravity visibly smears the interface.

What would settle it

Run the same micro-convection experiment with the cell inverted, so the denser magnetic fluid sits above the less dense non-magnetic fluid; the gravity-driven convection should vanish and $D_{\mathrm{eff}}$ should drop to the true diffusion coefficient $D$. If $D_{\mathrm{eff}}$ remains inflated in that orientation, the smearing is not (only) gravitational. Alternatively, measure the concentration profile across the channel thickness with confocal microscopy and look directly for the denser fluid sliding underneath.

Watch

Extended reading notes

Core claim

The central claim is that the enhanced interface smearing observed in magnetic micro-convection experiments arises from gravity-induced convective motion inside the microfluidic channel, caused by the density difference between the miscible magnetic and non-magnetic fluids, and that this motion can be described by an effective diffusion coefficient. The paper establishes a linear law $D_{\mathrm{eff}}/D_0 = 0.053 (Ra_g - Ra_c^g)$ for gravitational Rayleigh numbers above a critical value $Ra_c^g = 105$, with pure diffusion for smaller $Ra_g$. This explains the previously unexplained inflated $D_{\mathrm{eff}}$ used in the earlier Brinkman-model comparison and leaves the magnetic micro-convection dynamics itself described by that model once gravity is excluded.

Load-bearing premise

The observations assume that Taylor-Aris (shear-flow) dispersion does not contribute in the imaging window near the channel inlet, so the entire extra smearing is credited to gravity.

Editorial extensions

If this is right

The inflated effective diffusion coefficients used in previous magnetic micro-convection analyses were gravitational artifacts; the true nanoparticle diffusion coefficient should be used in the Brinkman model.
The gravitational Rayleigh number $Ra_g$ provides a simple criterion ($Ra_g > 100$) for when gravity will noticeably affect interface smearing in any colloidal microfluidic system.
Reducing channel thickness suppresses gravity-driven smearing: at $h = 25\,\mu$m ($Ra_g \approx 110$) the effective diffusion is only about five times the true diffusion, compared to 670 times at $h = 130\,\mu$m.
Gravity-driven smearing is distinct from Taylor-Aris dispersion: the effective diffusion grows linearly with $Ra_g$, whereas Taylor-Aris grows with the square of the Péclet number.
The magnetic micro-convection finger size remains close to the cell thickness (with a slight deviation at 25 µm), and the critical field measurements are consistent with the Brinkman model once gravity is accounted for.

Reading between the lines

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

The same gravitational mechanism likely affects other colloidal microfluidic mixers where a density mismatch exists, even without a magnetic field, so reported mixing efficiencies should be checked for gravitational contributions.
A testable extension: measure $D_{\mathrm{eff}}$ at intermediate $Ra_g$ values more densely to confirm the linear law and locate the critical threshold, or use density-matched magnetic fluids to isolate magnetic micro-convection cleanly.
The similarity between gravity-driven smearing and pure diffusion suggests that any technique relying on interface width as a diffusion measurement in microchannels must control for this effect; the slope-vs-time relation alone cannot distinguish the two.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this paper has a genuine claim — the inflated Deff in earlier magnetic micro-convection work is probably a gravitational artifact — and it supports that with a self-contained model and experiments across three channel heights. But it almost undoes itself in the last verification step. The critical-field check using the gravitational Deff predicts Hc = 53 Oe for the 130 μm cell; the measured value is 19 Oe. Only the 50 μm cell matches. The authors' response — that the straight-finger threshold may not come from magnetic micro-convection — is a hand-wave that undermines the conclusion that 'residual magnetic micro-convection follows earlier predictions.' If the gravitational Deff is the right effective diffusivity for the magnetic branch, the model should work there too; if it isn't, the paper hasn't established the complete story.

What's good: the gravitational model is self-contained. It uses Stokes plus convection-diffusion with measured inputs D, Δρ, h, η; the numerical Deff(Rag) curve is compared against experiments, not fitted. The thickness scaling goes in the right direction: the 130 μm cell smears hundreds of microns, the 50 and 25 μm cells much less. The proposed criterion Rag < 100 staying safe, with Deff/D0 = 1, is simple and potentially useful for other colloidal systems. The Taylor-Aris discussion honestly acknowledges the effect exists.

Soft spots, in order:

1. Hc contradiction. This is not minor noise: a 2.8x discrepancy for the 130 μm cell and a 10 Oe miss for the 25 μm cell point in opposite directions. The paper needs a physical explanation, not a remark about finger curvature.

2. Taylor-Aris. The claim that TA dispersion 'does not affect' the early images needs a quantitative entry time or a calculation showing Pe^2 * t_entry is negligible. At Pe ≈ 2000, an unquantified assumption is dangerous.

3. Fit quality. The thinnest cell point (Deff/D0 = 5.2 at Rag = 110) sits about twenty times above the Eq. (4) prediction, yet the paper calls that 'reasonably good agreement.' The error bars appear only in Fig. 7; no numerical values or fit residuals are given in the text, so readers cannot judge the scatter.

Minor: the citation pattern leans heavily on the authors' own prior papers, but that is not a defect here because the new claim is exactly the re-interpretation of their own data.

For someone in magnetic microfluidics, this is a useful corrective and worth reading. For the broader community, the Rag criterion is a nice rule of thumb. It deserves serious peer review, but I would condition acceptance on resolving or reframing the Hc inconsistency and quantifying the Taylor-Aris window.

Referee Report

4 major / 5 minor

Summary. The paper addresses the long-standing puzzle that effective diffusion coefficients inferred from magnetic micro-convection experiments are orders of magnitude larger than the true nanoparticle diffusion coefficient. It proposes that this excess smearing is caused by gravity-driven convective motion due to a small density difference between the miscible magnetic and non-magnetic fluids, not by enhanced mixing from the magnetic field. The process is characterized by a gravitational Rayleigh number Rag, and numerical simulations of coupled Stokes and convection-diffusion equations are used to derive a linear relation Deff/D0 = 0.053(Rag - 105), where D0 is the true diffusivity. Experiments in microfluidic cells of thickness 130, 50, and 25 µm, with Rag values of approximately 13500, 900, and 110, respectively, show qualitatively reduced smearing for thinner cells. The paper also attempts to verify the pre-existing Brinkman model for magnetic micro-convection by comparing predicted and measured critical magnetic fields.

Significance. If the gravitational interpretation is correct, it resolves a long-standing inconsistency in the magnetic micro-convection literature and provides a practical quantitative criterion for when gravity effects must be considered in miscible colloidal microfluidics. The model is conceptually simple, and the three-thickness experimental design is a good strategy for testing the Rag scaling. The paper also clearly documents the numerical simulations. However, the quantitative verification is incomplete: the experimental Deff values do not match Eq. (4) for the two thinner cells, and the magnetic critical-field comparison fails for two of three thicknesses. The dismissal of Taylor-Aris dispersion is not backed by a quantitative estimate. These issues are load-bearing because the central claim—that the inflated Deff is a gravitational artifact—rests on the agreement between the numerical model and experiment.

major comments (4)

[§3, Eq. (4) and Fig. 7] The numerical relation Deff/D0 = 0.053(Rag - 105) does not provide quantitative agreement with the experimental data for the two thinner cells. For Rag = 110, Eq. (4) gives Deff/D0 = 0.265, while the measured value is 5.2; for Rag = 900, the relation gives 42, while the measured value is 15.2. Only the h = 130 µm point (Rag = 13500) agrees well (predicted 710, measured 670). The statement that there is "reasonably good agreement" is therefore not supported, and the central scaling claim is not quantitatively verified.
[§3, critical magnetic field comparison] Using the measured gravitational Deff in the critical-field formula yields Hc = 53 Oe for h = 130 µm and Hc = 24 Oe for h = 25 µm, while the measured values are 19 Oe and 34 Oe, respectively; only the h = 50 µm cell agrees (21 Oe vs 21 Oe). The explanations offered—that straight fingers in the 130 µm cell may not originate from magnetic micro-convection, and that the 25 µm discrepancy is due to flow fluctuations—are ad hoc and are not supported by independent evidence. This inconsistency is load-bearing because the paper's conclusion that "residual magnetic micro-convection follows earlier predictions" depends on this verification.
[§3, Taylor-Aris dispersion] The exclusion of Taylor-Aris (shear-flow) dispersion is not quantified. For the h = 25 µm cell with v ≈ 333 µm/s and D0 = 2.5 × 10^-7 cm^2/s, the Péclet number is Pe ≈ 330, giving D_TA/D0 ≈ 1 + Pe^2/210 ≈ 500, which is two orders of magnitude above the reported Deff/D0 = 5.2. Although the observation times (≈ 1–4 s) are shorter than the diffusive cross-channel time h^2/D0 ≈ 25 s, the pre-asymptotic shear contribution can still be significant and must be estimated quantitatively to rule out a flow-induced component in the observed thickness-dependent smearing.
[§3, extraction of Deff for the thinnest cell] The experimental data for the h = 25 µm cell are described as "much noisier," and the linear fit in Fig. 6(b) appears to rely on a small number of points. The resulting Deff/D0 = 5.2 is the strongest outlier from Eq. (4) and is a key datum for the paper's claim. Without an uncertainty estimate or repeat measurements, it is difficult to judge whether this point indicates a physical discrepancy or an experimental artifact.

minor comments (5)

[§2.2, Eqs. (2)–(3)] The model uses the Stokes equations with no-slip boundaries, but for a thin Hele-Shaw cell the depth-averaged Darcy/Brinkman model is more conventional; a sentence justifying the 2D Stokes representation would be useful.
[§2.4] The viscosity of the magnetic fluid is assumed equal to that of water despite a nanoparticle volume fraction of 2.8%; a measurement or a brief justification of this assumption would strengthen the quantitative claims.
[§3, critical-field formula] The expression Hc = sqrt(12 η D Ra_m^crit / (χ h)) appears dimensionally inconsistent as written; please check whether the denominator should be χ h^2 and clarify which diffusion coefficient (D or Deff) is inserted.
[§3, scaling discussion] The statement that "Rag Pe" is imprecise; it would be clearer to write the proportionality explicitly, e.g., Rag = (Δρ g h^2 / (8 η D)) · Pe, or to present the relation in terms of the gravity velocity scale.
[Figure 5 caption] The caption says "Numerical simulation results for (d) Rag = 15000, (e) Rag = 1000 and (f) Rag = 100" but the text in §3 refers to "Fig.5(a)-(c)" for experimental panels; please ensure the panel references are consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the gravitational Deff prediction is parameter-free, and the critical-field check uses independently measured Deff with openly reported mismatches.

full rationale

The central derivation is self-contained. The gravitational model in §2.2 (Eqs. 2–3) uses the Stokes and convection–diffusion equations with an explicit dimensionless scaling; the gravitational Rayleigh number Rag = Δρ g h^3/(8Dη) is fixed entirely by independently measured inputs (density difference, channel thickness, particle diffusion coefficient, viscosity). The effective diffusion coefficient is not an input: it is extracted from numerical concentration profiles via the same Fick-law relation (1) that defines the experimental Deff, and the numerical Deff(Rag) curve is compared with experimental points in Fig. 7. No parameter is fitted to the experimental Deff values, so the comparison is a genuine prediction. Eq. (4) is a fit to the numerical data, not to experiments, and the experimental points plotted against it remain an external check. The only subsequent use of measured Deff is the critical-field estimate Hc = sqrt(12ηD Ra_m^crit/(χh)) in §3. There Deff is used as the effective diffusivity, but it comes from the no-field experiments, not from the Hc measurements; moreover the paper openly reports disagreement for h = 130 μm and h = 25 μm, so it is a consistency test rather than a forced agreement. Self-citations to [7], [13], and [17] supply the model equations, the critical magnetic Rayleigh number Ra_m^crit ≈ 6, and additional numerical details; those results are stated in the paper and are parameter-free theoretical inputs, so they are independent support rather than circular. The exclusion of Taylor-Aris dispersion is asserted without a quantitative calculation, but that is an external experimental concern, not a by-construction reduction. No circular step found.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a standard Stokes-convection-diffusion model with no new physical entities. The quantitative predictions depend on two parameters (0.053 and Rag_c=105) that are fitted to the authors' own simulations, and on the unquantified assumption that shear-flow (Taylor-Aris) dispersion is absent from the measurement window. The main model inputs (D, Δρ, h, η) are measured independently, which keeps the circularity burden low for the primary claim.

free parameters (2)

Proportionality constant in Deff/D0 versus Rag relation = 0.053
Coefficient in Eq. (4), obtained by fitting numerical simulation results; no closed-form derivation is given in this paper.
Critical gravitational Rayleigh number Rag_c = 105
Threshold for the onset of convective enhancement, taken from the same numerical simulations; no independent derivation is provided.

assumptions (4)

domain assumption Fluid viscosities are equal and constant across the interface
Stated in Section 2.1; real magnetic and non-magnetic fluids may have slightly different viscosities that could modify the convection.
domain assumption Taylor-Aris dispersion is negligible in the early observation region
Asserted in Section 3 without a quantitative estimate of the dispersion coefficient or entry time; a competing flow-driven mechanism could contribute to the measured smearing.
domain assumption The quasi-2D Hele-Shaw model (Stokes plus convection-diffusion in the x-z plane) captures the concentration dynamics
The model neglects the axial flow structure and edge effects; it is validated only qualitatively against experiments.
domain assumption Image intensity maps linearly to concentration via the Beer-Lambert law after manual corrections
Section 2.4; the authors note in Section 3 that nonlinear camera response may cause apparent bumps in concentration profiles, so the mapping is not strictly verified.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Rivalry of diffusion, external field and gravity in micro-convection of magnetic colloids." pith.science (2026). https://pith.science/paper/UUUBFQWY

@misc{pith2026190805011,
  author       = {Pith},
  title        = {Pith review of: Rivalry of diffusion, external field and gravity in micro-convection of magnetic colloids},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UUUBFQWY}},
  note         = {Machine review of arXiv:1908.05011}
}

read the original abstract

Magnetic fields and magnetic materials have promising microfluidic applications. For example, magnetic micro-convection can enhance mixing considerably. However, previous studies have not explained increased effective diffusion during this phenomenon. Here we show that enhanced interface smearing comes from a gravity induced convective motion within a thin microfluidic channel, caused by a small density difference between miscible magnetic and non-magnetic fluids. This motion resembles diffusive behavior and can be described with an effective diffusion coefficient. We explain this with a theoretical model, based on a dimensionless gravitational Rayleigh number, and verify it by numerical simulations and experiments with different cell thicknesses. Results indicate the applicability and limitations for microfluidic applications of other colloidal systems. Residual magnetic micro-convection follows earlier predictions.

Figures

Figures reproduced from arXiv: 1908.05011 by the authors.

**Figure 1.** Characteristic fingering pattern of the magnetic micro–convection phenomena. Finger size approximately agrees with the cell thickness ℎ. (a) ≈ ℎ = 130 m, (b) ≈ ℎ = 50 m, (c) ℎ = 25 m and ≈ 35 m. netic fluid is below the less dense nonmagnetic fluid, one can observe a normal diffusion with a coefficient [14]. Here we start with revisiting a model for gravity induced concentration smearing on the interface, as propos… view at source ↗

**Figure 2.** Numerical simulation results of concentration field dynamics as viewed from a side of the cell ( − plane) for three different gravitational Rayleigh numbers 10000, 750 and 0.001. Decrease in terminates convective motion, leaving only diffusion. Red corresponds to initial magnetic fluid, while blue - non–magnetic fluid. fabricated in the Institute of Solid State Physics of the University of Latvia. PDMS (Sylgard 184… view at source ↗

**Figure 3.** Average concentration ̄ profiles at four different times for numerical simulation results of three different gravitational Rayleigh numbers (a) = 10000, (b) = 750 and (c) = 0.001 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Terminating gravity induced convective motion by reducing the channel thickness. (a)ℎ = 130 m, ≈ 440 m/s, (b)ℎ = 50 m, ≈ 333 m/s, (c)ℎ = 25 m, ≈ 333 m/s. Red arrows identify interface smearing. Qualitatively we observe that the gravity induced convection is terminated.…

**Figure 5.** Figure 5: Average concentration ̄(, ) dynamics. Experimental results for (a) ℎ = 130 m ( ≈ 13500), (b) ℎ = 50 m ( ≈ 900) and (c) ℎ = 25 m ( ≈ 110). Numerical simulation results for (d) = 15000, (e) = 1000 and (f) = 100. Dotted lines are fits of concentration gradient ∕ near = 0.…

**Figure 7.** Figure 7: Normalized effective diffusion coefficient eff∕0 as a function of gravitational Rayleigh number . Numerical simulation results displayed with blue circles. Green line shows normal diffusion eff∕0 = 1. Dashed red line is a linear fit. Black squares with errorbars are ex…

**Figure 6.** Figure 6: Diffusive behavior of interface smearing. Experimental results in (a) and (b): ◊ ℎ = 130 m ( ≈ 13500), ○ ℎ = 50 m ( ≈ 900) and △ ℎ = 25 m ( ≈ 110). Numerical results in (c) and (d): ⋆ = 15000, × = 3000, ▽ = 1000, + = 100, □ = 1 and ∗ = 0.001. Red lines indicate linea…

**Figure 8.** Figure 8: Dynamics of magnetic micro–convection in microfluidics with = 0.1 L/min at = 92 Oe for a cell of thickness ℎ = 50 m. Corresponding times are (a) 0 s, (b) 0.2 s, (c) 0.4 s, (d) 0.6 s far from the critical field can be seen. A clear fingering instability appears and de…

**Figure 9.** Figure 9: The critical magnetic field dependence on the flow rate for two different cell thicknesses ℎ = 50 m (diamonds) and ℎ = 25 m (circles). Red dashed lines are linear fits. ℎ = 130 m, = 21 Oe for ℎ = 50 m and = 24 Oe for ℎ = 25 m. Experimental measurements agree well only…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

E. K. Sackmann, A. L. Fulton, D. J. Beebe, The present and future role of microﬂuidics in biomedical research, Nature 507 (2014) 181 – 189. Review Article

work page 2014
[2]

X.Chen,L.Zhang, Areviewonmicromixersactuatedwithmagnetic nanomaterials, Microchimica Acta 184 (2017) 3639 – 3649

work page 2017
[3]

Boroun, F

S. Boroun, F. Larachi, Role of magnetic nanoparticles in mixing, transport phenomena and reaction engineering – challenges and op- portunities, Current Opinion in Chemical Engineering 13 (2016) 91 – 99. Energy and Environmental Engineering / Reaction engineering and catalysis

work page 2016
[4]

R.-J.Yang,H.-H.Hou,Y.-N.Wang,L.-M.Fu,Micro-magnetoﬂuidics in microﬂuidic systems: A review, Sensors and Actuators B: Chemi- cal 224 (2016) 1 – 15

work page 2016
[5]

M. M. Maiorov, A. C¯ebers, Magnetic microconvection on the diﬀu- sion front of ferroparticles, Magnetohydrodynamics 19 (1983) 376 – 380

work page 1983
[6]

C.Derec, P.Boltenhagen, S.Neveu, J.-C.Bacri, Magneticinstability betweenmiscibleﬂuidsinaHele-Shawcell, Magnetohydrodynamics 44 (2008) 135 – 142

work page 2008
[7]

K. ¯Erglis,A.Tatulcenkov,G.Kitenbergs,O.Petrichenko,F.G.Ergin, B.B.Watz,A.C ¯ebers, Magneticﬁelddrivenmicro-convectioninthe hele-shaw cell, Journal of Fluid Mechanics 714 (2013) 612 – 633

work page 2013
[8]

Wen, C.-Y

C.-Y. Wen, C.-Y. Chen, D.-C. Kuan, Experimental studies of labyrinthine instabilities of miscible ferroﬂuids in a hele-shaw cell, Physics of Fluids 19 (2007) 084101

work page 2007

Show all 23 references

[9]

H.Li,C.-Y.Kao,C.-Y.Wen, Labyrinthineandsecondarywaveinsta- bilities of a miscible magnetic ﬂuid drop in a hele-shaw cell, Journal of Fluid Mechanics 836 (2018) 374 – 396

2018
[10]

Chen, W.-K

C.-Y. Chen, W.-K. Tsai, J. A. Miranda, Hybrid ferrohydrodynamic instability: Coexisting peak and labyrinthine patterns, Phys. Rev. E 77 (2008) 056306

2008
[11]

Kitenbergs, K.¯Erglis, R

G. Kitenbergs, K.¯Erglis, R. Perzynski, A. C¯ebers, Magnetic particle mixing with magnetic micro-convection for microﬂuidics, Journal of Magnetism and Magnetic Materials 380 (2015) 227 – 230

2015
[12]

J. G. Lee, V. Porter, W. A. Shelton, B. Bharti, Magnetic ﬁeld-driven convection for directed surface patterning of colloids, Langmuir 34 (2018) 15416 – 15424

2018
[13]

C¯ebers, Magnetic ﬁeld driven micro-convection in the hele- shaw cell: the Brinkman model and its comparison with experiment, Journal of Fluid Mechanics 774 (2015) 170 – 191

G.Kitenbergs,A.Tatul ,/uni010Denkovs,K.¯Erglis,O.Petrichenko,R.Perzyn- ski, A. C¯ebers, Magnetic ﬁeld driven micro-convection in the hele- shaw cell: the Brinkman model and its comparison with experiment, Journal of Fluid Mechanics 774 (2015) 170 – 191

2015
[14]

G.Kitenbergs,A.Tatul ,/uni010Denkovs,L.Puk,ina,A.C ¯ebers, Gravityeﬀects onmixingwithmagneticmicro-convectioninmicroﬂuidics, TheEu- ropean Physical Journal E 41 (2018) 138

2018
[15]

D. C. Duﬀy, J. C. McDonald, O. J. A. Schueller, G. M. Whitesides, Rapidprototypingofmicroﬂuidicsystemsinpoly(dimethylsiloxane), Analytical Chemistry 70 (1998) 4974–4984

1998
[16]

F.G.Ergin,G.Kitenbergs,A.C ¯ebers, Revisitingvelocity,concentra- tion and interface measurements in a magnetic micromixer, in: C. J. Kähler, R. Hain, S. Scharnowski, T. Fuchs (Eds.), Proceedings of the 13th International Symposium on Particle Image Velocimetry, 2019, pp. 1119–...

2019
[17]

Kitenbergs, Hydrodynamic instabilities in microﬂuidic magnetic ﬂuid ﬂows, Ph.D

G. Kitenbergs, Hydrodynamic instabilities in microﬂuidic magnetic ﬂuid ﬂows, Ph.D. thesis, University of Pierre and Marie Curie and University of Latvia, Paris, France and Riga, Latvia, 2015

2015
[18]

S. K. Yoon, M. Mitchell, E. R. Choban, P. J. A. Kenis, Gravity- induced reorientation of the interface between two liquids of diﬀer- ent densities ﬂowing laminarly through a microchannel, Lab Chip 5 (2005) 1259–1263. G.Kitenbergs et al.: Preprint submitted to Elsevier Page 7 o...

2005
[19]

M. A. Bennet, Multi-parameter quantitative mapping of microﬂuidic devices, Ph.D. thesis, University of Edinburgh, Edinburgh, United Kingdom, 2011

2011
[20]

Yamaguchi, T

Y. Yamaguchi, T. Honda, M. Briones, K. Yamashita, M. Miyazaki, H. Nakamura, H. Maeda, Inﬂuence of gravity on two-layer lami- nar ﬂow in a microchannel, Chemical Engineering & Technology 30 (2007) 379–382

2007
[21]

G. I. Taylor, Dispersion of soluble matter in solvent ﬂowing slowly through a tube, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 219 (1953) 186–203

1953
[22]

Series A

R.Aris, Onthedispersionofasolutebydiﬀusion,convectionandex- changebetweenphases, ProceedingsoftheRoyalSocietyofLondon. Series A. Mathematical and Physical Sciences 252 (1959) 538–550

1959
[23]

taylor dispersion of a so- luteinamicroﬂuidicchannel

K. D. Dorfman, H. Brenner, Comment on “taylor dispersion of a so- luteinamicroﬂuidicchannel”[j.appl.phys.89,4667(2001)],Journal of Applied Physics 90 (2001) 6553–6554. G.Kitenbergs et al.: Preprint submitted to Elsevier Page 8 of 8

2001

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

E. K. Sackmann, A. L. Fulton, D. J. Beebe, The present and future role of microﬂuidics in biomedical research, Nature 507 (2014) 181 – 189. Review Article

work page 2014

[2] [2]

X.Chen,L.Zhang, Areviewonmicromixersactuatedwithmagnetic nanomaterials, Microchimica Acta 184 (2017) 3639 – 3649

work page 2017

[3] [3]

Boroun, F

S. Boroun, F. Larachi, Role of magnetic nanoparticles in mixing, transport phenomena and reaction engineering – challenges and op- portunities, Current Opinion in Chemical Engineering 13 (2016) 91 – 99. Energy and Environmental Engineering / Reaction engineering and catalysis

work page 2016

[4] [4]

R.-J.Yang,H.-H.Hou,Y.-N.Wang,L.-M.Fu,Micro-magnetoﬂuidics in microﬂuidic systems: A review, Sensors and Actuators B: Chemi- cal 224 (2016) 1 – 15

work page 2016

[5] [5]

M. M. Maiorov, A. C¯ebers, Magnetic microconvection on the diﬀu- sion front of ferroparticles, Magnetohydrodynamics 19 (1983) 376 – 380

work page 1983

[6] [6]

C.Derec, P.Boltenhagen, S.Neveu, J.-C.Bacri, Magneticinstability betweenmiscibleﬂuidsinaHele-Shawcell, Magnetohydrodynamics 44 (2008) 135 – 142

work page 2008

[7] [7]

K. ¯Erglis,A.Tatulcenkov,G.Kitenbergs,O.Petrichenko,F.G.Ergin, B.B.Watz,A.C ¯ebers, Magneticﬁelddrivenmicro-convectioninthe hele-shaw cell, Journal of Fluid Mechanics 714 (2013) 612 – 633

work page 2013

[8] [8]

Wen, C.-Y

C.-Y. Wen, C.-Y. Chen, D.-C. Kuan, Experimental studies of labyrinthine instabilities of miscible ferroﬂuids in a hele-shaw cell, Physics of Fluids 19 (2007) 084101

work page 2007