REVIEW 5 major objections 6 minor 42 references
Confinement-induced evolution and breakup of viscoelastic filaments in microfluidic coflows
T0 review · 5 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash
Pith's one-line read In a confined microfluidic coflow, wall-induced shear—not just elastocapillary thinning—sets where and when a viscoelastic filament breaks.
desk verdict A careful experimental study with a valuable regime map and particle-tracking data, but the central wall-shear-localization claim is not uniquely established because the paper never reports the axial filament-radius profile and several 'predictive' scalings are fitted to the same data. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the wall-shear strain-rate estimate $\dot{\gamma}\sim u_d/e$, with the mean wall clearance taken as $\bar e\approx e_2/4$ from the droplet-migration model, giving $\dot{\gamma}\approx 4u_d/e_2$. This single scaling feeds every downstream prediction: it sets the elastic stress in the critical-thickness balance $2\mu_p\lambda_r\dot{\gamma}^2\approx 2\gamma/h_{\mathrm{cr}}$, enters the filament-length scaling $\bar l_f = 1.5(h_m/\bar e)(\mu_{2,\dot{\gamma}}/\mu_0)\,Ec\,(\beta Ca_1 + Ca_2)^2$, and defines the effective viscosity $\mu_{\mathrm{eff}}=2\mu_p\lambda_r\dot{\gamma}$ used in the Rayleigh–Plateau growth rate and wavelength. The companion piece is the migration model of §3.2.2, which converts droplet lift forces into the filament eccentricity $e_2$; without that eccentricity the wall shear is undetermined. Together these two elements carry the paper's claim that confinement supplies the strain rate that classical elastocapillary theory leaves unspecified.
What would settle it
Measure the velocity field in the continuous phase next to an inclined filament with micro-particle-image-velocimetry and check whether the interfacial shear rate follows $4u_d/e_2$ across different channel depths and flow rates; alternatively, repeat the breakup experiment in channels of different height-to-width ratio at the same $Ca_1$, $Ca_2$, and $Ec$—if the critical filament thickness and first-bead location do not shift with the wall gap, the wall-shear scaling is not the controlling mechanism.
Extended reading notes
Core claim
The central claim is that confined viscoelastic filament breakup is governed by a coupled wall-shear–elasticity mechanism rather than by classical elastocapillary thinning alone. After pinch-off, the primary droplet migrates toward the channel centre, leaving an inclined filament whose clearance from the wall varies along its length; the surrounding continuous phase therefore exerts a spatially non-uniform shear that stretches the filament and creates axial velocity differences inside it. The first bead-on-a-string perturbation consistently appears at the point of minimum wall clearance, where the interfacial shear stress is maximal. The authors close the argument by replacing the zero-shear or extensional viscosity in the classical viscous Rayleigh–Plateau formulas with an effective viscosity $\mu_{\mathrm{eff}}=2\mu_p\lambda_r\dot{\gamma}$ derived from the Oldroyd-B normal stress, and obtain instability wavelengths and growth rates in agreement with experiments to the correct order of magnitude. The claim is that the entire sequence—filament stretching, critical thickness, maximum length, instability site, and secondary droplet distribution—follows from one force-balance framework in which wall-induced shear supplies the strain rate.
Load-bearing premise
The whole quantitative structure depends on the assumption that the strain rate stretching the filament equals roughly four times the droplet velocity divided by the filament's distance from the wall, together with empirical migration parameters ($A\approx 2.5$, an integration time of $1.5\lambda_r$, and a fitted constant $C_c$); if the linear-gap shear profile or those fitted coefficients are wrong, the predicted thicknesses and lengths shift by large factors even if the qualitative wall-shear story survives.
Editorial extensions
If this is right
- Elasticity is a late-stage actor: the stable-coflow-to-droplet boundary collapses to $Ca_1\approx 2.3\,Ca_{2,\dot{\gamma}}$ for all fluids, so the onset of droplet formation can be predicted without rheological fitting.
- Once a filament exists, polymer relaxation time controls its life: longer $\lambda_r$ (higher $Ec$) delays capillary breakup, lengthens filaments, and shifts the squeezing–dripping–jetting boundaries.
- Where a filament breaks is set by geometry, not just fluid properties: the first bead-on-a-string always nucleates at the point of minimum wall clearance and maximum shear, so wall position is a deterministic variable.
- A modified Rayleigh–Plateau analysis with $\mu_{\mathrm{eff}}=2\mu_p\lambda_r\dot{\gamma}$ predicts instability wavelength and growth rate to the correct order of magnitude, bridging classical capillary instability and confined viscoelastic breakup.
- Secondary droplet yield and uniformity can be designed: increasing $Ca_1$ and $Ec$ gives more, smaller, more uniform satellite droplets, with lower $Ca_2$ and moderate $Ca_1$ yielding nearly monodisperse populations.
Reading between the lines
- If wall shear is the true strain-rate source, then channel geometry—height, width, aspect ratio, and wall slip—becomes a first-order control on breakup, so varying $h/W$ at fixed $Ca$ and $Ec$ is a direct test that could extend the regime maps into a design chart.
- The migration model's empirical constants ($A=2.5$, an integration time of $1.5\lambda_r$, and the fitted $C_c$) hint that a fully predictive droplet-lift theory for confined viscoelastic drops would replace the fits and strengthen the quantitative claims; until then, the eccentricity prediction carries the least ab initio support.
- Because the effective viscosity is built from $\lambda_r\dot{\gamma}$, the same framework might be inverted to extract relaxation times from confined breakup images—an in-situ extensional rheometer for microchannels—using the already-demonstrated exponential-thinning fits.
- The universal transition criterion $Ca_1\approx2.3\,Ca_{2,\dot{\gamma}}$ suggests the onset of breakup may be elasticity-independent for other shear-thinning polymer pairs; testing with different chemistries at matched $Ec$ would show how general the collapse is.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reports an experimental study of the breakup of shear-thinning viscoelastic filaments formed in a confined microfluidic coflow of an aqueous polymer solution and an immiscible Newtonian oil. Four flow regimes (stable coflow, squeezing, dripping, jetting) are mapped in terms of the capillary numbers and an elastocapillary number. The authors propose scaling laws for the primary droplet diameter, critical filament thickness at instability onset, maximum filament length, and jetting length, based on force balances that include wall-induced shear. Particle tracking shows axial velocity gradients along inclined filaments, and the first bead-on-a-string perturbation is reported to nucleate at the location of maximum wall-induced shear. A Rayleigh–Plateau analysis with an effective viscosity is used to predict instability wavelengths and growth rates.
Significance. If the proposed wall-shear–elasticity mechanism is substantiated, the paper would extend classical elastocapillary thinning theory to confined microfluidic flows and provide practically useful scaling relations for droplet and satellite-droplet sizes. The experimental strengths are the systematic variation of polymer relaxation time at nearly constant zero-shear viscosity, the extensive high-speed imaging and particle-tracking data, and the explicit attempt to connect filament geometry to instability location. However, the quantitative framework currently depends on several empirical or fitted inputs, and the central localization claim—that the first bead forms at the maximum wall-induced shear—is not uniquely supported without a measurement of the axial filament-radius profile. The stress-test concern about the confound between wall proximity, minimum filament radius, and the upstream neck therefore lands and needs to be addressed experimentally.
major comments (5)
- [Sec. 3.4 and Fig. 9] The central claim that the first bead-on-a-string perturbation nucleates at the location of maximum wall-induced shear (Fig. 9, y*=1) is not uniquely supported by the data presented. In the coflow geometry, the point of minimum wall clearance is also the part of the filament closest to the channel wall and is adjacent to the upstream neck where the filament connects to the reservoir; both capillary end-pinching and the paper's own critical-thickness criterion, Eq. (3.22), predict that breakup begins where the local filament radius is smallest. The paper does not report the axial filament-radius profile h_f(x) at the onset of instability, nor does it compare first-bead positions with the locus of minimum radius or with the upstream neck. The tracer-velocity data in Sec. 3.4 demonstrate axial velocity variation, but mass conservation in a thread of nonuniform radius requires such variation regardless of wall shear. The shear-stress distributions in Fig. 9(b) are model outputs based on gamma_dot ~ u_d/e, whose validity is the point under test. To support the mechanistic claim, please measure h_f(x) and compare the first-bead location with the locus of minimum filament radius, or design a condition in which the maximum-shear location is spatially separated from the minimum-radius/neck location.
- [Sec. 3.2.1, Eq. (3.12)] The simplified droplet-size expression Eq. (3.12) is obtained by inserting the fitted power laws bbar=0.3 Ca1^-0.225 and (1-bbar)=1.6 Ca1^0.47, which are themselves fitted from the same experimental data shown in Fig. 3, into Eq. (3.11). The 'prediction' therefore reduces, by construction, to these fits, and the agreement in Fig. 3(e) is partly in-sample. The predictive claim would be considerably strengthened by validating Eq. (3.12) against a subset of data not used for the fits, by reporting the uncertainty propagated from the fitted coefficients, or by testing the relation against an independent data set.
- [Sec. 3.2.2, Eqs. (3.21) and (3.24)] Equation (3.24) for the maximum filament length depends on the filament eccentricity e2, which is obtained from the migration model of Sec. 3.2.2. That model relies on the empirical coefficient A=2.5 in Eq. (3.18), the assumed integration time of 1.5 lambda_r, and the empirical constant C_c in Eq. (3.21). The agreement in Fig. 6(c) is therefore not an independent test of the wall-shear scaling: if the linear-gap shear profile or the migration prediction for e2 is incorrect, the predicted filament length shifts by factors that are not quantified. Please provide a sensitivity analysis of l_f with respect to e2 and A, or measure e2 directly and compare with the model prediction.
- [Sec. 3.3, Eq. (3.27)] The jetting time scale T_c = t_c Wi/Ca2_gamma is introduced in Sec. 3.3 without derivation or physical justification beyond a statement that elasticity increases the characteristic time 'approximately in proportion to Wi/Ca2_gamma'. Since l_J,Th in Eq. (3.27) is linear in this assumed time scale, the good agreement in Fig. 7(d) is largely a test of a fitted proportionality constant. Please derive this scaling from the disturbance growth rate or from an independent argument, and assess its sensitivity to the assumed Wi dependence.
- [Appendix E and Table 4] Appendix E reports that the apparent polymer relaxation time extracted from filament-thinning data depends on the capillary-number ratio, with variations of order 25-35% (e.g., F3: 0.008 s at Ca_r=0.35 versus 0.006 s at Ca_r=0.46; F5: 0.038 s versus 0.033 s). This is in tension with the use of a fixed lambda_r as a material property in the elastocapillary number Ec and in the scaling laws of Secs. 3.2.3 and 3.2.4. If the apparent relaxation time is flow-dependent, the collapse of the regime maps and the predictions of Eqs. (3.22)-(3.24) are not uniquely determined. Please clarify whether the lambda_r values used in the scaling analyses are the constant material values from Table 1 or the flow-dependent apparent values, and discuss the impact of the observed variation on the reported predictions.
minor comments (6)
- [General] Some figure references appear mismatched: the fitted power laws bbar and (1-bbar) are said to be from Fig. 3(d), but the relevant panel appears to be Fig. 3(b); the Supplementary section S1 refers to 'figure 2(e-g)' when describing main-text panels.
- [Appendix C] The transition line is written as 'Ca_1 approximately 2.3, Ca_{2,gamma_dot}' with a misplaced comma; it should read Ca_1 approximately 2.3 times Ca_{2,gamma_dot}.
- [Table 4] Table 4 lists the PEO 4 MDa concentration as 0.95 wt.%, while Table 1 and the main text give 0.97 wt.%; please harmonize these values.
- [Figure 10 caption] The caption gives Ec=10.77 for the highly elastic fluid, whereas Table 1 and the text use Ec=10.87 for fluid F5; correct the typo.
- [Eq. (3.13)] The reduced volume v is defined as 'the ratio of the enclosed volume to the droplet surface area', which has dimensions of length; the standard definition of reduced volume is the ratio of the droplet volume to the volume of a sphere with the same surface area, which is dimensionless.
- [Sec. 3.2.4] The expression t_ve = 1.5 h_m (mu_{2,gamma_dot}/gamma)(1+Wi_c) introduces a prefactor 1.5 whose origin is not explained; a one-sentence justification would improve transparency.
Circularity Check
Several central predictions reduce to fitted inputs: the l_f/h_cr loop is closed through C_c and e2, the jetting length inserts an empirical Wi/Ca2 factor, and the first-bead comparison is normalized by the same wall-clearance model that defines τmax.
-
fitted input called prediction
[§3.2.2–§3.2.4, Eqs. (3.20)–(3.24)]
"Using the scaling for the maximum stable filament length derived later in §3.2.4, l_f≈1.5 h_m W / ar e * μ2γdot/μ0 Ec(βCa1+Ca2)^2 ... and assuming that the centroid offset varies inversely with both filament length and filament eccentricity, the offset is obtained as Δy_c=C_c[1.5h_mWμ2,γdot/μ0 Ec(βCa1+Ca2)^2]^{-1/2} ... where C_c is an empirical constant determined from the experiments."
Equation (3.21) defines Δy_c, and hence e2=y_n−Δy_c, using the l_f scaling of Eq. (3.20) that Eq. (3.24) is later claimed to predict. C_c is fitted to the same experiments, and the 1.5λ_r integration time is also taken from the observed migration. This e2 then enters the wall-shear strain rate γdot≈4u_d/e2, which drives the critical-thickness balance (3.22) and the filament-length result (3.23)–(3.24). The predicted h_cr and l_f are therefore re-solutions of a closed fitting loop rather than independent derivations.
-
fitted input called prediction
[§3.3, Eq. (3.27), Fig. 7(d)]
"The present experiments demonstrate that elasticity increases this characteristic time approximately in proportion to Wi/Ca2,γdot, giving T_c = t_c Wi/Ca2,γdot. Since disturbances are convected downstream with the mean jet velocity, u_2=4Q_2/πW_J^2, the critical thread length becomes l_J,Th. ≈ ... (3.27)."
The factor Wi/Ca2,γdot is asserted directly from the same experiments whose thread length Eq. (3.27) is then compared with in Fig. 7(d). No independent force balance or stability calculation produces this factor; substituting T_c into l_J=u_2T_c is algebraic. The comparison therefore demonstrates consistency with an assumed empirical scaling rather than a predictive test.
2 more flagged steps
-
fitted input called prediction
[§3.3, Eqs. (3.25)–(3.26), Fig. 7(c) inset]
"Combining the experimentally fitted correlation, (3.25), with (3.26) yields d_J/W_J ≈2.9. This value is in excellent agreement with the direct experimental measurements shown in the inset of figure 7(𝑐)."
Equation (3.25) is W_J/W≈√(Q2/2Q1) and Eq. (3.26) is d_J/W≈2.9√(Q2/2Q1); both are fitted to the same jetting data. Their ratio is 2.9 identically, so the claimed agreement with the measured d_J/W_J is a restatement of the fitted coefficient, not an independent prediction.
-
self definitional
[§3.4, Fig. 9 and accompanying text]
"The bead locations are represented by their normalised wall-normal positions, y∗ = y/y_min, where y_min denotes the minimum wall clearance. For every operating condition investigated, the first bead forms at y∗=1, corresponding precisely to the point of minimum wall clearance. Furthermore, the vertical reference lines intersect the corresponding shear-stress distributions at τ∗ =1, demonstrating that bead nucleation always coincides with the location of maximum interfacial shear."
The shear-stress distributions are model outputs of the same wall-shear scaling γdot∼u_d/e, whose maximum by construction lies at the minimum wall clearance. Since bead position is normalized by y_min, ‘first bead at y*=1’ is equivalent to ‘first bead where the model puts τ*=1’. The comparison cannot distinguish wall-shear localization from capillary end-pinching or from the paper’s own critical-thickness criterion (3.22), and the axial filament-radius profile h_f(x) is not reported, so the unique attribution to wall shear is not established.
full rationale
The strongest independent content is experimental: regime maps, exponential filament-thinning data, particle-velocity gradients, and the order-of-magnitude Rayleigh–Plateau comparison. However, several of the paper’s ‘predictive’ scalings are not independent tests. The critical-thickness and maximum-filament-length predictions both depend on e2, which comes from Eq. (3.21) built on the very l_f scaling being predicted and on an empirical constant C_c, forming a closed fitting loop. The jetting-length relation inserts an empirical Wi/Ca2 factor asserted from the same data, and the d_J/W_J≈2.9 comparison is a tautology of two fitted correlations. The first-bead localization evidence is confounded: bead positions are normalized by y_min while the shear maximum is defined by the same wall-clearance model, so capillary end-pinching or the thinnest-filament criterion cannot be excluded. These are partial circularities rather than a total collapse of the paper: the empirical observations remain valid, and no load-bearing self-citation chain forces the result. Score 6 reflects that central quantitative claims reduce, in part by construction, to fitted inputs.
Assumptions & free parameters
free parameters (10)
- Droplet-width power law bbar=0.3Ca1^-0.225 =
0.3, -0.225
- Gap power law (1-bbar)=1.6Ca1^0.47 =
1.6, 0.47
- Neck-width correlation Wn/W=(1+3.6(phi*beta)^0.4)^-1 =
3.6, 0.4
- Migration saturation coefficient A in Vm=Vm0[(y/W)-A(y/W)^2] =
2.5
- Migration integration time 1.5 lambda_r =
1.5 lambda_r
- Filament-offset constant C_c in Eq (3.21) =
not reported
- Jetting time-scale proportionality T_c=t_c Wi/Ca2_gamma =
proportionality constant not reported
- Strain-rate prefactor 4 in gamma_dot ~ 4u_d/e2 =
4
- Thinning-time prefactor 1.5 in t_ve =
1.5
- Carreau-Yasuda parameters k1, a1, a2, mu_inf per fluid =
Table 1
assumptions (7)
- domain assumption Single-mode Oldroyd-B constitutive model with sigma_zz ~ 2 mu_p lambda_r gamma_dot^2 and neglected transverse normal stresses
- domain assumption Velocity varies linearly between the channel wall and the filament, giving gamma_dot ~ u_d/e with ebar ~ e2/4
- domain assumption Migration velocity model from Hazra et al. (2019) with f2 ~ (1/beta)^0.33 Wi_D
- domain assumption Classical Weber/Chandrasekhar Rayleigh-Plateau dispersion relations apply to viscoelastic filaments when viscosity is replaced by the effective viscosity mu_eff
- domain assumption Disturbance amplitude grows exponentially with a constant growth rate, giving d_f = d_0 exp(omega Delta t)
- domain assumption Acceleration term in the droplet momentum balance is negligible, with momentum change dominated by mass inflow
- domain assumption Clasen et al. exponential thinning relation (Eq E1) holds for t > lambda_r in the confined coflow
Cite this review
Pith. "Pith review of Confinement-induced evolution and breakup of viscoelastic filaments in microfluidic coflows." pith.science (2026). https://pith.science/paper/22PDW62V
@misc{pith2026260805343,
author = {Pith},
title = {Pith review of: Confinement-induced evolution and breakup of viscoelastic filaments in microfluidic coflows},
year = {2026},
howpublished = {\url{https://pith.science/paper/22PDW62V}},
note = {Machine review of arXiv:2608.05343}
}
read the original abstract
Viscoelastic filament thinning is classically described by elastocapillary dynamics in extensional flows, yet in confined microchannels the combined effects of wall-induced shear, elasticity, and capillarity remain poorly understood. Here, we experimentally investigate the breakup of a shear-thinning viscoelastic liquid coflowing with an immiscible Newtonian fluid in a rectangular microchannel, focusing on the formation, stretching, instability, and breakup of the thin filament connecting the primary droplet to the upstream liquid. Four regimes: stable coflow, squeezing, dripping, and jetting are identified and mapped using the capillary numbers of the dispersed and continuous phases and an elastocapillary parameter. Although elasticity weakly affects the onset of primary droplet formation, it strongly alters later filament dynamics by delaying capillary breakup and stabilising long-lived filaments. Scaling analyses based on capillary, viscous, and elastic force balances predict the primary droplet size, critical filament thickness at instability onset, maximum filament length, and critical jet length. Particle tracking shows that confinement creates a non-uniform wall-induced shear field along the inclined filament, producing spatial variations in interfacial velocity and initiating the first bead-on-a-string instability at the location of maximum shear. A Rayleigh-Plateau analysis incorporating an effective viscosity derived from the Oldroyd-B model predicts the instability wavelength and growth rate to the correct order of magnitude. These results show that confined viscoelastic breakup is governed not solely by classical elastocapillary thinning, but by a coupled wall-shear-elasticity mechanism controlling filament stretching, instability, and secondary droplet formation, thereby providing a predictive framework for filament-mediated breakup in confined viscoelastic multiphase flows.
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Reference graph
Works this paper leans on
-
[1]
Abkarian, M., Lartigue, C. & Viallat, A.2002 Tank treading and unbinding of deformable vesicles in shear flow: Determination of the lift force.Phys. Rev. Lett.88(6)
work page 2002
-
[2]
Aggarwal, N. & Sarkar, K.2008 Effects of matrix viscoelasticity on viscous and viscoelastic drop deformation in a shear flow.J. Fluid Mech.601, 63–84
work page 2008
-
[3]
Amarouchene, Y., Bonn, D., Meunier, J. & Kellay, H.2001 Inhibition of the finite-time singularity during droplet fission of a polymeric fluid.Phys. Rev. Lett.86(16), 3558–3561
work page 2001
-
[4]
Anna, S. L. & McKinley, G. H.2001 Elasto-capillary thinning and breakup of model elastic liquids.J. Rheol.45(1), 115–138
work page 2001
-
[5]
Ardekani, A. M., Sharma, V. & McKinley, G. H.2010 Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets.J. Fluid Mech.665, 46–56
work page 2010
-
[6]
Arnolds, O., Buggisch, H., Sachsenheimer, D. & Willenbacher, N.2010 Capillary breakup extensional rheometry (caber) on semi-dilute and concentrated polyethyleneoxide (peo) solutions.Rheologica Acta49(11-12), 1207–1217
work page 2010
-
[7]
Arratia, P. E., Gollub, J. P. & Durian, D. J.2008 Polymeric filament thinning and breakup in microchannels.Phys. Rev. E77(3), 036309
work page 2008
-
[8]
& Leal, L.1979 The motion of a deformable drop in a second-order fluid.J
Chan, P.C.-H. & Leal, L.1979 The motion of a deformable drop in a second-order fluid.J. Fluid Mech. 92(1), 131–170
work page 1979
Show all 42 references
-
[9]
& Ashgriz, N.2025 Droplet size in the breakup of a viscoelastic filament.Phys
Chen, S. & Ashgriz, N.2025 Droplet size in the breakup of a viscoelastic filament.Phys. Fluids37(2), 023108
2025
-
[10]
& Kumacheva, E.2022 Trends in droplet microfluidics: From droplet generation to biomedical applications.Langmuir38(20), 6233–6248
Chen, Z., Kheiri, S., Young, E.W. & Kumacheva, E.2022 Trends in droplet microfluidics: From droplet generation to biomedical applications.Langmuir38(20), 6233–6248
2022
-
[11]
F., Noharuddin, N
Christopher, G. F., Noharuddin, N. N., Taylor, J. A. & Anna, S. L.2008 Experimental observations of the squeezing-to-dripping transition in t-shaped microfluidic junctions.Phys. Rev. E78(3), 036317
2008
-
[12]
A., Li, J
Clasen, C., Eggers, J., Fontelos, M. A., Li, J. & McKinley, G. H.2006 The beads-on-string structure of viscoelastic threads.J. Fluid Mech.556, 283–308
2006
-
[13]
& Mason, T.G.2008 Capillary threads and viscous droplets in square microchannels.Phys
Cubaud, T. & Mason, T.G.2008 Capillary threads and viscous droplets in square microchannels.Phys. Fluids20(5), 053302
2008
-
[14]
A., Eggers, J
Deblais, A., Herrada, M. A., Eggers, J. & Bonn, D.2020 Self-similarity in the breakup of very dilute viscoelastic solutions.J. Fluid Mech.904, R2
2020
-
[15]
& Bekkour, K.2009 Rheological characterization of poly(ethylene oxide) solutions of different molecular weights.Journal of Colloid and Interface Science336(1), 360–367
Ebagninin, K.W., Benchabane, A. & Bekkour, K.2009 Rheological characterization of poly(ethylene oxide) solutions of different molecular weights.Journal of Colloid and Interface Science336(1), 360–367
2009
-
[16]
Fluids26(3), 033106
Eggers, J.2014 Instability of a polymeric thread.Phys. Fluids26(3), 033106
2014
-
[17]
Eggers, J., Herrada, M. A. & Snoeijer, J. H.2020 Self-similar breakup of polymeric threads as described by the oldroyd-b model.J. Fluid Mech.887, A19
2020
-
[18]
& Villermaux, E.2008 Physics of liquid jets.Rep
Eggers, J. & Villermaux, E.2008 Physics of liquid jets.Rep. Prog. Phys.71(3), 036601
2008
-
[19]
& Hinch, E.J.1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid.J
Entov, V.M. & Hinch, E.J.1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid.J. Non-Newtonian Fluid Mech.72(1), 31–53
1997
-
[20]
J., Stone, H
Garstecki, P., Fuerstman, M. J., Stone, H. A. & Whitesides, G. M.2006 Formation of droplets and bubbles in a microfluidic t-junction—scaling and mechanism of break-up.Lab Chip6(3), 437–446
2006
-
[21]
Hazra, S., Mitra, S. K. & Sen, A. K.2019 Lateral migration of viscoelastic droplets in a viscoelastic confined flow: role of discrete phase viscoelasticity.Soft Matter15(44), 9003–9010
2019
-
[22]
& Cooper-White, J.J.2006 The effect of elasticity on drop creation in T-shaped microchannels
Husny, J. & Cooper-White, J.J.2006 The effect of elasticity on drop creation in T-shaped microchannels. J. Non-Newt. Fluid Mech.137(1-3), 121–136. 39
2006
-
[23]
& Martin, G.2009 Links between ink rheology, drop-on-demand jet formation, and printability.J
Hutchings, I., Tuladhar, T., Mackley, M., Vadillo, D., Hoath, S. & Martin, G.2009 Links between ink rheology, drop-on-demand jet formation, and printability.J. Imaging Sci. Technol53(4), 41208
2009
-
[24]
F.2009 Boger fluids.Annu
James, D. F.2009 Boger fluids.Annu. Rev. Fluid Mech.41(1), 129–142
2009
-
[25]
& Pathak, M.2022 Droplet formation under wall slip in a microfluidic T-junction.J
Kumar, P. & Pathak, M.2022 Droplet formation under wall slip in a microfluidic T-junction.J. Mol. Liq. 345, 117808
2022
-
[26]
& Yin, X.Z.2017 Oscillation of satellite droplets in an oldroyd-b viscoelastic liquid jet
Li, F., Yin, X.Y. & Yin, X.Z.2017 Oscillation of satellite droplets in an oldroyd-b viscoelastic liquid jet. Phys. Rev. Fluids2(1), 013602
2017
-
[27]
H.2005 Dimensionless groups for understanding free surface flows of complex fluids.SOR Rheology Bulletin (MIT)
McKinley, G. H.2005 Dimensionless groups for understanding free surface flows of complex fluids.SOR Rheology Bulletin (MIT)
2005
-
[28]
Montanero, J. M. & Ganan-Calvo, A. M.2008 Viscoelastic effects on the jetting–dripping transition in co-flowing capillary jets.J. Fluid Mech.610, 249–260
2008
-
[29]
& Harlen, O.G.2010 Viscoelasticity in inkjet printing.Rheologica Acta49(6), 619–632
Morrison, N.F. & Harlen, O.G.2010 Viscoelasticity in inkjet printing.Rheologica Acta49(6), 619–632
2010
-
[30]
& Leonetti, M
Naillon, A., de Loubens, C., Ch `evremont, W., Rouze, S. & Leonetti, M. ans Bodiguel, H.2019 Dynamics of particle migration in confined viscoelastic poiseuille flows.Physical Review Fluids 4(5)
2019
-
[31]
& Izadifard, M.H.2025 Viscoelastic droplets via flow-focusing: From dripping to jetting and beads-on-a-string structures.Phys
Neshat, A., Norouzi, M., Nazari, M., Gerivani, H. & Izadifard, M.H.2025 Viscoelastic droplets via flow-focusing: From dripping to jetting and beads-on-a-string structures.Phys. Fluids37(11), 113101
2025
-
[32]
& Higuchi, T.2002 Droplet formation in a microchannel network.Lab Chip2(1), 24–26
Nisisako, T., Torii, T. & Higuchi, T.2002 Droplet formation in a microchannel network.Lab Chip2(1), 24–26
2002
-
[33]
Oliveira, M. S. & McKinley, G. H.2005 Iterated stretching and multiple beads-on-a-string phenomena in dilute solutions of highly extensible flexible polymers.Phys. Fluids17(7), 071704
2005
-
[34]
S., Yeh, R
Oliveira, M. S., Yeh, R. & McKinley, G. H.2006 Iterated stretching, extensional rheology and formation of beads-on-a-string structures in polymer solutions.J. Non-Newt. Fluid Mech.137(1–3), 137–148
2006
-
[35]
M.1984 The deformation of small viscous drops and bubbles in shear flows.Annu
Rallison, J. M.1984 The deformation of small viscous drops and bubbles in shear flows.Annu. Rev. Fluid Mech.16(1), 45–66
1984
-
[36]
& Eggers, J.2008 Blistering pattern and formation of nanofibers in capillary thinning of polymer solutions.Phys
Sattler, R., Wagner, C. & Eggers, J.2008 Blistering pattern and formation of nanofibers in capillary thinning of polymer solutions.Phys. Rev. Lett.100(16), 164502. van Steijn, V., Kleijn, C. R. & Kreutzer, M. T.2010 Predictive model for the size of bubbles and droplets created...
2008
-
[37]
& Sureshkumar, R.2007 Dynamics of viscoelastic fluid filaments in microfluidic devices.Phys
Steinhaus, B., Shen, A.Q. & Sureshkumar, R.2007 Dynamics of viscoelastic fluid filaments in microfluidic devices.Phys. Fluids19(7), 073103
2007
-
[38]
Tirtaatmadja, V., McKinley, G. H. & Cooper-White, J. J.2006 Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration.Phys. Fluids18(4), 043101
2006
-
[39]
& Weitz, D.A.2007 Dripping to jetting transitions in coflowing liquid streams.Phys
Utada, A.S., Fernandez-Nieves, A., Stone, H.A. & Weitz, D.A.2007 Dripping to jetting transitions in coflowing liquid streams.Phys. Rev.Lett.99(9), 094502. V Giri, N., Cui, W. & Ren, C.L.2024 An experimental investigation into filament formation during drop generation by pseudo...
2007
-
[40]
Wagner, C., Amarouchene, Y., Bonn, Daniel & Eggers, J.2005 Droplet detachment and satellite bead formation in viscoelastic fluids.Phys. Rev. Lett.95(16), 164504
2005
-
[41]
& Fu, T.2024 Formation of viscoelastic droplets in symmetrical parallelized microchannels.Chem
Wang, H., Dong, Y., Lei, Z., Zhu, C., Cui, X., Ma, Y. & Fu, T.2024 Formation of viscoelastic droplets in symmetrical parallelized microchannels.Chem. Eng. Sci.292, 120001
2024
-
[42]
Weber, C.1931 On the breakdown of a fluid jet.ZAMM - J. Appl. Math. Mech.11(2), 136–154. 40 Supplementary material S1. Validation of the cross-stream migration model To assess the predictive capability of the proposed model, we compare the theoretically predicted cross-stream ...
2002
Reviewed August 8, 2026 · model on record in the stance chip above.
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