{"id":"cbfeb559-75b4-474d-a0ad-8f9e443e3201","arxiv_id":"1908.07183","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A steady-state rheology method is proposed to estimate the shear jamming onset stress in dense suspensions by fitting deviations from the Krieger-Dougherty relation with the Wyart-Cates model.","lead":"This paper reports that in dense suspensions of polystyrene particles, the measured viscosity at high shear stress and high particle fraction falls below the prediction of the Krieger-Dougherty relation. The authors interpret this deviation as a signature of shear jamming and use the Wyart-Cates model to estimate the onset stress of the jammed state from steady-state flow curves.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The WC fit is underdetermined: the four-parameter model is fitted to only four phi_J(sigma) values per particle size, making the predicted sigma_SJ an interpolation product rather than a validated boundary.","rationale":"The reader's CONDITIONAL verdict is appropriate. I focus on the WC fit because the paper's entire prediction of sigma_SJ is produced by that fit: the KD baseline gives phi_J(sigma), but the onset is read from the WC model. The manuscript presents Fig. 2 with four stress levels per particle size; if those are the only data entering Fig. 3, then the four-parameter WC model passes through all points exactly, so the 'excellent agreement' cannot be used as evidence. The reported phi_m ~ 0.561 and phi_0 ~ 0.62 are essentially pinned by the high- and low-stress endpoints, while sigma* and beta are tuned by the two intermediate points. The extrapolated sigma_SJ for phi = 0.58 and 0.60 is thus sensitive to the chosen functional form and to the exact placement of the intermediate stress levels. A leave-one-out test would immediately show whether the prediction is stable; if it is not, the method needs additional stress levels or a constrained model. The paper does deserve credit for careful reversibility checks, for comparing two fitting ranges for the KD baseline (S.I. Fig. S2), and for the qualitative high-stress imaging, but those do not validate the WC extrapolation. I therefore keep the verdict CONDITIONAL rather than ACCEPT.","tokens_in":11022,"tokens_out":11585,"duration_ms":117825,"concrete_test":"Count N, the number of independent stress levels used in each WC fit in Fig. 3. If N <= 4, perform leave-one-out cross-validation: refit phi_0, phi_m, sigma*, and beta to the remaining N-1 phi_J values and recompute sigma_SJ for phi = 0.58 and 0.60. If the predicted sigma_SJ varies by more than a factor of 2 across folds, or if any refit fails to converge, the reported sigma_SJ is not constrained by the data.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on the WC fit that converts KD-derived phi_J(sigma) values into a prediction of sigma_SJ. For each particle size, phi_J(sigma) is obtained by a one-parameter KD fit (exponent fixed at -2) over phi in [0.45, 0.55] at the stress levels shown in Fig. 2 (four per size; e.g., 28, 200, 448 and 2000 Pa for d = 1.21 um). The WC model (Eq. 1 with f = exp[-(sigma*/sigma)^beta]) contains four free parameters: phi_0, phi_m, sigma*, and beta. If only four independent phi_J values are used, the fit is exactly determined and has zero degrees of freedom, so the 'excellent agreement' in Fig. 3 is an interpolation rather than a validation. The sigma_SJ values read from phi = phi_J(sigma) are then outputs of an unconstrained four-parameter curve through four derived points. The paper does not report the number of independent stress levels used, parameter uncertainties, or any goodness-of-fit statistic, and it explicitly defers direct comparison with transient SJ measurements as future work. The KD-baseline question is upstream, but the underdetermination of the WC fit is the most load-bearing weakness in the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports steady-state rheology of polystyrene/ polyethylene glycol suspensions at volume fractions φ = 0.45–0.60 for three particle sizes. The authors fit viscosity-versus-φ data at fixed stress to the Krieger–Dougherty (KD) relation over 0.45 ≤ φ ≤ 0.55, obtaining a stress-dependent jamming fraction φJ(σ); at φ = 0.58 and 0.60 and high stress, the measured viscosities fall systematically below the KD fit. These φJ(σ) values are then fitted to the Wyart–Cates relation φJ(σ) = f(σ)φm + [1 − f(σ)]φ0 with f(σ) = exp[−(σ*/σ)^β], and the onset stress for shear jamming is defined as the stress σSJ(φ) at which φ = φJ(σ). The paper reports that σSJ decreases with increasing φ, in qualitative agreement with prior transient measurements, and supports the picture with optical imaging showing macroscopic sample detachment and edge fracture at high stress.","tokens_in":11283,"tokens_out":5044,"duration_ms":54313,"significance":"If the proposed method were validated, it would be a useful advance: shear jamming is normally distinguished from discontinuous shear thickening by transient stress-response protocols, and a steady-state criterion would simplify the characterization of dense suspensions. The paper has concrete strengths: systematic rheology over three particle sizes; checks of waiting-time dependence, reversibility, and geometry reported in the SI (Fig. S1); a partial check of the KD fitting-range dependence (Fig. S2); and direct imaging of edge fracture at high stress (Fig. 3e,f). The internal consistency φm ≈ φrlp ≈ 0.56 in all three systems is also suggestive. However, the central quantitative claim is not yet established: the Wyart–Cates fit that converts φJ(σ) into σSJ has too few constraints, and alternative explanations of the KD shortfall (wall slip, edge fracture, breakdown of the KD form at high φ) are not excluded. The authors are explicit that direct comparison with transient shear-jamming measurements remains future work, which is a key missing test.","major_comments":[{"comment":"The Wyart–Cates fit is underdetermined. For each particle size, φJ(σ) is obtained at only four stress values (for d = 1.21 µm: 28, 200, 448, and 2000 Pa), while Eq. (1) with f(σ) = exp[−(σ*/σ)^β] contains four free parameters (φ0, φm, σ*, β). A four-parameter curve through four points has zero degrees of freedom, so the reported 'excellent agreement' in Fig. 3a–c is an interpolation rather than a validation. The paper should report the number of independent stress levels, parameter uncertainties or covariance, and a goodness-of-fit or cross-validation statistic; without this, the extracted σSJ values are not independent predictions but outputs of an unconstrained fit.","section":"Section III, Fig. 3"},{"comment":"The interpretation of the KD shortfall at φ = 0.58 and 0.60 as a signature of shear-jamming failure is not uniquely supported. The KD baseline is fitted only over 0.45 ≤ φ ≤ 0.55, and the SI (Fig. S2) checks the wider range 0.4–0.55 only for σ = 28, 200, and 448 Pa, not for the 2000 Pa point used in Fig. 2b. The manuscript itself notes sample protrusion from the plates at high shear rates; wall slip, edge fracture, or breakdown of the KD functional form at high φ could produce the same apparent viscosity shortfall without implying shear jamming. The optical imaging (Fig. 3e,f) detects only macroscopic brittle failure and the conclusions explicitly state that no failure is visible just beyond the predicted σSJ. A direct comparison with transient stress measurements on the same suspensions, or a control experiment varying geometry and gap, is needed to rule out these confounds.","section":"Section III, Figs. 2 and S2"},{"comment":"The term 'prediction' overstates what is demonstrated. The σSJ values are read from the WC curve whose parameters are fitted to the same steady-state data from which φJ(σ) was extracted, so the agreement with the qualitative trend from transient measurements (refs. 28, 31) is a postdiction, not an independent validation. The paper should either validate σSJ against transient shear-jamming measurements on the same suspensions, or reframe σSJ as a consistency check and provide a concrete falsifiable prediction, such as a hold-out stress level or a predicted shear-rate discontinuity, that could be tested in future work.","section":"Section III, Conclusions"}],"minor_comments":[{"comment":"The stretched-exponential form f(σ) = exp[−(σ*/σ)^β] is adopted from the literature, but the paper does not report the fit residuals or parameter bounds for β, σ*, φ0, and φm; adding a table of fitted values with uncertainties would greatly improve reproducibility.","section":"Section III, Eq. (1) and Fig. 3"},{"comment":"The claim σ* ∼ 1/d² is presented alongside the empirical fit σ*(d) = A/d² + B with B = 65.89 Pa, which is not a pure inverse-square law; the role of the constant offset should be discussed or the claim should be softened to 'approximately consistent with σ* ∼ 1/d² plus a constant.'","section":"SI, Fig. S4"},{"comment":"Minor typographical and formatting issues: 'Sayantan majumdar' should be capitalized, '2o' should be '2°', and the SI abbreviation is used inconsistently as 'S.I.' and 'SI'; these do not affect the science.","section":"Section II, Experimental"},{"comment":"The shaded 'SJ' region in Fig. 3d is model-derived and could be confused with measured data; the caption should state explicitly that the shaded region is the phase boundary obtained from the WC fit, and the numeric values of σSJ for φ = 0.58 and 0.60 should be given.","section":"Section III, Fig. 3d"},{"comment":"Reference [39] is a commercial web page; the residual-interaction discussion should cite a peer-reviewed source, and reference [31] should be updated to its published version if available.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses a timely and interesting question in dense suspension rheology, and the experimental data appear carefully collected. However, the central methodological claim currently rests on an underdetermined four-parameter fit to four derived data points per particle size, and the steady-state signature has not been validated against transient shear-jamming measurements. I believe the paper is suitable for serious consideration after the authors address the fit degeneracy, report uncertainties, and either provide an independent validation or substantially soften the predictive claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper floats a nice idea—find shear jamming onset from steady-state flow curves by looking for deviations from the Krieger-Dougherty relation—but the validation is not there yet. The WC fit that converts those deviations into a σ_SJ prediction is four parameters fitted to four data points per particle size. That is interpolation wearing a lab coat.\n\nThe genuinely useful parts: they report clean steady-state data for three particle sizes, check waiting time and geometry effects, and are unusually frank about the limitations of their optical imaging. The observation that KD systematically overestimates viscosity at high φ and σ is real, and the trend of φ_J decreasing with σ is qualitatively consistent with the WC picture.\n\nNow the soft spots, in order of weight. First, the load-bearing fit: for each particle size they extract four φ_J values from KD fits (which themselves are one-parameter fits to three points) and then fit the four-parameter WC curve through them. Zero degrees of freedom. The 'excellent agreement' in Fig. 3 proves nothing; the predicted σ_SJ is just where that interpolated curve crosses φ. There are no error bars on φ_J or on the WC parameters, so we don't know if the crossing is even meaningful. Second, the KD baseline is fit to φ ≤ 0.55 by design, on the grounds that SJ doesn't occur below random loose packing. That assumption is essentially the thing they're trying to test, so the deviation at higher φ could be a symptom of the fitting range rather than of jamming failures. Wall slip or edge fracture would produce the same signature; the imaging shows cracks only at stresses well above the predicted σ_SJ. Third, they explicitly say comparing with transient SJ measurements is future work—so the method is currently an unvalidated proposal.\n\nIs this worth a referee? Yes. The question matters, the data are solid enough to be a starting point, and the idea, if it holds up, would be a useful cheap probe. But I would not accept it in this form. A serious referee should demand: more stress levels per size, error bars on the WC/KD parameters, a direct comparison with transient measurements for at least one system, and some handle on whether the observed deviation is distinguishable from slip or edge fracture. If the authors can close at least one of those gaps, the paper becomes genuinely interesting. As it stands, the central claim is an interpolated curve, and I'd want to see the method survive contact with an independent measurement before treating σ_SJ from flow curves as real.","headline":"Nice idea, underdetermined fit: the WC prediction of σ_SJ is a four-parameter curve through four points per particle size, so the method is not yet validated.","tokens_in":11812,"tokens_out":2988,"would_cite":false,"duration_ms":30998,"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":"Steady-state flow curves alone can locate the shear-jamming boundary in dense suspensions.","keywords":["shear jamming","discontinuous shear thickening","dense suspensions","Wyart-Cates model","Krieger-Dougherty relation","jamming packing fraction","colloidal rheology","steady-state rheology"],"falsifier":"Run the same PS/PEG suspensions through an independent transient stress protocol, or image the bulk (not just the boundary) for internal crack and shear-band formation, and compare the measured sigma_SJ(phi) with the steady-flow prediction at phi = 0.58 and 0.60; a mismatch larger than experimental error would falsify the claim that steady flow curves alone locate the SJ boundary.","tokens_in":1654,"feed_emoji":"","tokens_out":3856,"duration_ms":88349,"temperature":0.7,"pith_summary":"The paper aims to show that the onset of shear jamming in dense particulate suspensions can be read off ordinary steady-state flow curves, without needing transient stress protocols. It argues that at high stress and high volume fraction the measured viscosity falls systematically below the Krieger-Dougherty prediction, because the sample is a solid-like jammed state that can only flow through failures; that shortfall is the signature. Fitting the Wyart-Cates model to the stress-dependent jamming packing fraction extracted from the data yields, for each packing fraction phi, a stress sigma_SJ where phi equals phi_J($\\sigma$). If this works, any rheometer can map the shear-jamming boundary from the same measurements that already detect shear-thickening.","feed_headline":"Flow curves alone can predict shear-jamming onset","feed_subtitle":"Steady viscosity data yields the stress-dependent jamming fraction that separates thickening from solid-like jamming.","key_machinery":"The load-bearing object is the stress-dependent jamming packing fraction phi_J($\\sigma$) from the Wyart-Cates model, phi_J($\\sigma$) = f($\\sigma$) phi_m + [1 - f($\\sigma$)] phi_0, where f($\\sigma$) is the fraction of frictional particle contacts, taken as a stretched exponential exp(-($\\sigma$*/$\\sigma$)^$\\beta$). The Krieger-Dougherty relation eta_r = (1 - phi/phi_J)^(-2) is fitted to low-phi data at each stress to extract phi_J($\\sigma$), and shear jamming is identified at the crossing phi = phi_J($\\sigma$). The work of this machinery is to convert ordinary viscosity measurements into a prediction of the stress at which a suspension of given packing fraction becomes a jammed solid.","core_discovery":"The paper's central claim is that shear jamming leaves a quantitative signature in steady-state flow curves, despite the jammed state itself being unable to sustain steady flow. At fixed applied stress, viscosity as a function of volume fraction follows the Krieger-Dougherty relation eta_r = (1 - phi/phi_J)^(-2) for phi <= 0.55, but at high stress and high volume fraction the measured viscosity falls below the KD prediction; the paper interprets this shortfall as weakening of the sample by flow-induced failures of a solid-like shear-jammed state. Fitting the Wyart-Cates form phi_J($\\sigma$) = f($\\sigma$) phi_m + [1 - f($\\sigma$)] phi_0 with f($\\sigma$) = exp(-($\\sigma$* / $\\sigma$)^$\\beta$) to the extracted jamming fractions, the onset stress for shear jamming is defined by phi = phi_J(sigma_SJ). The claim is supported by the decrease of sigma_SJ with increasing phi, matching transient studies, and by optical imaging that shows sample detachment and edge fracture deep inside the predicted SJ regime.","pith_inferences":["A testable extension, which the paper notes is left for future work, is to compare its steady-flow sigma_SJ with values from transient stress responses or bulk imaging that can see interior failures; agreement would close the loop, and disagreement would pinpoint where the steady-flow signature misreads.","The method, if it holds, should be able to map the entire SJ boundary in the (sigma, phi) plane rather than just individual points; for phi just above phi_m the predicted sigma_SJ should rise steeply, a prediction that could be checked with the same flow-curve data.","Because the KD baseline is fitted below phi_rlp, the method implicitly assumes the same diverging viscosity law holds into the jammed regime; applying the analysis to systems with attractions or non-spherical particles would test how general the shortfall signature is."],"forward_implications":["For a fixed packing fraction, sigma_SJ can be obtained from steady-state rheology alone, avoiding the need for transient or oscillatory protocols.","sigma_SJ decreases as phi increases, matching the trend reported in transient shear-jamming experiments.","The fitted phi_m ~ 0.56 across all particle sizes, near random loose packing, indicates that stress-induced frictional contacts control the jamming onset.","phi_0 approaches random close packing (about 0.64) for the largest particles and drops for smaller ones, a size dependence the paper attributes to residual surface interactions.","Because the same data also give the shear-thickening onset stress sigma_0 and the stress scale sigma*, one set of flow curves yields both the thickening and the jamming phase boundaries."],"supporting_citations":[{"why":"Supplies the Wyart-Cates model, Eq. (1), that defines the stress-dependent jamming packing fraction phi_J(sigma).","marker":"[32]"},{"why":"Supplies the Krieger-Dougherty relation used to extract phi_J(sigma) from viscosity versus packing fraction data.","marker":"[33]"},{"why":"Established the shear-jammed state through transient measurements; the paper compares its sigma_SJ trend with this work.","marker":"[28]"},{"why":"Provides the stretched-exponential form for f(sigma) and demonstrates broad agreement with the Wyart-Cates model.","marker":"[10]"},{"why":"Gives the random loose packing value phi_rlp ~ 0.55 used to choose the KD fitting range.","marker":"[38]"},{"why":"Another shear-jamming study via transient response and imaging that supports the interpretation of failures in the solid-like state.","marker":"[30]"},{"why":"Reports sigma_SJ decreasing with phi under transient forcing, the trend the paper reproduces from steady-state data.","marker":"[31]"}],"fun_headline_variants":["Flow curves reveal hidden shear-jamming onset","Steady shear exposes jamming signature","Viscosity shortfall flags jamming","Predicting shear jamming from steady flow","Steady rheology predicts jamming onset"],"cache_read_input_tokens":13952,"weakest_assumption_plain":"The load-bearing premise is that the Krieger-Dougherty formula fitted to the lower packing fractions (phi = 0.45-0.55) remains the correct baseline at higher phi, so the shortfall at phi = 0.58 and 0.60 is a physical consequence of shear-jamming failures rather than an artifact of the fitting range, wall slip, edge fracture, or breakdown of the formula itself.","fun_headline_variants_meta":{"raw":{"variants":["Flow curves reveal hidden shear-jamming onset","Steady shear exposes jamming signature","Viscosity shortfall flags jamming","Predicting shear jamming from steady flow","Steady rheology predicts jamming onset"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000182,"raw_usage":{"total_tokens":1333,"prompt_tokens":993,"completion_tokens":340,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":609,"completion_tokens_details":{"reasoning_tokens":275}},"tokens_in":609,"tokens_out":340,"duration_ms":3667,"temperature":1.0,"reasoning_tokens":275,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:23:34.106845+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same PS/PEG suspensions through an independent transient stress protocol, or image the bulk (not just the boundary) for internal crack and shear-band formation, and compare the measured sigma_SJ(phi) with the steady-flow prediction at phi = 0.58 and 0.60; a mismatch larger than experimental error would falsify the claim that steady flow curves alone locate the SJ boundary.","supporting_citations":[{"cited_title":"Wyart, and M","cited_arxiv_id":null,"evidence_quote":"Supplies the Wyart-Cates model, Eq. (1), that defines the stress-dependent jamming packing fraction phi_J(sigma)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Krieger-Dougherty relation used to extract phi_J(sigma) from viscosity versus packing fraction data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Established the shear-jammed state through transient measurements; the paper compares its sigma_SJ trend with this work."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the stretched-exponential form for f(sigma) and demonstrates broad agreement with the Wyart-Cates model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the random loose packing value phi_rlp ~ 0.55 used to choose the KD fitting range."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Another shear-jamming study via transient response and imaging that supports the interpretation of failures in the solid-like state."},{"cited_title":"Stress controlled rheology of dense suspensions using transient flows","cited_arxiv_id":"1810.11887","evidence_quote":"Reports sigma_SJ decreasing with phi under transient forcing, the trend the paper reproduces from steady-state data."}],"review_version":1}