{"id":"e5bc10ea-8ab0-444a-a3ed-f50e36747b7f","arxiv_id":"2505.22256","paper_version":5,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A local, density-dependent solid-fluid adhesion parameter and an eighth-order boundary reconstruction reduce spurious currents and remove mass-transfer artifacts in immiscible pseudopotential LBM.","lead":"The authors propose a tweak to how lattice Boltzmann simulations handle the attraction between a fluid and a solid wall, making the strength depend on local fluid composition. The change is reported to suppress numerical artifacts at wetting boundaries and to widen the range of contact angles the method can simulate.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The curved-boundary second-layer copying rule (Sec. II.D, Fig. 2(b3)) is untested and underpins every curved-surface contact-angle result; without a grid/curvature-convergence check the 10–165° claim is not yet established.","rationale":"The paper has real independent support in the planar/straight-wall benchmarks: co-current Poiseuille and Couette profiles agree with analytical solutions below 1.84%, flat-substrate contact angles match experiments to a mean absolute deviation of 2.1°, and the immiscible-displacement results agree with Kang et al. within about 5%. The local-adhesion idea is also plausible and is benchmarked against Li's scheme. However, the unique curved-boundary contribution rests entirely on the second-layer copying rule, and the paper offers no convergence or curvature-sensitivity evidence for it. This matches the reader's weakest assumption exactly. Since the central claims are numerical claims about curved geometries, the missing test is not a minor addition; it is a condition that should be satisfied before the wide-range 10–165° statement is treated as established. The reader's conditional verdict already captures this, so no verdict change is needed.","tokens_in":18509,"tokens_out":5408,"duration_ms":57530,"concrete_test":"Recompute the cylindrical-surface benchmark (Sec. III.B) at fixed lattice spacing for R = 35, 70, and 140 (and R = 50 vs 100 for the sphere in Sec. III.E), and additionally at R = 70 with doubled resolution/domain, using both the proposed copying rule and a non-copying reference boundary treatment (e.g., second-order interpolated ghost nodes). If the extracted θ(λ) curve or the classification of a mass-transfer layer shifts by more than roughly 2° when R/resolution changes, or differs measurably from the reference treatment, the copying rule is not converged and the wide-range claim needs to be re-scoped.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The improved scheme's strongest claims—curved-surface contact angles from 10° to 165° and 'complete elimination' of the unphysical mass-transfer layer—are all evaluated on cylindrical or spherical substrates. On those substrates the 8th-order interaction stencil needs data on second-layer nodes that are outside the fluid. The paper fills them by copying the corresponding first-layer node (Sec. II.D, Fig. 2(b3), Table I). This is a local-uniformity assumption: it treats the macroscopic fields at a fluid node one lattice spacing from the wall as representative of a node two spacings away, even where wall curvature changes the local surface-normal direction. The paper gives no grid-convergence study, no variation of cylinder/sphere radius at fixed resolution, and no comparison with an independent boundary closure (e.g., ghost nodes, interpolation). Because all quantitative claims (contact angle vs λ, spurious-current statistics, density stability) are measured on curved geometries, a bias in this copying rule would propagate into the central claim; the absence of a sensitivity test is therefore load-bearing, not a cosmetic omission.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes an improved solid-fluid interaction scheme for immiscible pseudopotential lattice Boltzmann simulations. Instead of a constant adhesion parameter, Eqs. (11) and (12) define a local interaction parameter based on the normalized effective density, with piecewise interpolation controlled by a threshold δ = 0.8. The scheme is combined with an eighth-order isotropic interaction stencil and a boundary treatment that copies first-layer fluid-node values to missing second-layer nodes at curved interfaces (Sec. II.D). The proposed scheme is tested on four benchmarks: co-current Poiseuille and Couette flow, static contact angles on cylindrical and spherical surfaces, droplet dynamics past a square obstacle in a microchannel, and immiscible displacement in a channel and in a porous-media-like geometry. The central claims are that the scheme eliminates the unphysical mass-transfer layer near solid boundaries, extends the accessible contact-angle range to roughly 10°–165°, and reduces spurious currents relative to the original scheme.","tokens_in":18747,"tokens_out":5185,"duration_ms":52392,"significance":"If the claims are substantiated, this is a useful contribution to pseudopotential LBM practice: the scheme is simple, uses a single calibration parameter, and is benchmarked against analytical velocity profiles (relative error below 1.84%), against Kang et al.'s displacement data (errors below 5%), and against a dedicated experiment (mean absolute deviation 2.1°). The manuscript also provides implementation details in an appendix and a source-code link. The main weakness is that the headline claims are measured on curved geometries where the boundary treatment relies on a copying rule that is not subjected to any sensitivity or convergence test; the significance is therefore conditional on additional evidence.","major_comments":[{"comment":"The curved-boundary copying rule is load-bearing for the paper's central claims. With the eighth-order stencil, the interaction range needs data on second-layer nodes outside the fluid, and the paper fills those nodes by copying information from corresponding first-layer nodes. This is a local-uniformity assumption over two lattice spacings, and it is used in all curved-surface benchmarks (Secs. III.B and III.E). The manuscript gives no grid-convergence study, no variation of cylinder or sphere radius at fixed resolution, and no comparison with an independent boundary closure such as ghost nodes or interpolation. Because the contact-angle range (10–165°) and the claimed elimination of the mass-transfer layer are measured on curved geometries, the absence of a sensitivity test is load-bearing; either add such tests or qualify the headline claims.","section":"Section II.D, Fig. 2(b3), Table I"},{"comment":"The threshold δ = 0.8 is hand-set by matching an interface width of about five lattice grids, but no δ-sensitivity study is reported. Since δ controls the width of the piecewise interpolation interval for the local adhesion parameter, the reported contact-angle range and the suppression of the mass-transfer layer could depend on this choice. A short sweep of δ at a fixed λ, or a stated criterion for selecting δ, is needed to show that the results are robust.","section":"Section III.B, Eq. (11) and the paragraph defining δ"},{"comment":"The correlation θ = -13.76λ² + 94.62λ + 9.47 is presented as a predictive tool, but it is a polynomial fit to the authors' own simulation data. The paper should state explicitly that this is an empirical fit, report its fit quality and range of validity, and avoid giving the impression that the 10–165° range is a parameter-free consequence of the scheme. This matters because Table III uses the range as a headline comparison.","section":"Section III.B, Fig. 5(b)"},{"comment":"The claim of 'complete elimination' of unphysical mass-transfer layers is supported only by visual inspection of density contour plots. No quantitative metric (such as thickness or amplitude of the dissolved-density layer, or a mass-flux measure) is defined, and Fig. 8 shows localized spurious-current maxima at the contact line. Please define a measurable criterion for the mass-transfer layer and quantify the reduction, or soften the claim to the demonstrated level of suppression.","section":"Section III.B, Fig. 5(a), and Section IV"}],"minor_comments":[{"comment":"There are numerous typographical errors and garbled equations (for example, Eq. (1) has missing superscripts, Eq. (11) contains unclear definitions of the s and t coefficients, and the text includes 'boudnary', 'V olume of Fluid', and 'k ∈ 11, 2}'). A careful proofread is needed.","section":"Throughout"},{"comment":"The text states a 'solid cylinder of radius R=50' for the spherical-surface test; this should read 'sphere'.","section":"Section III.E"},{"comment":"Table III lists Li's scheme as also achieving a 10–165° contact-angle range, so the improved scheme's claimed extension of the operating range is relative to the original scheme only; the text should make this comparison explicit.","section":"Table III"},{"comment":"The abstract and introduction state a 33% reduction in average spurious currents, while the conclusion states 40–50% in hydrophilic regimes and 30–40% in hydrophobic regimes; these numbers should be reconciled or the conditions for each figure stated.","section":"Abstract and Section IV"},{"comment":"The experimental comparison is limited to flat substrates, whereas the numerical benchmarks are on curved surfaces; the paper should note explicitly that the experimental validation does not exercise the curved-boundary copying rule.","section":"Section III.B, Fig. 7"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The paper is within the journal's scope and the empirical benchmarking is useful. My main concern is that the headline claims rest on an untested curved-boundary closure; this is fixable with additional convergence and sensitivity studies and with more qualified language in the conclusions. I do not see evidence of citation problems or hidden limitations, and the manuscript's self-described scope is reasonable. I therefore recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a look if you work on pseudopotential LBM contact angles. The paper offers a simple, single-parameter way to set wettability that avoids the mass-transfer layer seen in the original Martys-Chen scheme and in Li et al. 2019. What's new: the piecewise local adhesion parameter based on normalized effective density (Eqs. 10-12), and the second-layer copying rule for 8th-order isotropy at curved boundaries (Sec. II.D). Neither is in the prior work, and the improvement is plausible, not just cosmetic.\n\nThe benchmarking is genuinely good. Co-current flow matches analytical velocity profiles to under 1.84% error across three contact angles; the displacement case agrees with Kang et al. within 5%; the flat-surface contact angles reproduce experiments to within 2.1 degrees mean absolute deviation. That's real evidence the scheme works, at least on flat and mildly curved walls.\n\nThe soft spots are in the curved-boundary claims, not the flat ones. The second-layer copying rule is introduced as a way to handle 8th-order stencils at non-straight walls, and it is then used for every cylinder and sphere contact angle in the paper. But there's no grid-convergence test, no variation of cylinder or sphere radius at fixed resolution, and no comparison with an independent boundary closure. That matters because the 10-165 degree range and the 'complete elimination' claim are demonstrated on curved substrates. If the copying rule is biased, those numbers shift. It may well be fine - local uniformity over two lattice spacings is a reasonable guess - but the absence of a sensitivity test is a real gap, not a nitpick.\n\nA few smaller issues: delta=0.8 is hand-set with a width-matching rationale but no sensitivity study; the theta-lambda correlation in Fig. 5(b) is a polynomial fit to the authors' own simulation data and is labeled 'predictive,' which is an overstatement; and the source code is provided as a bare repository string without a commit hash. None of these sink the paper. The central idea holds up better than the conclusion suggests.\n\nThe paper deserves a serious referee. A revision should add a curvature/grid-convergence check for the copying rule and a short delta-sensitivity scan. If those come out clean, the scheme is a solid contribution. I'd send it to review.","headline":"A useful local-adhesion fix for immiscible pseudopotential LBM, with solid benchmarks, but the curved-boundary copying rule is under-tested and the strongest claims outrun the evidence.","tokens_in":19256,"tokens_out":3668,"would_cite":false,"duration_ms":32780,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["76M28","76D45","76Txx"],"pacs":["47.11.-j"],"model":"deepseek-v4-flash","headline":"A local adhesion parameter lets lattice Boltzmann wetting simulations reach contact angles from 10 to 165 degrees.","keywords":["Lattice Boltzmann method","Pseudopotential model","Immiscible multiphase flow","Solid-fluid interaction","Wetting behavior","Contact angle","Spurious currents","Curved boundary treatment"],"falsifier":"Run the static-droplet-on-a-cylinder benchmark at the same physical settings with cylinder radii of 35, 70, and 140 lattice units, and record the measured contact angle plus the minimum fluid density near the wall. If the contact angle drifts with radius or the mass-transfer layer reappears at the smallest radius, then the copy rule, not the local adhesion parameter, is responsible for the curved-surface results.","tokens_in":18286,"feed_emoji":"💧","tokens_out":8298,"duration_ms":71663,"temperature":0.7,"pith_summary":"This paper proposes an improved way to model the attraction between a fluid and a solid wall in the pseudopotential lattice Boltzmann method, a mesoscopic scheme for simulating immiscible two-phase flows. Instead of applying one constant adhesion strength near every wall node, the improved scheme computes a local adhesion parameter from the normalized effective density at each lattice point, interpolating smoothly across the diffuse interface. The paper argues that this localized parameter restores mechanical stability at the wall, removing the unphysical mass-transfer layer that the constant-parameter scheme produces at low contact angles. As a result, the claimed usable contact-angle range widens from roughly 33–120 degrees to about 10–165 degrees, with lower spurious currents and no extra calibration burden beyond a single strength coefficient. The paper supports the claim with static droplets on cylinders and spheres, droplets passing square obstacles, immiscible displacement, and co-current flow benchmarks.","feed_headline":"Lattice Boltzmann wetting fix reaches contact angles 10 to 165 degrees","feed_subtitle":"Replacing the constant wall-adhesion parameter with a local one removes the unphysical mass-transfer layer near solid surfaces.","key_machinery":"The load-bearing object is the local adhesion parameter $G_{w,1}(\\rho_e)$, built from the normalized effective density $\\rho_e=(\\rho_1-\\rho_2)/(\\rho_1+\\rho_2)$. For $|\\rho_e|>\\delta$ the parameter saturates to the bulk value $G_{w,1}$ or to $G_{w,2}=G_{12}$; inside the interface, quadratic interpolation functions $g_1(\\rho_e)$ and $g_2(\\rho_e)$ smooth the transition, with $\\delta=0.8$ chosen to match an interface width of about five lattice spacings at $G_{12}=0.17$. The second mechanism is the eighth-order isotropic force stencil, whose two-layer interaction range leaves second-layer nodes undefined near walls; the paper fills those nodes by copying the information from the geometrically corresponding first-layer node, which is what makes curved boundaries work in this scheme.","core_discovery":"This paper claims that the failure mode of the original Martys–Chen solid-fluid interaction—an unphysical layer through which one fluid appears to dissolve into the other near the wall—is caused by applying a uniform adhesion parameter regardless of local phase composition. The improved scheme defines an effective density $\\rho_e=(\\rho_1-\\rho_2)/(\\rho_1+\\rho_2)$ and chooses $G_{w,1}$ from a piecewise function of $\\rho_e$, with a transition width $\\delta$ matched to the diffuse interface width. That makes the wall force respond locally to which fluid dominates and to how close the node is to the interface, so the interface stays sharp at the boundary. The paper reports that the scheme attains static contact angles from about 10 to 165 degrees, eliminates the mass-transfer layer, cuts average spurious currents by roughly half relative to the original scheme, and conserves mass. It also introduces a boundary reconstruction for the eighth-order isotropic interaction stencil: the second-layer fluid-node values are copied from the corresponding first-layer nodes, allowing curved walls to be handled without ghost nodes.","pith_inferences":["Editorial inference: the same local-adhesion construction could be ported to other diffuse-interface lattice Boltzmann variants by replacing the constant wall coupling with a function of the local order parameter.","Editorial inference: the claimed complete elimination of the mass-transfer layer is demonstrated at one interface width ($\\delta=0.8$, $G_{12}=0.17$); retuning $\\delta$ for other surface tensions or density ratios would be needed to confirm universality.","Editorial inference: the copying rule for second-layer nodes is plausible but untested for high curvature; a grid-convergence study varying cylinder radius would show whether the boundary reconstruction itself introduces a curvature-dependent error.","Editorial inference: the operating-range comparison across schemes is made on static equilibrium droplets; dynamic contact angles under strong flow or high capillary number may reveal larger differences than the static benchmarks."],"forward_implications":["Contact angles below about 30 degrees and above about 120 degrees become accessible without the mass-transfer artifact, so strongly hydrophilic and strongly hydrophobic microfluidic and porous-media flows can be simulated.","Average spurious currents near the wall drop by roughly half in hydrophilic regimes and by about a third in hydrophobic regimes, improving numerical stability for body-force-driven flows.","The scheme retains the simple single-parameter calibration of the original method, since only the strength coefficient $\\lambda = G_{w,1}/G_{w,2}$ needs to be tuned.","The second-layer copying rule extends the eighth-order isotropic stencil to curved no-slip surfaces, making the improved scheme usable on cylinders and spheres without ghost nodes.","Quantitative benchmarks—velocity profiles, finger length, width, slip distance in displacement, and droplet height-to-diameter ratios—stay within about 5% of analytic or reference results."],"supporting_citations":[{"why":"Introduces the constant-adhesion-parameter solid-fluid force that the improved scheme replaces.","marker":"[18]"},{"why":"Provides the mechanical-stability analysis identifying instability of constant adhesion at the wall and the resulting unphysical layers.","marker":"[23]"},{"why":"Baseline curved-boundary contact-angle scheme; the improved scheme is compared against it and claims to remove its residual mass-transfer layer.","marker":"[46]"},{"why":"High-order isotropy multirange pseudopotential; source of the reported unphysical mass-transfer layer and basis for the eighth-order stencil.","marker":"[3]"},{"why":"Gives the contact-angle approximation for Shan-Chen multicomponent models that justifies taking $G_{w,2}=G_{12}$.","marker":"[30]"},{"why":"Supplies the forcing scheme used in the evolution equation for the force coupling.","marker":"[31]"},{"why":"Provides the immiscible-displacement benchmark used for quantitative comparison of finger length, width, and slip distance.","marker":"[50]"},{"why":"Provides the Zou-He velocity boundary conditions used at inlet and outlet in the droplet dynamics and displacement cases.","marker":"[5]"}],"fun_headline_variants":["LBM wetting fix kills mass-transfer layer, hits 10-165° contact","Local wall adhesion in LBM stops fake mass transfer, widens angles","Pseudopotential LBM upgrade: sharp interfaces on curved walls, 10-165°","Eighth-order LBM wetting: local adhesion kills spurious currents, 10-165°","Improved LBM solid-fluid force hits 10-165° contact, no mass leak"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The curved-boundary results stand on the assumption that the flow is locally uniform enough that copying first-layer node values to second-layer nodes two lattice spacings away is accurate; the paper reports no grid-convergence or curvature-sensitivity test of this rule.","fun_headline_variants_meta":{"raw":{"variants":["LBM wetting fix kills mass-transfer layer, hits 10-165° contact","Local wall adhesion in LBM stops fake mass transfer, widens angles","Pseudopotential LBM upgrade: sharp interfaces on curved walls, 10-165°","Eighth-order LBM wetting: local adhesion kills spurious currents, 10-165°","Improved LBM solid-fluid force hits 10-165° contact, no mass leak"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000649,"raw_usage":{"total_tokens":2983,"prompt_tokens":954,"completion_tokens":2029,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":570,"completion_tokens_details":{"reasoning_tokens":1917}},"tokens_in":570,"tokens_out":2029,"duration_ms":16874,"temperature":1.0,"reasoning_tokens":1917,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:11:40.404099+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the static-droplet-on-a-cylinder benchmark at the same physical settings with cylinder radii of 35, 70, and 140 lattice units, and record the measured contact angle plus the minimum fluid density near the wall. If the contact angle drifts with radius or the mass-transfer layer reappears at the smallest radius, then the copy rule, not the local adhesion parameter, is responsible for the curved-surface results.","supporting_citations":[],"review_version":1}