{"id":"9f9812e4-eb6e-4264-a6c9-a5e3f89e9e17","arxiv_id":"2608.05343","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"In confined microfluidic coflows, viscoelastic filaments break up at the point of maximum wall-induced shear, a mechanism captured by scaling laws and a modified Rayleigh-Plateau analysis.","lead":"This paper studies how viscoelastic liquids break into droplets inside narrow microchannels and finds that the channel wall, not just surface tension, controls where and when the connecting filament ruptures. The result offers design rules for making uniform micro-droplets in lab-on-chip devices.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"First-bead location also tracks minimum filament radius and the upstream neck; without measuring axial h_f(x), the wall-shear localization claim lacks a unique control.","rationale":"The reader's weakest-assumption analysis focused on the quantitative wall-shear scaling γdot ~ u_d/e and the empirical migration coefficients. That is a legitimate concern, but the more load-bearing issue is interpretational: the central mechanistic claim that wall shear localizes the first bead is supported by an observation that is equally consistent with classical capillary/elastic mechanisms. The paper's own critical-thickness model predicts breakup where 2γ/h is largest, and end-pinching predicts breakup at the upstream neck; both coincide with the wall-side region in the present geometry. Without measuring the axial radius profile and separating the neck contribution, the unique role of wall shear is not established. This does not invalidate the paper's data or its qualitative regime characterization; the first-bead observation is robust and the tracer-velocity results are valuable. The recommended verdict remains CONDITIONAL, as the central claim needs one additional control measurement before it can be accepted as uniquely demonstrated. The reader's verdict is unchanged, but the required condition is more specific than the reader's stated quantitative concern.","tokens_in":30872,"tokens_out":7628,"duration_ms":71130,"concrete_test":"Measure h_f(x) along the filament and identify the upstream neck location in high-speed images immediately before the first visible undulation for the conditions of Fig. 9(a)-(d); overlay the first-bead position with (i) the location of minimum local radius, (ii) the upstream neck/end-pinching site, and (iii) the modeled maximum-shear location. If the first bead coincides with the minimum-radius or neck location in cases where the maximum shear is shifted elsewhere (e.g., a more parallel filament at lower Ca2), the wall-shear localization claim is not uniquely supported; if beads track maximum shear while the radius profile is uniform or the minimum lies elsewhere, the claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central mechanistic claim rests on Fig. 9: the first bead-on-a-string perturbation consistently appears at y*=1, the location of maximum wall-induced shear. But y*=1 is also the part of the filament closest to the channel wall and, in the coflow geometry, adjacent to the upstream neck where the filament connects to the reservoir. Two well-known mechanisms predict bead nucleation at exactly this location without invoking wall shear. First, capillary end-pinching localizes breakup at concave necks or filament ends. Second, the paper's own critical-thickness criterion, Eq. (3.22), says instability begins where 2γ/h_cr is first reached, i.e., where the local filament radius is smallest. The paper never reports 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 shear-stress distributions in Fig. 9(b) are model outputs based on γdot ~ u_d/e, whose validity is the very point at issue, not independent measurements. 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. Thus the unique support for the wall-shear-localization claim is currently an uncontrolled correlation between wall proximity and bead position.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":31284,"tokens_out":5452,"duration_ms":47109,"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":[{"comment":"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.","section":"Sec. 3.4 and Fig. 9"},{"comment":"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.","section":"Sec. 3.2.1, Eq. (3.12)"},{"comment":"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.","section":"Sec. 3.2.2, Eqs. (3.21) and (3.24)"},{"comment":"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.","section":"Sec. 3.3, Eq. (3.27)"},{"comment":"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.","section":"Appendix E and Table 4"}],"minor_comments":[{"comment":"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.","section":"General"},{"comment":"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}.","section":"Appendix C"},{"comment":"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.","section":"Table 4"},{"comment":"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.","section":"Figure 10 caption"},{"comment":"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.","section":"Eq. (3.13)"},{"comment":"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.","section":"Sec. 3.2.4"}],"recommendation":"major_revision","confidential_remarks":"The paper contains a large amount of carefully collected experimental data and a coherent scaling framework, but several of the headline predictions are in-sample fits or depend on empirical inputs whose sensitivity is not quantified. The most important issue for the journal is the uncontrolled correlation in Fig. 9 between maximum wall shear and minimum filament radius/upstream neck; this needs an additional measurement or a decoupling experiment before the central mechanistic claim can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The experimental core is genuinely useful. The regime maps, the clean collapse of the coflow-to-droplet transition onto Ca1 ≈ 2.3Ca2, and the systematic variation of polymer relaxation time at matched viscosity and interfacial tension are all solid contributions. The particle-tracking data showing velocity gradients along an inclined filament are direct evidence that the filament does not move as a rigid body, and the observation that the first bead consistently appears on the wall-side portion of the filament is robust and worth explaining.\n\nThat said, the stress-test note lands. The first-bead location at y* = 1 is also the location of minimum wall clearance, the most probable location of minimum local radius, and it sits near the upstream neck. The paper does not report h_f(x) at the onset of instability, so capillary end-pinching or a critical-thickness criterion applied locally would predict the same location without invoking wall shear. The shear-stress distributions in Fig. 9(b) are model outputs built on the same wall-shear scaling whose validity is the question at issue, so they do not provide independent support. The tracer velocities are real, but axial velocity variation is required by mass conservation in a thread of nonuniform radius, so they do not uniquely implicate wall shear.\n\nThe quantitative framework is also more correlative than predictive. Several constants—the bbar power laws, the neck-width correlation, the migration coefficient A = 2.5, the 1.5 lambda_r integration time, C_c in Eq. (3.21), and the jetting time-scale proportionality—are fitted from the same experiments they are used to predict. The comparisons are honest in showing good agreement, but readers should treat the scalings as compact empirical descriptions rather than independent predictions. The Rayleigh–Plateau analysis delivers only order-of-magnitude agreement, which is acceptable but not a strong test.\n\nThese are real soft spots, not fatal ones. The experimental observations stand, and the central claim is plausible even if not uniquely supported. The paper deserves a serious referee. I would ask the referees to require axial filament-radius measurements at instability onset, a head-to-head comparison of first-bead location against the minimum-radius locus, and ideally an out-of-sample test of at least one scaling with a fluid or geometry not used in the fits.","headline":"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.","tokens_in":31838,"tokens_out":2022,"would_cite":true,"duration_ms":20614,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In a confined microfluidic coflow, wall-induced shear—not just elastocapillary thinning—sets where and when a viscoelastic filament breaks.","keywords":["microfluidics","viscoelastic coflow","bead-on-a-string","wall-induced shear","elastocapillary thinning","Rayleigh-Plateau instability","secondary droplet generation","shear-thinning polymer solutions"],"falsifier":"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.","tokens_in":30650,"feed_emoji":"💧","tokens_out":9386,"duration_ms":108948,"temperature":0.7,"pith_summary":"This paper tries to establish that, inside a narrow microchannel, a viscoelastic filament connecting a forming droplet to the upstream liquid is not simply drawn thin by capillary and elastic forces; the channel wall imposes a shear field on the inclined filament that actively stretches it and decides where it first destabilises. Using a Newtonian oil coflowing with aqueous polymer solutions of different relaxation times, the authors map four regimes—stable coflow, squeezing, dripping, jetting—and show that elasticity barely shifts the onset of droplet formation while strongly lengthening filament lifetime afterwards. They derive scaling laws from capillary, viscous, elastic, and wall-shear balances that predict the primary droplet diameter, the filament thickness at instability, the maximum filament length, and the jet breakup length, with data collapsing onto the predictions. Particle-tracking images show the first bead-on-a-string perturbation always nucleating where wall-induced shear is largest, and a Rayleigh–Plateau analysis with a shear-dependent effective viscosity captures the measured wavelength and growth rate to order of magnitude. If the picture is right, the wall gap and shear profile become independent controls on filament breakup and secondary droplet size.","feed_headline":"Wall shear sets where a viscoelastic filament first breaks","feed_subtitle":"Particle tracking shows the first bead-on-a-string forms where wall shear peaks, not at the thinnest neck.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Establishes the exponential elastocapillary-thinning regime that the paper's filament evolution builds on and extends to confined shear.","marker":"Entov & Hinch 1997"},{"why":"Provides the canonical experimental picture of long-lived viscoelastic filaments whose breakup the paper re-examines under confinement.","marker":"Anna & McKinley 2001"},{"why":"Supplies the beads-on-a-string model and the exponential-thinning relation used to extract relaxation times from the present filament data.","marker":"Clasen et al. 2006"},{"why":"Gives the Newtonian confined-coflow regime map, thread-width scaling, and jetting baseline that the paper generalises to viscoelastic fluids.","marker":"Cubaud & Mason 2008"},{"why":"Supplies the pressure-drop scaling for droplet formation in confined channels used in the primary-droplet force balance.","marker":"Garstecki et al. 2006"},{"why":"Shows confinement changes elastocapillary-to-inertia-capillary transitions, motivating the wall-shear mechanism.","marker":"Steinhaus et al. 2007"},{"why":"Provides the viscoelastic lift force and migration velocity that set the filament's wall eccentricity.","marker":"Hazra et al. 2019"},{"why":"Shows zero-shear and extensional viscosities fail to predict viscoelastic filament instability, motivating the effective-viscosity approach.","marker":"Chen & Ashgriz 2025"},{"why":"Establishes that the axial polymeric normal stress dominates the final thinning stage, which the effective-viscosity formula exploits.","marker":"Eggers et al. 2020"},{"why":"Provides the classical viscous-jet growth-rate formula that the modified Rayleigh–Plateau analysis starts from.","marker":"Weber 1931"}],"fun_headline_variants":["Wall shear decides where viscoelastic filaments snap","First bead-on-a-string forms at peak shear, not thinnest neck","Shear and elasticity override classical thinning in confined flow","Filament rupture site set by wall shear, not capillary thinning","Confined viscoelastic breakup follows a wall-shear-elasticity rule"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Wall shear decides where viscoelastic filaments snap","First bead-on-a-string forms at peak shear, not thinnest neck","Shear and elasticity override classical thinning in confined flow","Filament rupture site set by wall shear, not capillary thinning","Confined viscoelastic breakup follows a wall-shear-elasticity rule"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000896,"raw_usage":{"total_tokens":3924,"prompt_tokens":1075,"completion_tokens":2849,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":691,"completion_tokens_details":{"reasoning_tokens":2762}},"tokens_in":691,"tokens_out":2849,"duration_ms":19770,"temperature":1.0,"reasoning_tokens":2762,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T14:55:31.042006+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"& Hinch, E.J.1997 Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid.J","cited_arxiv_id":null,"evidence_quote":"Establishes the exponential elastocapillary-thinning regime that the paper's filament evolution builds on and extends to confined shear."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the canonical experimental picture of long-lived viscoelastic filaments whose breakup the paper re-examines under confinement."},{"cited_title":"A., Li, J","cited_arxiv_id":null,"evidence_quote":"Supplies the beads-on-a-string model and the exponential-thinning relation used to extract relaxation times from the present filament data."},{"cited_title":"& Mason, T.G.2008 Capillary threads and viscous droplets in square microchannels.Phys","cited_arxiv_id":null,"evidence_quote":"Gives the Newtonian confined-coflow regime map, thread-width scaling, and jetting baseline that the paper generalises to viscoelastic fluids."},{"cited_title":"J., Stone, H","cited_arxiv_id":null,"evidence_quote":"Supplies the pressure-drop scaling for droplet formation in confined channels used in the primary-droplet force balance."},{"cited_title":"& Sureshkumar, R.2007 Dynamics of viscoelastic fluid filaments in microfluidic devices.Phys","cited_arxiv_id":null,"evidence_quote":"Shows confinement changes elastocapillary-to-inertia-capillary transitions, motivating the wall-shear mechanism."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the viscoelastic lift force and migration velocity that set the filament's wall eccentricity."},{"cited_title":"& Ashgriz, N.2025 Droplet size in the breakup of a viscoelastic filament.Phys","cited_arxiv_id":null,"evidence_quote":"Shows zero-shear and extensional viscosities fail to predict viscoelastic filament instability, motivating the effective-viscosity approach."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes that the axial polymeric normal stress dominates the final thinning stage, which the effective-viscosity formula exploits."}],"review_version":1}