{"id":"2a240820-1c93-4f66-bcb9-c88137be98e2","arxiv_id":"2507.23573","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Cohesive grains in a sheared granular mixture segregate into layers or stripes, with cluster size and pressure collapsing as c_oC, and a shear-activated Cahn-Hilliard-type free energy model reproduces this layering.","lead":"This paper shows that sticky grains in a sheared mixture can line up into stripes or layers, with cluster size and pressure controlled by the product of sticky grain fraction and stickiness strength. It proposes that this pattern formation behaves like phase separation in molecular mixtures, described by an effective free energy that only acts while the system is being sheared.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The effective free energy is imposed, not derived; the DEM-continuum agreement rests on a scaling collapse of one observable, so the central mechanism is asserted rather than tested.","rationale":"The reader's weakest assumption is exactly the effective-free-energy ansatz, and I agree that this is the most load-bearing concern. The paper provides a plausible analogy and a continuum model that reproduces the DEM layering, but the model's double-well free energy is chosen precisely to produce demixing, and the mobility is chosen to vanish without shear. The DEM-to-continuum correspondence is based on a scaling collapse of ⟨|∇c|^2⟩ as a function of c_oC and of sqrt(K/(4κ)); this is a single observable and does not identify the free energy parameters from the particle-scale forces or the Bond number. In particular, the computation of ΔF_o and ΔF_interface in Fig. 4(a,b) uses the authors' own functional, so the apparent validation of the free-energy competition is circular. The paper's own limitation statements—the model fails at high C where agglomerates become solid and the imposed linear velocity profile breaks down—narrow the regime of validity and reinforce that the mechanism is not yet established. These gaps are addressable: a direct measurement of the segregation flux and its alignment with the chemical-potential gradient would test the gradient-flow structure, while calibrating K and κ from the microscopic interaction would test the free-energy form. Until such tests are done, the correct disposition is CONDITIONAL, not ACCEPT or REJECT. My read does not change the reader's verdict, so I recommend UNCHANGED.","tokens_in":103,"tokens_out":8556,"duration_ms":157394,"concrete_test":"Measure the non-advective segregation flux in the DEM as j = c(1-c)(u_cohesive - u_noncohesive), coarse-grained on the same mesh used for c. Independently compute ∇(δF/δc) from the same concentration field using the proposed free energy, with K and κ either calibrated from the DEM pair potential or treated as free parameters. Then test whether the volume-averaged cosine of the angle between j and -∇(δF/δc) is close to 1 and whether the inferred mobility M = -j·∇(δF/δc)/|∇(δF/δc)|^2 is positive and scales linearly with strain rate. If the flux is not aligned with the chemical-potential gradient, the gradient-flow ansatz is falsified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The continuum model is constructed to produce the observed pattern: Eq. (3) 'forces f_o to have a double well shape' with its maximum at the imposed mean concentration c_o, and the mobility is set to zero at zero strain rate. With these choices, any simulation of Eq. (1) must demix and form layers; the double-well form is not derived from the interparticle force law (Eqs. 9-10) or from the granular Bond number C. The only quantitative link between DEM and continuum is the scaling collapse of the coarse-grained interfacial energy ⟨|∇c|^2⟩ with c_oC (Fig. 4c) and with sqrt(K/(4κ)) (Fig. 4d). But this scaling is observed for a single aggregate observable; it does not determine K or κ from C or c_o, and it would also be produced by many other double-well models, as the authors themselves show for a different free energy in the Supplement. Moreover, the reported DEM 'free energy changes' in Fig. 4(a,b) are evaluated using the authors' own F_o and F_interface (Eq. 3), so the competition between bulk and interface energy is a consequence of any segregation, not an independent test of the ansatz. Since the model cannot fail to produce layers, the observed agreement is a necessary consequence of the construction, and the central mechanistic claim—that granular cohesion maps onto an effective free energy—is not supported by a falsifiable measurement.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript reports DEM simulations of a sheared binary mixture of cohesionless and cohesive grains, characterized by a cohesive grain concentration c_o and a cohesion strength C (granular Bond number). It finds that with increasing c_oC, cohesive grains form percolating stripes or layers rather than distributed agglomerates, and that both the agglomerate size ℓ/L and the average normal stress collapse onto c_oC. The authors propose an effective free-energy ansatz: a Cahn–Hilliard-type concentration equation with flux j = -M(γdot)∇(δF/δc), where F has a double-well bulk term and a gradient term, and the mobility M(γdot) = M0γdot vanishes at zero shear. The continuum model reproduces steady-state layers, and the paper reports a correspondence between c_oC and the critical wavenumber sqrt(K/(4κ)) based on the scaling of ⟨|∇c|²⟩ in the DEM and continuum simulations. A threshold behavior at low C is attributed to K ~ C - C_th. The paper also reports transient pinch-off of a single agglomerate as a qualitative test and acknowledges failure at very high C.","tokens_in":11021,"tokens_out":7205,"duration_ms":80033,"significance":"If the proposed effective-free-energy mechanism were validated, it would provide a useful conceptual bridge between granular segregation and equilibrium phase separation, and it could offer a practical route to predicting layer formation in cohesive granular flows. The DEM data collapse onto c_oC is an interesting and potentially robust empirical result, and the paper is transparent about the ansatz nature of the model, with the full DEM contact model provided in the supplement. However, as it stands, the continuum model is constructed in such a way that it cannot fail to phase-separate under shear, and the quantitative evidence linking it to the DEM is a single scaling observable. The central claim therefore needs a stronger, falsifiable test before the correspondence can be regarded as established. The paper also provides no code or data availability statement, which limits reproducibility.","major_comments":[{"comment":"The model cannot fail to produce layering. In Eq. (3) the bulk free energy is explicitly forced to have a double-well shape with f''(c_o) < 0, and the mobility M(γdot) = M0γdot means that any nonzero shear activates the Cahn–Hilliard instability. The steady-state stripes in Fig. 3(b,c) are therefore a necessary consequence of the construction rather than a test of the proposed physical mechanism. To make the central claim load-bearing, the authors should provide an independent prediction—for example, the layer spacing or the full concentration profile from the DEM, or a calibrated relation between (c_o, C) and (K, κ) obtained outside the scaling in Fig. 4—and then compare it with the continuum model.","section":"Main text, Eqs. (1)–(3)"},{"comment":"The DEM estimates of 'free energy changes' do not provide an independent test. ΔF_o and ΔF_interface are evaluated with the authors' own F_o and F_interface of Eq. (3), so any segregated configuration will by construction decrease the double-well bulk term and increase the gradient term. The observed competition between the two terms in Fig. 4(a,b) is thus a property of the chosen functional, not evidence that the DEM obeys that functional. A null test—for example, a comparison with a random or non-phase-separating concentration field at the same c_o—is needed before this can be read as validation.","section":"Fig. 4(a,b) and Eqs. (5)–(6)"},{"comment":"The claimed correspondence c_oC ↔ sqrt(K/(4κ)) rests on the observation that ⟨|∇c|²⟩ is linearly increasing in both variables. This is a one-observable scaling match, not a quantitative mapping: the DEM control parameter c_oC is dimensionless, while sqrt(K/(4κ)) has the dimension of inverse length, and no conversion factor or calibration relation is given. Moreover, the Supplement shows that a different double-well free energy (Eq. 24) produces the same qualitative behavior, so this scaling is not discriminating. The authors should state what observable would be needed to falsify the correspondence, or calibrate K and κ independently.","section":"Fig. 4(c,d) and critical wavenumber k_c"},{"comment":"The paper's own limitation statement—that for C ~ 100 the agglomerates behave almost like solid objects and the imposed velocity profile u = γdot z i fails—restricts the domain of validity of the continuum model. This limitation is acknowledged in the text and in Supplement Fig. 9, but it should be incorporated into the central claim rather than appended as an aside, because it implies that the model is applicable only in an intermediate cohesion range where the flux ansatz is most likely to be correct.","section":"Eq. (2) and final paragraph"}],"minor_comments":[{"comment":"Use c_o consistently for the concentration parameter; the printed text frequently uses 'co' (e.g., Eq. (7) and Fig. 2), which is confusing next to the concentration field c.","section":"Throughout"},{"comment":"The statement ℓ/L ∼ c_oC should include the prefactor, the fit range, and the uncertainty; as printed the reader cannot tell whether the collapse is linear or merely monotonic.","section":"Fig. 2(b)"},{"comment":"The statement that 'K in the continuum model is akin to C - C_th' is an analogy, not a measurement; K is not directly measured and C_th is not defined quantitatively. Please label it as such and, if possible, report C_th from the threshold in Fig. 4(e).","section":"Main text after Fig. 4(e)"},{"comment":"The supplement's validation figure is described as replicating standard results, but no quantitative comparison (e.g., Bagnold scaling exponent or velocity-profile residual) is given; a brief quantitative measure would strengthen the DEM section.","section":"Supplement, Fig. 6"},{"comment":"No code or data availability statement is included. Given that the DEM parameter table and interaction model are described in detail, releasing the simulation or analysis scripts would substantially improve reproducibility.","section":"Data availability"},{"comment":"The abstract and conclusion claim that the free-energy approach closely reproduces the layering, while the high-C failure appears only in the final paragraph; consider stating the moderate-cohesion range of applicability in the abstract.","section":"Abstract and conclusion"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely of interest to granular/soft-matter readers, and the DEM collapse onto c_oC is a useful empirical observation. My main concern is that the effective free energy is simultaneously the explanatory mechanism and the object being tested, so the current evidence is partly circular. I do not see this as grounds for rejection, but the authors should be asked to add a falsifiable prediction (e.g., layer wavelength scaling with C, or an independently calibrated K(C,c_o) and κ(C,c_o)) before the correspondence can be considered established. The paper's claims are more modest than the abstract suggests once the ansatz and high-C limitation are read carefully."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The one thing worth knowing about this paper is the DEM observation: cohesive grains in a sheared binary mixture form percolating layers, and both cluster size and pressure collapse cleanly as c_oC. That collapse is new, looks convincing, and is likely to survive scrutiny. The continuum model is a different story—it is a Cahn-Hilliard ansatz with a forced double-well potential and shear-activated mobility, and it reproduces layering without actually testing the mechanism.\n\nWhat the paper does well: the empirical section is solid. The collapse in Fig. 2 is clean, the coarse-graining procedure is standard, and the authors are honest that the free energy is an ansatz. They even show an alternative free energy in the supplement, which is good practice. The model does capture the steady-state layering and some transient breakup at moderate C, so as a qualitative demonstration it works.\n\nThe load-bearing claim—that granular cohesion maps onto an effective free energy—rests on a model that cannot fail to phase-separate. The double well is imposed, not derived from the interparticle forces; mobility is zero without shear, so the homogeneous state is unstable only under driving, and the layers are a consequence of construction. The quantitative link between DEM and continuum is the scaling of interfacial energy with c_oC and with sqrt(K/4κ), which is a single aggregate observable and does not determine K or κ from C and c_o. The ΔF measurements in Fig. 4(a,b) are computed using the authors' own functional, so they are not independent evidence for the mechanism. The paper itself concedes the model breaks down at high C, where agglomerates behave like solid objects and the imposed linear velocity profile is no longer valid. These are real gaps, but the paper is transparent about them, which is why I still read this as a serious attempt rather than a hand-wave.\n\nWho gets value from this? Granular physics and powder-processing readers will take away the empirical collapse as a design rule. The continuum model is a reasonable starting point, but to move from ansatz to mechanism the authors would need to derive or independently measure K, κ, and M from microscopic parameters, make falsifiable predictions (e.g., layer spacing dependence on shear rate or system size), and provide code/data. The paper deserves a serious referee, not a desk reject; I would send it to review and expect a revision that tightens the model-observation correspondence. I would cite the DEM collapse if I were working in segregation, but I would not yet cite the free energy mapping as established.","headline":"The DEM collapse is the real result here; the Cahn-Hilliard model is a promising but unproven ansatz that should not be mistaken for a mechanism yet.","tokens_in":11548,"tokens_out":1737,"would_cite":true,"duration_ms":21614,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["45.70.-n"],"model":"deepseek-v4-flash","headline":"A sheared mixture of cohesive and non-cohesive grains forms percolating stripes once the product of cohesive-grain concentration and cohesion strength crosses a threshold, and the stripe formation can be predicted from a shear-activated…","keywords":["cohesive granular mixtures","granular segregation","pattern formation","Cahn-Hilliard dynamics","effective free energy","discrete element method","shear flow","phase separation"],"falsifier":"Stop the shear after layers form and watch the concentration field. The ansatz $M=M_0\\dot\\gamma$ predicts $j=0$ at $\\dot\\gamma=0$, so the layer pattern should freeze in place; any coarsening, sharpening, or dissolution of the stripes after the top wall stops would falsify the mobility assumption. A second check is to increase the bed height $L_z$ by a factor of two and verify that the number of layers doubles as required by the critical wavenumber $k_c$.","tokens_in":10436,"feed_emoji":"🌾","tokens_out":7362,"duration_ms":71092,"temperature":0.7,"pith_summary":"The paper aims to establish that cohesion in a sheared granular mixture, normally a lump-forming ingredient, can drive the mixture to segregate into percolating layers or stripes once the cohesive-grain concentration $c_o$ and cohesion strength $C$ are large enough. It reports that the average agglomerate size and the average normal stress collapse onto one curve when plotted against the product $c_oC$, with percolation setting in near $c_oC \\approx 2$. The central proposal is that interface formation between cohesive and non-cohesive grains behaves like phase separation in a binary molecular mixture, governed by an effective free energy whose mobility vanishes without external shear. A continuum model built on this idea reproduces the steady-state layering, and the microscopic control parameter $c_oC$ is mapped to the continuum parameter $\\sqrt{K/(4\\kappa)}$ that sets the number of layers. If right, the work gives a systematic way to construct segregation fluxes for cohesive granular mixtures.","feed_headline":"Sticky grains form stripes as cohesion and concentration climb","feed_subtitle":"A shear-activated double-well free energy matches DEM layer patterns and collapses the data onto one curve.","key_machinery":"The carrying object is a double-well effective free energy functional, $F[c] = F_o[c] + F_{\\rm interface}[c]$, whose bulk density $f_o(c) = K[c_o c^2/2 - (1+c_o)c^3/3 + c^4/4]$ has minima at $c=0$ and $c=1$ and a maximum at $c=c_o$, plus a gradient penalty $\\frac{1}{2}\\kappa(\\nabla c)^2$. The segregation flux $j=-M_0\\dot\\gamma\\,\\nabla(\\delta F/\\delta c)$ has mobility proportional to strain rate, so the free energy exerts no dynamics at rest; its linear stability gives a critical wavenumber $k_c=\\sqrt{K/(4\\kappa)}$, which sets the layer count in a system of size $2\\pi$ and is matched against $c_oC$ from the particle simulations.","core_discovery":"The discovery is that increasing $c_o C$ switches the cohesive component from distributed, irregular agglomerates to percolating stripes in plane shear, and that this transition is quantitatively described by a Cahn-Hilliard-type effective free energy. The authors construct $F[c] = \\int [K(c_o c^2/2 - (1+c_o)c^3/3 + c^4/4) + \\frac{1}{2}\\kappa(\\nabla c)^2]\\,dr$, impose a segregation flux $j = -M(\\dot\\gamma)\\nabla(\\delta F/\\delta c)$ with $M(\\dot\\gamma)=M_0\\dot\\gamma$, and show that the steady-state solutions of the resulting advection-diffusion equation form layers. The DEM measurements of interfacial energy $\\langle|\\nabla c|^2\\rangle$ scale linearly with $c_oC$, and the continuum model gives the same linear scaling with $\\sqrt{K/(4\\kappa)}$; the paper takes this correspondence as evidence that the double-well free energy is the right macroscopic description, activated only by shear.","pith_inferences":["Beyond the paper, the same construction should be testable for segregation driven by size or friction differences: if mobility proportional to strain rate is the only ingredient needed, stripes in those systems should also follow a critical-wavenumber scaling set by an effective free-energy curvature.","Beyond the paper, the correspondence between $c_oC$ and $\\sqrt{K/(4\\kappa)}$ suggests the dimensionless product is a practical control parameter for experiments, letting one dial layer spacing by changing liquid content or cohesive coating at fixed total concentration.","Beyond the paper, because the polynomial double well and the logarithmic free energy in the supplementary materials give equivalent critical wavenumbers, the specific functional form is probably not important; what matters is the double-well curvature near $c_o$, which may make the prediction robust to the microscopic cohesion model."],"forward_implications":["For $c_o C \\lesssim 2$, cohesive grains form agglomerates whose normalized size grows roughly linearly with $c_o C$; beyond that, agglomerates percolate and stripes span the system.","The continuum model reproduces steady-state layering from the double-well flux, including the balance between $\\partial_z^2 c$, $(\\partial_z c)^2$, and $\\partial_z^4 c$ terms in the one-dimensional steady state.","Average interfacial energy is a linear function of $c_o C$ in particle simulations and of $\\sqrt{K/(4\\kappa)}$ in the continuum model, giving a parameter map between the two descriptions.","There is an effective threshold cohesion $C_{\\rm th}$: below it the interfacial energy stays negligible, matching a negative bulk curvature $K<0$ in the free energy, for which the homogeneous state is stable.","For moderate cohesion the flux also captures transient pinchoff during breakup of a single agglomerate, though at very high $C$ the agglomerate acts like a solid and the simplified linear velocity profile breaks down."],"supporting_citations":[{"why":"Supplies the Cahn-Hilliard gradient free energy and interfacial-cost term that the paper's $F[c]$ is built on.","marker":"[24]"},{"why":"Supplies the phase-separating-fluid framework whose flux form is adapted to the sheared granular mixture.","marker":"[25]"},{"why":"Provides the segregation-flux formulation that the paper adapts by deriving the flux from a free-energy derivative.","marker":"[22]"},{"why":"Reviews granular segregation mechanisms and flux construction, giving the baseline that the proposed effective free-energy flux extends.","marker":"[23]"},{"why":"Demonstrates that adding cohesion can switch granular mixing to segregation, motivating the study of cohesion-driven patterns.","marker":"[1]"},{"why":"Validates the DEM velocity-profile setup used in the simulations.","marker":"[26]"}],"fun_headline_variants":["Cohesive grains stripe up as cohesion and concentration rise","Shear activates free energy that orders sticky grains into layers","Cahn-Hilliard model captures granular layering under shear","Sticky grains self-organize into stripes under plane shear","Cohesion concentration product collapses granular layering data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that sheared granular mixtures can be described by an effective double-well free energy at all, with dynamics switched on only by shear; if the real grain-scale motion cannot be represented by such a free energy, the predicted layers are built into the assumed shape rather than derived from the physics.","fun_headline_variants_meta":{"raw":{"variants":["Cohesive grains stripe up as cohesion and concentration rise","Shear activates free energy that orders sticky grains into layers","Cahn-Hilliard model captures granular layering under shear","Sticky grains self-organize into stripes under plane shear","Cohesion concentration product collapses granular layering data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00069,"raw_usage":{"total_tokens":3122,"prompt_tokens":937,"completion_tokens":2185,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":553,"completion_tokens_details":{"reasoning_tokens":2106}},"tokens_in":553,"tokens_out":2185,"duration_ms":17026,"temperature":1.0,"reasoning_tokens":2106,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T10:37:48.116019+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Stop the shear after layers form and watch the concentration field. The ansatz $M=M_0\\dot\\gamma$ predicts $j=0$ at $\\dot\\gamma=0$, so the layer pattern should freeze in place; any coarsening, sharpening, or dissolution of the stripes after the top wall stops would falsify the mobility assumption. A second check is to increase the bed height $L_z$ by a factor of two and verify that the number of layers doubles as required by the critical wavenumber $k_c$.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the phase-separating-fluid framework whose flux form is adapted to the sheared granular mixture."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the segregation-flux formulation that the paper adapts by deriving the flux from a free-energy derivative."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reviews granular segregation mechanisms and flux construction, giving the baseline that the proposed effective free-energy flux extends."},{"cited_title":"Li and J","cited_arxiv_id":null,"evidence_quote":"Demonstrates that adding cohesion can switch granular mixing to segregation, motivating the study of cohesion-driven patterns."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Validates the DEM velocity-profile setup used in the simulations."}],"review_version":1}