{"id":"3c26341a-1a21-468d-9896-07e3d6b2e0cb","arxiv_id":"2607.25444","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A local geometric ghost-node wetting boundary condition for conservative Allen-Cahn lattice Boltzmann simulations imposes contact angles accurately and matches droplet spreading, impact, and orifice-passage benchmarks.","lead":"This paper presents a numerical method that makes computer simulations of droplets on solid surfaces respect the correct contact angle—how strongly the liquid wets the surface—inside a fast lattice Boltzmann solver. It matters for engineering-scale predictions in printing, microfluidics, oil recovery, and porous-media flows where wetting controls the path of liquids.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Wall-normal reconstruction is the load-bearing assumption; it is only validated on planar walls and one symmetric edge, so the complex-geometry claim rests on an untested geometric input.","rationale":"The reader identified the same weakest assumption: the reconstructed wall normal and donor extrapolation. My stress-test concurs and sharpens it: the normal reconstruction (Eqs. 36-38) is a purely geometric input that can be checked directly against analytic normals, and the current validation does not exercise the regimes where it is most likely to fail. The fact that the authors explicitly call for broader assessment supports the concern. However, no evidence yet shows the normal is wrong; a concrete geometric test could either confirm or refute the concern. The reader's conditional verdict already reflects this uncertainty, so my analysis does not change it. The paper's static benchmarks on planar walls and the symmetric orifice are credible, but they cannot license the complex-geometry claim without the proposed test.","tokens_in":16178,"tokens_out":7404,"duration_ms":78738,"concrete_test":"Compute n_w via Eqs. (36)-(38) for every solid node adjacent to fluid on a voxelized sphere of radius R=20 (D3Q27 lattice). Compare with the analytic inward normal (from fluid to solid), i.e., the vector from the solid node to the sphere center. Record the angular error distribution (mean and 95th percentile). Repeat for R=10, 20, 40 and for a 45°-inclined plane. If the mean angular error exceeds 3°, the ghost-node wetting condition will impose contact angles with comparable systematic error on curved surfaces, directly falsifying the complex-geometry claim. This test isolates the geometric input from any dynamics and settles whether the concern lands.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the ghost-node wetting BC is accurate on complex geometries rests entirely on the wall-normal reconstruction of Eqs. (36)-(38). This normal is computed as a weighted sum of discrete lattice links from a solid node to its fluid neighbors. For a planar wall aligned with the lattice, the reconstruction is exact. For curved or arbitrarily oriented walls, the discrete sum is biased by the lattice discretization; at sharp edges and corners, the fluid-neighbor set is asymmetric and the resulting normal can deviate markedly from the true geometric orientation. The donor extrapolation of Eq. (46) then propagates this error directly into the ghost phase-field value and hence into the imposed contact angle. The only non-planar validation is the axisymmetric sharp-edged orifice of Sec. III.D, whose edges are aligned with the coordinate axes; it does not test oblique edges, stair-stepped roughness, or curved surfaces. The authors concede in the Conclusion that 'a broader assessment on curved and rough surfaces would be required,' but without such evidence the claim of applicability to complex geometries is unsupported. This is a correctness risk: if the reconstructed normal is systematically wrong on such geometries, the effective contact angle is wrong and the method fails in the very regime it claims to address.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a local geometric wetting boundary condition for a conservative Allen–Cahn-based lattice Boltzmann (CAC-LB) framework. The wall normal is reconstructed locally from fluid–solid occupancy (Eqs. 36–38), a donor fluid node is selected by alignment with this normal, and a ghost phase-field value is computed by a first-order extrapolation with an interface-localization factor (Eqs. 39–47). A separate global correction redistributes any phase-field mass imbalance over the diffuse interface (Eqs. 48–53). The method is validated on four benchmarks: static contact angles on a planar wall, short-time inertial–capillary spreading, droplet impact on a hydrophobic surface, and gravity-driven droplet passage through a sharp-edged orifice. The paper claims that the approach provides an accurate and scalable framework for wetting-controlled flows in complex geometries.","tokens_in":16599,"tokens_out":8282,"duration_ms":100895,"significance":"If the results hold, the contribution is practically valuable: a wetting boundary condition that is local, explicit, race-free, and compatible with thread-safe GPU implementations, without requiring a predefined Cartesian wall direction. The dynamic benchmarks are compared against independent experimental scalings (Bird–Mandre–Stone, Clanet et al., Bordoloi–Longmire) and do not use those data to fit model constants, which is a strength. The method also addresses the known mass-conservation issue of non-neutral wetting in second-order phase-field models. However, the validation is partly qualitative, particularly the spreading-exponent claim, and the paper's generality claim about complex geometries extends beyond the demonstrated evidence.","major_comments":[{"comment":"The abstract and §III.B claim that the model reproduces contact-angle-dependent spreading exponents between approximately 1/2 and 1/4. This is not supported by a quantitative measurement. The text says the curves 'approach' the limiting scalings and are 'consistent with' Bird et al., but no exponent is fitted; the dashed 1/2 and 1/4 lines are only visual references. On a log-log plot, a curve can appear between two power laws without actually following a power law over a defined window. Please fit r(t)/R0 = A (t/τ_i)^α for each θ_eq over a specified early-time interval, report the fitted α with confidence intervals or residuals, and compare systematically with the theoretical trend.","section":"§III.B, Fig. 4"},{"comment":"The global volume correction modifies the phase field at every time step by adding ΔMφ/W χ(x), with χ(x) nonzero only in the diffuse-interface band, which includes the contact-line region. This correction could therefore alter the very wetting dynamics used to validate the model. The paper states that the correction is 'small' but provides no magnitude, no time series, and no sensitivity study. Please report ΔMφ/Mφ for the dynamic benchmarks, test at least two values of the threshold ϵφ, and demonstrate that the spreading exponents and We^{1/4} scaling are insensitive to the correction (or to its amplitude). Without this, one cannot exclude that the mass-correction mechanism, rather than the wetting boundary condition, is responsible for part of the observed dynamic behavior.","section":"§II.C, Eq. (53)"},{"comment":"The abstract and conclusions claim that the scheme 'can be applied directly to voxelized solid geometries and sharp edges.' The evidence for this is limited: the static-angle tests are planar, and the orifice benchmark, while using a circular stair-stepped edge, is one symmetric geometry. The wall-normal reconstruction, Eqs. (36)–(38), is a weighted occupancy sum whose accuracy on oblique, rough, or strongly curved voxelized surfaces is not established and is not guaranteed by construction; the donor extrapolation, Eq. (46), propagates any normal error into the ghost value. The conclusions themselves concede that 'a broader assessment on curved and rough surfaces would be required.' Either add a quantitative test on a curved or oblique wall (e.g., a static angle on an inclined or stair-stepped plane, or a droplet on a curved surface) or temper the generality claim in the abstract and con","section":"§III.D and Conclusions"}],"minor_comments":[{"comment":"The set D(x_s) of 'admissible donor links' is used before being defined. The text later says wall-adjacent fluid nodes are considered first, but this should be stated formally when D(x_s) is introduced.","section":"Eq. (40)"},{"comment":"The localization factor λ_s is a heuristic; no derivation or reference is provided. Since it scales the entire ghost extrapolation, a brief justification or a sensitivity test with respect to λ_s would strengthen the method.","section":"Eq. (47)"},{"comment":"The static-angle test reports deviations of 'a few degrees' without a table or error quantification. This is acceptable as a consistency check, but numerical values for each θ_th would make the claim more precise and reproducible.","section":"§III.A"},{"comment":"The caption contains a grammatical error: 'the left plot report the non dimensional spreading diameter' should be 'the left plot reports the non-dimensional spreading diameter.'","section":"Fig. 5 caption"},{"comment":"The Weber number is typeset as 'W e' in several places (e.g., 'W e= ρℓU^2_0 D0/σ' and in Fig. 6). This is a typographical issue; it should be 'We.'","section":"§III.C, Eq. (62)"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the proposed wetting update is plausible and the benchmark suite is useful, but the paper currently overclaims generality. The three major comments are all addressable within the manuscript's scope: add an exponent-fit analysis, quantify the mass-correction effect, and either validate on a curved/oblique geometry or soften the abstract/conclusion claims. I do not see a fundamental error in the derivation, but the evidence as presented is not yet strong enough for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: this is a competent incremental contribution to the LB-CAC wetting toolbox. The new ghost-node construction — occupancy-based wall normal, donor-link selection, and interface-localized global mass correction — is clearly described, locally implementable, and thread-safe by construction. That combination is not in the prior art they cite, so the novelty claim is fair, though it is a variant within an established program, not a paradigm shift.\n\nWhat the paper does well: the static angle tests cover a wide range (30–160°) and the self-consistency is fine — you're checking that the imposed BC is recovered, so of course it's a consistency check, and they report only 'a few degrees' deviation. More convincing are the dynamic benchmarks: the spreading exponent ordering between t^1/2 and t^1/4, the We^1/4 maximum deformation, and the capture/release/breakup regime map for the orifice. These are compared to independent experimental scalings and are not used to fit parameters, so they carry real weight. The authors are also honest about what's not tested: they explicitly say a broader assessment on curved and rough surfaces is required.\n\nSoft spots, in proportion: the wall-normal reconstruction (Eqs. 36–38) is the load-bearing ingredient for complex geometries, and the only non-planar validation is the axisymmetric sharp-edged orifice with axis-aligned edges. That does not exercise oblique edges, stair-stepped roughness, or curved walls. So the stress-test concern lands: the complex-geometry claim is plausible but unsupported as written. That said, this is an addressable validation gap, not a demonstrated failure. Minor issues: the spreading exponents are read visually from Fig. 4 rather than fitted; no convergence study; no code or data shipped. The global mass correction is a sensible fix for the known flux imbalance, though calling the whole scheme 'local' while having a global volume redistribution step is a slight overstatement.\n\nMy own take: the central construction is sound and the benchmarks are reasonable for a first report in a subfield where this kind of validation is standard. The paper would benefit from a convergence study, a quantitative fit of the spreading exponents, and one test with an oblique or curved wall. The citation pattern looks appropriate; they build on Refs. 25, 27, 29 and their own Ref. 16 rather than overselling.\n\nWho this is for: anyone working on diffuse-interface LB with wetting, especially on voxelized porous-media or microfluidic geometries. It deserves a serious referee. I'd send it to review with the expectation that the authors extend the geometric validation — that's the one thing standing between 'promising' and 'convincing'.","headline":"A useful, well-explained incremental wetting boundary condition for conservative Allen–Cahn lattice Boltzmann, with honest validation and one genuinely load-bearing assumption that needs more testing before the complex-geometry claims are trusted.","tokens_in":16991,"tokens_out":893,"would_cite":true,"duration_ms":12555,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper proposes a local geometric ghost-node wetting condition that lets a conservative Allen–Cahn lattice Boltzmann method impose a prescribed contact angle on voxelized solid walls of arbitrary orientation, and validates it on static,","keywords":["conservative Allen–Cahn","lattice Boltzmann","contact angle","wetting boundary condition","ghost node","phase-field multiphase flow","droplet spreading","droplet impact"],"falsifier":"Run a static-droplet test on a curved or randomly roughened voxel wall where the true local normal is known analytically (for example, a sphere or cylinder) and compare the measured equilibrium contact angle with the prescribed angle across a range of θ. If the error grows systematically with surface curvature or in stair-step patches, the occupancy-based normal reconstruction is the limiting component; if the error remains small, the method extends beyond planar validation.","tokens_in":16140,"feed_emoji":"💧","tokens_out":3797,"duration_ms":42851,"temperature":0.7,"pith_summary":"The paper introduces a boundary treatment that imposes a target contact angle in a conservative Allen–Cahn lattice Boltzmann solver without assuming any predefined wall direction. At each solid node, a wall normal is reconstructed from nearby fluid links, a donor fluid node is selected, and a ghost phase-field value is extrapolated so that the interface meets the wall at the prescribed angle. A separate interface-localized global correction keeps the phase-field mass exactly conserved. The method is validated on static droplets from 30° to 160°, spreading droplets that follow contact-angle-dependent power laws between t^1/2 and t^1/4, impacting droplets that follow We^1/4 scaling, and gravity-driven passage through a sharp-edged orifice that reproduces capture, release, and breakup regimes. If correct, this gives a local, thread-safe, GPU-compatible way to simulate wetting in complex geometries.","feed_headline":"A local ghost node sets droplet contact angles on voxel walls","feed_subtitle":"Static angles, spreading exponents, and impact scaling all follow from one geometric rule.","key_machinery":"The ghost-node wetting update is the load-bearing mechanism. At each wall-adjacent solid node, the wall normal n_w is reconstructed from the fluid–solid occupancy as n_w = Σ w_q(-c_q)/|Σ w_q(-c_q)|, where the weights w_q are 1, 1/2, or 1/3 depending on link length. A donor fluid node is chosen by maximizing the alignment score S_q = (-c_q)·n_w/|c_q|. The gradient at the donor node is split into wall-tangent and wall-normal parts, the normal part is set by ∂_n ϕ = -|∇∥ϕ| cot(π - θ), and the ghost value is extrapolated as ϕ_g = ϕ_f + λ_s ∇ϕ_c · r_fs with λ_s = sqrt(4ϕ_f(1-ϕ_f)). A separate mass-correction step adds an interface-localized source term proportional to ϕ(1-ϕ) to enforce global con","core_discovery":"The central claim is that a prescribed contact angle can be enforced in a conservative Allen–Cahn lattice Boltzmann model by constructing ghost phase-field values from the local voxelized geometry alone. For each solid node adjacent to fluid, the unnormalized wall normal is computed as the weighted sum of inward-pointing lattice links, then normalized. A donor fluid node is chosen by maximum alignment with that normal, and the phase field is extrapolated along the donor-to-solid direction using a wall-normal derivative set by the target angle and a localization factor that concentrates the correction at the diffuse interface. The authors show that this local update recovers prescribed equili","pith_inferences":["Inference: Because the wall normal is reconstructed from binary fluid–solid occupancy, the effective angle on stair-stepped voxel surfaces may differ from the intended angle; a curvature-aware or higher-order normal reconstruction is a natural extension the paper leaves untested.","Inference: The first-order donor extrapolation with the localization factor λ_s could be upgraded to second order or combined with a local contact-line velocity model, which would allow rate-dependent dynamic contact angles and hysteresis to be represented within the same ghost-node structure.","Inference: The global mass correction acts as a Lagrange multiplier that redistributes mass over the diffuse interface; applying it independently of the local wetting update may interact with contact-line pinning when the interface is anchored at a sharp edge, a scenario the current benchmarks only partially explore."],"forward_implications":["Conservative Allen–Cahn lattice Boltzmann simulations can now prescribe wetting on arbitrarily oriented voxelized solids without ad hoc wall-direction corrections.","The local, thread-safe update is directly compatible with GPU-based large-scale simulations, enabling wetting-controlled flows in porous media and microfluidic geometries.","The interface-localized mass correction prevents long-time phase-field drift caused by non-neutral wetting boundary conditions, which is critical for confined flows with persistent contact lines.","The method reproduces dynamic wetting scalings (spreading exponents between 1/2 and 1/4, We^1/4 impact scaling), so it can be used to study contact-line dynamics and droplet impact beyond its static validation.","The sharp-edged orifice results show that the treatment captures edge-pinning and the transition from capture to release, opening a route to study droplet transport through constrictions."],"fun_headline_variants":["Ghost-node wetting rule sets contact angles on voxel walls","Local geometric boundary nails droplet spreading exponents","One voxel-wall rule captures droplet impact and breakup","Voxel-only wetting law matches classic scaling laws","Droplet dynamics from a single ghost-node update"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The wall normal reconstructed from local fluid–solid occupancy is assumed to faithfully represent the true solid orientation, including at corners and sharp edges, and the first-order donor extrapolation is assumed sufficient to impose the stated angle; the authors note that curved and rough surfaces still require assessment.","fun_headline_variants_meta":{"raw":{"variants":["Ghost-node wetting rule sets contact angles on voxel walls","Local geometric boundary nails droplet spreading exponents","One voxel-wall rule captures droplet impact and breakup","Voxel-only wetting law matches classic scaling laws","Droplet dynamics from a single ghost-node update"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000159,"raw_usage":{"total_tokens":1029,"prompt_tokens":673,"completion_tokens":356,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":417,"completion_tokens_details":{"reasoning_tokens":280}},"tokens_in":417,"tokens_out":356,"duration_ms":4691,"temperature":1.0,"reasoning_tokens":280,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T02:24:32.350232+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a static-droplet test on a curved or randomly roughened voxel wall where the true local normal is known analytically (for example, a sphere or cylinder) and compare the measured equilibrium contact angle with the prescribed angle across a range of θ. If the error grows systematically with surface curvature or in stair-step patches, the occupancy-based normal reconstruction is the limiting component; if the error remains small, the method extends beyond planar validation.","supporting_citations":[],"review_version":1}