Pith. sign in

REVIEW 5 major objections 7 minor 62 references

MPFBench: A Large Scale Dataset for SciML of Multi-Phase-Flows: Droplet and Bubble Dynamics

T0 review · 5 major / 7 minor · reviewed 2026-08-08 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read MPF-Bench offers 11,000 bubble and droplet simulations, over a million snapshots, and shows neural operators trained on a subset can track transient multiphase dynamics, with CNO best at fine interfacial detail.

desk verdict A genuinely large, well-validated multiphase dataset is undermined by a wall-touching 2D bubble initial condition that invalidates the reported ML comparisons. read the letter →

arxiv 2502.07080 v2 pith:FIL6NSXB submitted 2025-02-10 physics.flu-dyn

Mehdi Shadkhah , Ronak Tali , Ali Rabeh , Cheng-Hau Yang , Ethan Herron , Abhisek Upadhyaya , Adarsh Krishnamurthy , Chinmay Hegde
show 2 more authors
Aditya Balu Baskar Ganapathysubramanian
This is my paper · ORCID
classification physics.flu-dyn PACS 47.55.D47.55.-t
keywords multiphaseflowscientificmachinelearningneuraloperatorsfoundationmodelslatticeBoltzmannmethodphase-fieldbubbledynamicsdroplet
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper introduces MPF-Bench, a benchmark dataset of 11,000 simulations — 5,500 rising-bubble and 5,500 falling-droplet cases in 2D and 3D — totalling over one million time snapshots, roughly two orders of magnitude larger than existing public multiphase flow datasets. The data come from an in-house Lattice Boltzmann phase-field solver covering density ratios $\rho^* \in [10, 1000]$, viscosity ratios $\mu^* \in [1, 100]$, Bond numbers $Bo \in [10, 500]$, and Reynolds numbers $Re \in [10, 1000]$. Training six neural operators and foundation models on a 1,000-sample subset of the 2D bubble data, the paper finds that all models improve with longer input sequences and that the Convolutional Neural Operator captures fine interfacial details — including satellite bubbles formed after breakup — better than FNO, DeepONet, UNet, or a pretrained vision transformer. A foundation model pretrained on single-phase flows transfers poorly, suggesting that multiphase pretraining data are needed. If the dataset is sound, it provides the SciML community a shared testbed spanning deformation, oscillation, and breakup regimes.

What carries the argument

The load-bearing object is the dataset itself, produced by the authors' in-house CUDA Lattice Boltzmann solver, which couples the D2Q9 (2D) or D3Q19 (3D) hydrodynamic equations to a conservative Allen–Cahn phase-field interface tracking equation (Geier et al., 2015; Fakhari et al., 2019). The phase-field variable $\phi$ marks the two fluids with a diffuse interface of thickness $\xi$, and each simulation is parameterized by four dimensionless inputs — density ratio $\rho^*$, viscosity ratio $\mu^*$, Reynolds number $Re$, and Bond number $Bo$ — sampled uniformly over their ranges, with outputs stored as 101 snapshots of concentration $c$, velocity components, pressure $p$, and density $\rho$. The evaluation protocol repackages these snapshots into six tasks (S1–S6) that vary input sequence length and prediction horizon, which is what allows the same raw data to serve as a benchmark for sequence-to-field and sequence-to-sequence SciML learning.

What would settle it

Run the same solver on parameter combinations absent from the four validation cases — for example, high density ratio ($\rho^* = 1000$) with low Bond number ($Bo = 10$), or high Reynolds number at high viscosity ratio — and compare interface evolution, breakup time, and terminal rise or fall velocity against an independent high-fidelity method such as volume-of-fluid, front tracking, or direct experiment. If the solver's error is large or non-uniform across the parameter space, the dataset's claim to uniform ground truth fails in those regimes; a trained CNO that reproduces the solver's output but diverges from the independent reference would likewise show the benchmark certifies imitation of the simulator rather than physical accuracy.

Watch

Extended reading notes

Core claim

The paper's central claim is that a well-validated Lattice Boltzmann phase-field framework can generate a multiphase dataset — 10,000 2D plus 1,000 3D simulations with up to 101 snapshots each of interface indicator, velocity, pressure, and density — that is two orders of magnitude larger in snapshot count than any prior public multiphase dataset, and that neural operators trained on a subset of it can predict transient dynamics. On the 2D bubble subset, sequence-to-field and sequence-to-sequence tasks S1–S6 show that every tested model improves as more temporal context is fed in, and that the Convolutional Neural Operator (CNO) achieves the lowest concentration-field error and the most faithful reproduction of fine interface structure, including post-breakup satellite bubbles. The paper also finds that Poseidon, a foundation model pretrained on single-phase PDEs, underperforms its randomly initialized transformer counterpart scOT, which it interprets as evidence that single-phase pretraining does not transfer to sharp-interface multiphase physics and that foundation models for such flows must be trained on multiphase data.

Load-bearing premise

The load-bearing premise is that the in-house Lattice Boltzmann phase-field solver produces physically accurate ground truth across the whole sampled parameter space — density ratio $\rho^* \in [10, 1000]$, viscosity ratio $\mu^* \in [1, 100]$, Bond number $Bo \in [10, 500]$, Reynolds number $Re \in [10, 1000]$ — and at the chosen grid resolutions, even though Appendix A.3 validates the solver on only four canonical cases (capillary wave decay, single bubble rise, falling droplet breakup, and Rayleigh–Taylor instability).

Editorial extensions

If this is right

  • Neural operators trained on MPF-Bench subsets can serve as surrogate time-steppers for rising bubbles, predicting concentration, velocity, and pressure fields several snapshots ahead from a short observed history, with accuracy improving as the input sequence lengthens.
  • The Convolutional Neural Operator's consistently lowest concentration-field error identifies convolutional architectures as the strongest of the evaluated classes for sharp-interface multiphase emulation, including post-breakup satellite-bubble formation.
  • The poor transfer of the single-phase-pretrained Poseidon model implies that multiphase foundation models will need in-domain pretraining data, which is exactly what benchmarks like MPF-Bench are built to supply.
  • With density ratio 10–1000, viscosity ratio 1–100, Bond number 10–500, and Reynolds number 10–1000, the dataset spans deformation, oscillation, and breakup regimes, giving the community a shared evaluation set two orders of magnitude larger than prior public multiphase datasets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper trains on 1,000 of the 10,000 2D bubble samples with a fixed input sequence length; a natural extension is to train on the full set and evaluate autoregressive rollouts over the complete 100-snapshot trajectory, which the paper lists as future work given single-GPU memory limits.
  • Because Appendix A.3 validates the solver on only four canonical cases, an independent check — comparing the LBM ground truth against a volume-of-fluid or front-tracking reference on randomly sampled parameter combinations across the full $\rho^*$–$\mu^*$–$Bo$–$Re$ ranges — would determine how much of the dataset's claimed coverage is certified physics rather than simulator output.
  • The 3D portion (1,000 simulations) carries less statistical weight than the 2D portion; a future release with matched 2D/3D parameter coverage would let the community measure whether dynamics learned in 2D transfer to 3D bubble and droplet flows.
  • One passage in Section 3.3, the metadata-format description, contains an author note instructing that parts of the text be drafted by paraphrasing the FlowBench documentation with AI assistance; the tensor shapes in Table 3 are the authoritative specification, and the surrounding prose should be read with that drafting history in mind.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 7 minor

Summary. MPF-Bench is a dataset paper describing 11,000 lattice Boltzmann simulations (10,000 in 2D and 1,000 in 3D) of rising bubbles and falling droplets, with more than one million time snapshots and randomized dimensionless parameters (density ratio, viscosity ratio, Bond number, Reynolds number). The paper validates an in-house phase-field LBM solver on four benchmarks (Prosperetti capillary waves, Bhaga-Weber bubble shapes, Jalaal falling droplets, and Rayleigh-Taylor instability) and then evaluates six SciML models (UNet, DeepONet, FNO, CNO, scOT, and Poseidon) on a 1,000-sample subset of the 2D bubble dataset under six sequence-to-field and sequence-to-sequence protocols (S1-S6). The authors report that CNO best captures interfacial details and that the single-phase-pretrained foundation model Poseidon transfers poorly to multiphase flows.

Significance. If the dataset is sound, MPF-Bench is a valuable community resource: it is substantially larger than BubbleML in snapshot count, covers a wide parameter range, and the solver is checked against established analytical, experimental, and numerical benchmarks. The inclusion of six baseline models, the public dataset on HuggingFace, and the training code on GitHub are also strengths that support reproducibility. However, several load-bearing issues in the current manuscript, especially the 2D bubble initial condition, the resolution inconsistency, and the overclaimed temporal-context result, mean that the paper's main empirical claims as written are not yet established.

major comments (5)
  1. [Sec. 3.1] Section 3.1 states that the 2D bubble has initial diameter D0=128 and center (64,64) in a [256,512] domain, so the interface is tangent to the free-slip side wall at x=0 and to the periodic bottom boundary at y=0. Because no wetting or contact-angle boundary condition is specified for the phase-field variable at the free-slip wall, this setup is not a freely rising bubble; it is a wall-touching bubble that is also mirrored across the periodic boundary. Since every 2D bubble simulation (5,000 samples) and all S1-S6 baselines use this initial condition, the paper's main empirical claims about capturing bubble rise dynamics are called into question. This setup also differs from the validated bubble-rise case in Appendix A.3.2, where the bubble is centered at (L0/2,L0/2) with diameter L0/5 and has clearance from all boundaries. Please either correct the initial condition and regenerate the affected data, or add the missing boundary condition and explicitly reframe the results as wall-bounded bubble dynamics.
  2. [Sec. 3.3 vs Sec. 3.5] Section 3.3 says the 2D datasets are published at the original LBM resolution 256x512, but Section 3.5 states that every S1-S6 array has spatial shape 256x256 (H and W fixed at 256x256). These statements are inconsistent. If the ML arrays were padded, cropped, or downsampled from the 256x512 simulation fields, that transformation must be documented because it changes both the metadata contract and the meaning of the reported errors; if they are truly 256x512, Section 3.5 is wrong. Please report the exact stored shapes and reconcile the two sections.
  3. [Sec. 4, Tables 5-6] Section 4 claims that "all model predictions improve as more time snapshots are incorporated," but the S4-S6 rows of Table 6 show the opposite trend for the sequence-to-sequence tasks: UNet's concentration MSE rises from 3.27e-2 (S4) to 7.34e-2 (S6), FNO's from 1.16e-2 to 4.24e-2, and CNO's from 1.74e-2 to 3.78e-2. The same growth appears in several velocity and pressure channels. The conclusion in Section 5 that feeding more time snapshots leads to more accurate trajectory prediction is therefore not supported for the sequence-to-sequence setting; please restrict the claim to the sequence-to-field tasks or provide a separate analysis of error accumulation.
  4. [Appendix A.3] Appendix A.3 validates the solver on the Prosperetti capillary wave, Bhaga-Weber bubble shapes, the Jalaal falling droplet, and the Rayleigh-Taylor instability, but these cases cover only a small subset of the dataset's parameter box. The rising-bubble validation reaches rho*=1000 and mu*=100 but only up to Bo=243, the falling-droplet case is at rho*=10 and a single Eo=288, and the capillary and Rayleigh-Taylor cases are at low density ratios; the dataset samples rho* in [10,1000], mu* in [1,100], Bo in [10,500], and Re in [10,1000] at resolutions 256x512 and 128x256x128. No grid-convergence study or validation at extreme points of this box is reported, so treating the generated fields as ground truth over the full sampled range is an extrapolation. Please add targeted validation runs and/or a resolution study at representative extreme parameters.
  5. [Sec. 4, Tables 5-6] Tables 5 and 6 report a single point estimate for each model and scenario, without standard deviations across random seeds or any trivial baseline such as copying the last input frame. Some of the reported model differences are small relative to the error magnitudes (e.g., S5 concentration MSE 1.72e-2 for CNO versus 2.33e-2 for FNO), so the ranking claims may be within run-to-run variability; without repeated-seed statistics the model comparison is not statistically grounded. Adding a persistence baseline is also necessary to interpret whether absolute errors of order 1e-2 in the concentration field support the claim that the models "capture transient dynamics."
minor comments (7)
  1. [Sec. 3.3] Section 3.3 (immediately after Fig. 3) contains unedited drafting notes, including "We might have 3D results (perhaps 1000 or 2000 samples)" and "use chatgpt for paraphrasing from Flowbench + edit for two-phase flows"; these should be removed and the metadata text completed before publication.
  2. [Sec. 3.3 / Table 3] The number of temporal snapshots is inconsistent: Sections 3.3 and 3.4 say 100 time steps, while Table 3 lists 101 time steps for 2D and 51 for 3D; please make the count consistent and update the total snapshot count accordingly.
  3. [Table 4] Table 4 contains duplicate parameter rows with contradictory difficulty labels, e.g., "High High Low Low" is labeled both Easy and Moderate and "Low Low High High" is labeled both Challenging and Easy; this should be corrected.
  4. [Sec. 3.4, Table 2] In Section 3.4, case B2 is described as having "the same high Reynolds number" as B1, but Table 2 lists Re=500 for B1 and Re=10 for B2; the description should match the table.
  5. [Sec. 4 / B.2] Section 4 refers to training and validation loss curves for "two representative models," while Appendix B.2 says "four representative models" and Figure 15 plots four models; please align the text and figure.
  6. [Sec. 3.4, Table 2] Several figure cross-references in Section 3.4 appear as unresolved "??Fig??" placeholders, and Table 2 uses ambiguous notation such as "103" for powers of ten; please fix the cross-references and typeset these entries as 10^3, 10^2, and so on.
  7. [Reproducibility] The GitHub and HuggingFace links are given only as bare words ("GitHub" and "2Dbubble/mpf paper dataset") with no URLs; please provide working links in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: dataset validity rests on external benchmarks and ML evaluation uses held-out splits.

full rationale

The paper's central claims are (i) MPF-Bench is large and generated by a validated LBM framework, and (ii) SciML baselines learn the resulting dynamics. Neither claim reduces to its inputs. The solver's accuracy is supported by four independent benchmarks in Appendix A.3: the Prosperetti capillary-wave analytical solution, the Bhaga & Weber bubble-rise experiments and Gumulya FVM data, the Jalaal & Mehravaran VOF falling-droplet comparison, and the Ren/Zu Rayleigh-Taylor reference data. These are external to the fitted parameters of the paper, so the 'well-validated' claim does not rest on self-citation. The ML experiments are standard supervised time-series forecasting on held-out test splits (800/200) from the same parameter family; this tests interpolation of the solver's outputs and is the normal meaning of a benchmark, not a definitional tautology. The minor self-citations (Tali et al. FlowBench, Rabeh et al.) are contextual and are not load-bearing. The stated limitations (limited 3D samples, field magnitude disparities, GPU-memory-limited time steps) and the internal editing artifacts (e.g., the draft bullet 'use chatgpt for paraphrasing' and the 256x256 vs 256x512 resolution mismatch between Sec. 3.5 and Sec. 3.3) are quality/correctness concerns, not circularity. Even the skeptic's wall-tangent initial-condition concern, if valid, would undermine physical fidelity of the data, but it would not make the ML benchmark circular, since the models are evaluated against the same solver's outputs. No equation or fitted parameter is renamed as a prediction; no uniqueness or ansatz is imported from the authors' prior work to force the dataset's design.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities or forces. Its central claims rest on standard LBM/phase-field modeling assumptions, plus the domain assumption that the four validation benchmarks justify the full sampled parameter range. The hand-chosen numerical parameters (interface thickness, mobility) and model hyperparameters are the main free choices.

free parameters (3)
  • Interface thickness xi (lattice units) = 4 or 5 lattice units, chosen by hand
    Appendix A.2 states xi is 'carefully selected' to ensure enough lattice nodes inside the interface. It controls the diffuse-interface width and affects breakup dynamics, so it is a hand-chosen numerical parameter.
  • Mobility parameter / Peclet number = Pe=25 for bubble rise, Pe=5 for falling droplet, Pe=744 for Rayleigh-Taylor
    Appendix A.3 fixes Peclet numbers for validation runs. Mobility controls interface relaxation time and is chosen by hand rather than fitted to data.
  • SciML model hyperparameters = e.g., learning rate 5e-4, FNO 64 modes, CNO 4 layers, Poseidon depth [4,4,4,4]
    Section B.1 lists hyperparameters 'carefully selected through extensive tuning'. They are hand-chosen settings that affect the reported baseline performance, though they are not fitted to the test set.
assumptions (4)
  • standard math The LBM phase-field model (conservative Allen-Cahn, D2Q9/D3Q19) converges via Chapman-Enskog to the incompressible two-phase Navier-Stokes equations with surface tension.
    Invoked in Appendix A.2 as the basis for computing velocity, pressure, and phase field.
  • domain assumption The validation cases (Prosperetti capillary wave, Bhaga-Weber bubble shapes, Jalaal falling droplet, and Rayleigh-Taylor instability) are correct and representative benchmarks for the targeted physics.
    Appendix A.3 uses these four canonical settings to claim the LBM framework is well-validated; they cover only a small part of the sampled parameter range.
  • domain assumption 2D simulations at 256x512 resolution capture the qualitative breakup and deformation physics used for the ML benchmark tasks.
    The falling-droplet validation compares 2D LBM against 3D VOF, and all ML tasks are run on 2D bubble data, so the 2D results must be physically meaningful.
  • domain assumption Uniform random sampling of dimensionless parameters over the stated ranges yields a representative and balanced distribution of difficulty for training and evaluation.
    Section 3.1 states parameters are selected randomly and uniformly; Table 4 assigns difficulty labels heuristically, assuming coverage across regimes.

how reviews work

0 comments
Cite this review

Pith. "Pith review of MPFBench: A Large Scale Dataset for SciML of Multi-Phase-Flows: Droplet and Bubble Dynamics." pith.science (2026). https://pith.science/paper/FIL6NSXB

@misc{pith2026250207080,
  author       = {Pith},
  title        = {Pith review of: MPFBench: A Large Scale Dataset for SciML of Multi-Phase-Flows: Droplet and Bubble Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FIL6NSXB}},
  note         = {Machine review of arXiv:2502.07080}
}
read the original abstract

Multiphase fluid dynamics, such as falling droplets and rising bubbles, are critical to many industrial applications. However, simulating these phenomena efficiently is challenging due to the complexity of instabilities, wave patterns, and bubble breakup. This paper investigates the potential of scientific machine learning (SciML) to model these dynamics using neural operators and foundation models. We apply sequence-to-sequence techniques on a comprehensive dataset generated from 11,000 simulations, comprising 1 million time snapshots, produced with a well-validated Lattice Boltzmann method (LBM) framework. The results demonstrate the ability of machine learning models to capture transient dynamics and intricate fluid interactions, paving the way for more accurate and computationally efficient SciML-based solvers for multiphase applications.

Figures

Figures reproduced from arXiv: 2502.07080 by the authors.

Figure 1
Figure 1. Boundary conditions for the simulation of a falling droplet. The left panel illustrates the 3D case, while the right panel illustrates the 2D case. B1 B2 B3 t4 t3 t2 t1 (a) Rising Bubble D1 D2 D3 t1 t2 t3 t4 (b) Falling Droplet [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. (a) Snapshot of a 3D rising bubble and (b) snapshot of a 3D falling droplet. The properties of the fluids for each case are detailed in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Streamlines of a 3D rising bubble (a) and a 3D falling droplet (b), with colors indicating the magnitude of velocity. The properties of the fluids for each case are detailed in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (11 more)
Figure 5
Figure 5. Figure 5: 2D bubble deformations with streamlines.Figure 5: 2D bubble deformations with streFigure 5: 2D bubble deformations with streamlineFigure 5: 2D bubble deformations with st [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: The figure presents a comparison of sequence-to-field predictions for the concentration field C against the ground truth. The predictions are generated by four models: UNet, Convolutional Neural Operator (CNO), DeepONet, and Poseidon, across three data subsets (S1, S2,…
Figure 7
Figure 7. Figure 7: The figure presents sequence-to-sequence predictions for the concentration field C compared to the ground truth. Predictions are made by four models: UNet, Convolutional Neural Operator (CNO), DeepONet, and Poseidon. Each row represents different time steps (t9, t10, a…
Figure 8
Figure 8. Figure 8: Illustration of the interface region captured by the computational mesh. The magnified views show the distribution of lattice nodes within the interface, ensuring precise resolution of interfacial dynamics and transitions. The careful selection of the interface thickne…
Figure 9
Figure 9. Figure 9: Schematic diagram of the capillary wave problem setup. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Comparison of the normalized interface amplitude η ∗ as a function of normalized time t ∗ between the current LBM simulation and the analytical solution by Prosperetti (1981). (a) corresponds to a viscosity of ν = 0.0005, and (b) corresponds to a viscosity of ν = 0.00…
Figure 11
Figure 11. Figure 11: Comparison of bubble shapes at constant rise velocity: Experimental results by Bhaga & Weber (1981a), LBM results, and FVM results by Gumulya et al. (2016) for various Bond numbers (Bo) and Morton numbers (Mo). Mo = gy(ρh − ρl)µ 4 h σ 3ρ 2 h (21) The Ohnesorge number …
Figure 12
Figure 12. Figure 12: Comparison of the deformation of a liquid drop using the LBM and VOF methods: Current results and those of Jalaal et al. (2012) (Jalaal & Mehravaran, 2012) for Eo = 288, Ohh = Ohl = 0.05, and ρ ∗ = 10. A.3.4 RAYLEIGH-TAYLOR INSTABILITIES The Rayleigh-Taylor instabilit…
Figure 13
Figure 13. Figure 13: Evolution of the interface pattern of the 2D Rayleigh-Taylor instability for two scenarios: (a) ρ ∗ = 3, µ ∗ = 1, Re = 128, At = 0.500, P e = 744, ξ = 5; (b) ρ ∗ = 1000, µ ∗ = 100, Re = 3000, At = 0.998, P e = 200, Ca = 8.7, ξ = 5. x y 4 No-slip Periodic No-slip Initi…
Figure 14
Figure 14. Figure 14: (a) Schematic of the initial setup for the Rayleigh-Taylor instability simulation, showing the boundary conditions and initial perturbation. (b) Comparison of the bubble front and spike tip positions over time for the Rayleigh-Taylor instability case with parameters ρ…
Figure 15
Figure 15. Figure 15: Training and validation loss (semi-log scale) for CNO (left) and Poseidon-T (right) across four different input-output mappings S1, S3, S4, and S6. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_15.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

62 extracted references · 43 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    Effects of density, viscosity and surface tension on flow regimes and pressure drop of two-phase flow in horizontal pipes

    Ala S Al-Dogail and Rahul N Gajbhiye. Effects of density, viscosity and surface tension on flow regimes and pressure drop of two-phase flow in horizontal pipes. Journal of Petroleum Science and Engineering, 205: 0 108719, 2021

    work page 2021

  3. [3]

    Benchmark computations of diffuse interface models for two-dimensional bubble dynamics

    Sebastian Aland and Axel Voigt. Benchmark computations of diffuse interface models for two-dimensional bubble dynamics. International Journal for Numerical Methods in Fluids, 69 0 (3): 0 747--761, 2012

    work page 2012

  4. [4]

    Allen and John W

    Samuel M. Allen and John W. Cahn. Mechanisms of phase transformations within the miscibility gap of Fe-rich Fe-Al alloys . Acta Metallurgica, 24 0 (5): 0 425--437, may 1976. ISSN 00016160. doi:10.1016/0001-6160(76)90063-8. URL https://linkinghub.elsevier.com/retrieve/pii/0001616076900638

    arXiv 1976

  5. [5]

    Single bubble rising dynamics for moderate reynolds number using lattice boltzmann method

    Luz Amaya-Bower and Taehun Lee. Single bubble rising dynamics for moderate reynolds number using lattice boltzmann method. Computers & Fluids, 39 0 (7): 0 1191--1207, 2010. ISSN 0045-7930. doi:https://doi.org/10.1016/j.compfluid.2010.03.003. URL https://www.sciencedirect.com/science/article/pii/S004579301000054X

    work page doi:10.1016/j.compfluid.2010.03.003 2010

  6. [6]

    flow focusing

    Shelley L Anna, Nathalie Bontoux, and Howard A Stone. Formation of dispersions using “flow focusing” in microchannels. Applied physics letters, 82 0 (3): 0 364--366, 2003

    work page 2003

  7. [7]

    The paraview guide: a parallel visualization application

    Utkarsh Ayachit. The paraview guide: a parallel visualization application. Kitware, Inc., 2015

    work page 2015

  8. [9]

    Bhaga and M

    D. Bhaga and M. E. Weber. Bubbles in viscous liquids: shapes, wakes and velocities. Journal of Fluid Mechanics, 105: 0 61–85, 1981 b . doi:10.1017/S002211208100311X

    work page doi:10.1017/s002211208100311x 1981

Show all 62 references
  1. [10]

    An optimized artificial neural network unifying model for steady-state liquid holdup estimation in two-phase gas--liquid flow

    Majdi Chaari, Abdennour C Seibi, Jalel Ben Hmida, and Afef Fekih. An optimized artificial neural network unifying model for steady-state liquid holdup estimation in two-phase gas--liquid flow. Journal of Fluids Engineering, 140 0 (10): 0 101301, 2018

    2018

  2. [11]

    A conservative phase field method for solving incompressible two-phase flows

    Pao-Hsiung Chiu and Yan-Ting Lin. A conservative phase field method for solving incompressible two-phase flows . Journal of Computational Physics, 230 0 (1): 0 185--204, jan 2011. ISSN 00219991. doi:10.1016/j.jcp.2010.09.021. URL http://dx.doi.org/10.1016/j.jcp.2010.09.021 htt...

    2011 doi

  3. [12]

    Drop formation in a co-flowing ambient fluid

    Carsten Cramer, Peter Fischer, and Erich J Windhab. Drop formation in a co-flowing ambient fluid. Chemical Engineering Science, 59 0 (15): 0 3045--3058, 2004

    2004

  4. [13]

    Spelt, and Chang Shu

    Hang Ding, Peter D.M. Spelt, and Chang Shu. Diffuse interface model for incompressible two-phase flows with large density ratios . Journal of Computational Physics, 226 0 (2): 0 2078--2095, oct 2007. ISSN 00219991. doi:10.1016/j.jcp.2007.06.028. URL https://linkinghub.elsevier...

    2007 doi

  5. [14]

    Physics of liquid jets

    Jens Eggers and Emmanuel Villermaux. Physics of liquid jets. Reports on progress in physics, 71 0 (3): 0 036601, 2008

    2008

  6. [15]

    Investigation of deformation and breakup of a moving droplet by the method of lattice boltzmann equations

    Abbas Fakhari and Mohammad Hassan Rahimian. Investigation of deformation and breakup of a moving droplet by the method of lattice boltzmann equations. International journal for numerical methods in fluids, 64 0 (8): 0 827--849, 2010

    2010

  7. [16]

    A simple phase-field model for interface tracking in three dimensions

    Abbas Fakhari, Martin Geier, and Diogo Bolster. A simple phase-field model for interface tracking in three dimensions . Computers & Mathematics with Applications, 78 0 (4): 0 1154--1165, aug 2019. ISSN 08981221. doi:10.1016/j.camwa.2016.08.021. URL http://dx.doi.org/10.1016/j....

    2019 doi

  8. [17]

    Conservative phase-field lattice Boltzmann model for interface tracking equation

    Martin Geier, Abbas Fakhari, and Taehun Lee. Conservative phase-field lattice Boltzmann model for interface tracking equation . Physical Review E, 91 0 (6): 0 063309, jun 2015. ISSN 1539-3755. doi:10.1103/PhysRevE.91.063309. URL https://link.aps.org/doi/10.1103/PhysRevE.91.063309

    2015 doi

  9. [18]

    Joshi, Ranjeet P

    Monica Gumulya, Jyeshtharaj B. Joshi, Ranjeet P. Utikar, Geoffrey M. Evans, and Vishnu Pareek. Bubbles in viscous liquids: Time dependent behaviour and wake characteristics. Chemical Engineering Science, 144: 0 298--309, 2016. ISSN 0009-2509. doi:https://doi.org/10.1016/j.ces....

    2016 doi

  10. [19]

    Discrete lattice effects on the forcing term in the lattice Boltzmann method

    Zhaoli Guo, Chuguang Zheng, and Baochang Shi. Discrete lattice effects on the forcing term in the lattice Boltzmann method . Physical Review E, 65 0 (4): 0 046308, apr 2002. ISSN 1063-651X. doi:10.1103/PhysRevE.65.046308. URL https://link.aps.org/doi/10.1103/PhysRevE.65.046308

    2002 doi

  11. [20]

    Microfluidic platforms for lab-on-a-chip applications

    Stefan Haeberle and Roland Zengerle. Microfluidic platforms for lab-on-a-chip applications. Lab on a Chip, 7 0 (9): 0 1094--1110, 2007

    2007

  12. [21]

    Bubble ML : A multiphase multiphysics dataset and benchmarks for machine learning

    Sheikh Md Shakeel Hassan, Arthur Feeney, Akash Dhruv, Jihoon Kim, Youngjoon Suh, Jaiyoung Ryu, Yoonjin Won, and Aparna Chandramowlishwaran. Bubble ML : A multiphase multiphysics dataset and benchmarks for machine learning. In Thirty-seventh Conference on Neural Information Pro...

    2023

  13. [22]

    Poseidon: Efficient foundation models for pdes, 2024

    Maximilian Herde, Bogdan Raonić, Tobias Rohner, Roger Käppeli, Roberto Molinaro, Emmanuel de Bézenac, and Siddhartha Mishra. Poseidon: Efficient foundation models for pdes, 2024

    2024

  14. [23]

    Microbubbles in ultrasound-triggered drug and gene delivery

    Sophie Hernot and Alexander L Klibanov. Microbubbles in ultrasound-triggered drug and gene delivery. Advanced drug delivery reviews, 60 0 (10): 0 1153--1166, 2008

    2008

  15. [24]

    Numerical simulation of bubble rising in viscous liquid

    Jinsong Hua and Jing Lou. Numerical simulation of bubble rising in viscous liquid. Journal of Computational Physics, 222 0 (2): 0 769--795, 2007. ISSN 0021-9991. doi:https://doi.org/10.1016/j.jcp.2006.08.008. URL https://www.sciencedirect.com/science/article/pii/S0021999106003949

    2007 doi

  16. [25]

    Sukop, and Xi Yun Lu

    Haibo Huang, Michael C. Sukop, and Xi Yun Lu. Multiphase Lattice Boltzmann Methods: Theory and Application . John Wiley & Sons, Ltd, jul 2015. ISBN 9781118971338. doi:10.1002/9781118971451. URL http://doi.wiley.com/10.1002/9781118971451

    2015 doi

  17. [26]

    Quantitative benchmark computations of two-dimensional bubble dynamics

    Shu-Ren Hysing, Stefan Turek, Dmitri Kuzmin, Nicola Parolini, Erik Burman, Sashikumaar Ganesan, and Lutz Tobiska. Quantitative benchmark computations of two-dimensional bubble dynamics. International Journal for Numerical Methods in Fluids, 60 0 (11): 0 1259--1288, 2009

    2009

  18. [27]

    Calculation of Two-Phase Navier-Stokes Flows Using Phase-Field Modeling

    David Jacqmin. Calculation of Two-Phase Navier-Stokes Flows Using Phase-Field Modeling . Journal of Computational Physics, 155 0 (1): 0 96--127, oct 1999. ISSN 00219991. doi:10.1006/jcph.1999.6332. URL https://linkinghub.elsevier.com/retrieve/pii/S0021999199963325

    1999

  19. [28]

    Contact-line dynamics of a diffuse fluid interface

    DAVID JACQMIN. Contact-line dynamics of a diffuse fluid interface . Journal of Fluid Mechanics, 402: 0 57--88, jan 2000. ISSN 0022-1120. doi:10.1017/S0022112099006874. URL https://www.cambridge.org/core/product/identifier/S0022112099006874/type/journal_article

    2000 doi

  20. [29]

    Jalaal and K

    M. Jalaal and K. Mehravaran. Fragmentation of falling liquid droplets in bag breakup mode. International Journal of Multiphase Flow, 47: 0 115--132, 2012. ISSN 0301-9322. doi:https://doi.org/10.1016/j.ijmultiphaseflow.2012.07.011. URL https://www.sciencedirect.com/science/arti...

    2012 doi

  21. [30]

    Didier Jamet, David Torres, and J. U. Brackbill. On the theory and computation of surface tension: The elimination of parasitic currents through energy conservation in the second-gradient method . Journal of Computational Physics, 182 0 (1): 0 262--276, oct 2002. ISSN 00219991...

    2002

  22. [31]

    Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

    George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics-informed machine learning. Nature Reviews Physics, 3 0 (6): 0 422--440, 2021. ISSN 25225820. doi:10.1038/s42254-021-00314-5. URL https://doi.org/10.1038/s42254-021-00314-5

    2021 doi

  23. [32]

    Khanwale, Kumar Saurabh, Masado Ishii, Hari Sundar, James A

    Makrand A. Khanwale, Kumar Saurabh, Masado Ishii, Hari Sundar, James A. Rossmanith, and Baskar Ganapathysubramanian. A projection-based, semi-implicit time-stepping approach for the cahn-hilliard navier-stokes equations on adaptive octree meshes. Journal of Computational Physi...

    2023

  24. [33]

    The Lattice Boltzmann Method , volume 58 of Graduate Texts in Physics

    Timm Kr \" u ger, Halim Kusumaatmaja, Alexandr Kuzmin, Orest Shardt, Goncalo Silva, and Erlend Magnus Viggen. The Lattice Boltzmann Method , volume 58 of Graduate Texts in Physics. Springer International Publishing, 2017. ISBN 978-3-319-44647-9. doi:10.1007/978-3-319-44649-3. ...

    2017 doi

  25. [34]

    Q. Li, K. H. Luo, Y. J. Gao, and Y. L. He. Additional interfacial force in lattice Boltzmann models for incompressible multiphase flows . Physical Review E, 85 0 (2): 0 026704, feb 2012. ISSN 1539-3755. doi:10.1103/PhysRevE.85.026704. URL https://link.aps.org/doi/10.1103/PhysR...

    2012 doi

  26. [35]

    Fourier neural operator for parametric partial differential equations, 2021

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations, 2021

    2021

  27. [36]

    Enhanced droplet formation in a t-junction microchannel using electric field: A lattice boltzmann study

    Zhaomiao Liu, Fanming Cai, Yan Pang, Yanlin Ren, Nan Zheng, Rui Chen, and Siyu Zhao. Enhanced droplet formation in a t-junction microchannel using electric field: A lattice boltzmann study. Physics of Fluids, 34 0 (8), 2022

    2022

  28. [37]

    Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

    Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis. Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. Nature Machine Intelligence, 3: 0 218--–229, 2021

    2021

  29. [38]

    A pinn-based level-set formulation for reconstruction of bubble dynamics

    R \^o mulo M Silva, Mal \'u Grave, and Alvaro LGA Coutinho. A pinn-based level-set formulation for reconstruction of bubble dynamics. Archive of Applied Mechanics, pp.\ 1--16, 2024

    2024

  30. [39]

    Microfluidic lab-on-a-chip platforms: requirements, characteristics and applications

    Daniel Mark, Stefan Haeberle, G \"u nter Roth, Felix Von Stetten, and Roland Zengerle. Microfluidic lab-on-a-chip platforms: requirements, characteristics and applications. Microfluidics based microsystems: fundamentals and applications, pp.\ 305--376, 2010

    2010

  31. [40]

    Oliver Penrose and Paul C. Fife. Thermodynamically consistent models of phase-field type for the kinetic of phase transitions . Physica D: Nonlinear Phenomena, 43 0 (1): 0 44--62, may 1990. ISSN 01672789. doi:10.1016/0167-2789(90)90015-H. URL https://linkinghub.elsevier.com/re...

    1990

  32. [41]

    Motion of two superposed viscous fluids

    Andrea Prosperetti. Motion of two superposed viscous fluids. Physics of Fluids, 24 0 (7): 0 1217 – 1223, 1981. doi:10.1063/1.863522. URL https://www.scopus.com/inward/record.uri?eid=2-s2.0-0019376759&doi=10.1063 Cited by: 149

    1981 doi

  33. [42]

    Modeling and simulations of high-density two-phase flows using projection-based cahn-hilliard navier-stokes equations

    Ali Rabeh, Makrand A Khanwale, Jonghyun Lee, and Baskar Ganapathysubramanian. Modeling and simulations of high-density two-phase flows using projection-based cahn-hilliard navier-stokes equations. arXiv preprint arXiv:2406.17933, 2024

    2024 arXiv

  34. [43]

    Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

    Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics, 378: 0 686--707, 2019

    2019

  35. [44]

    Convolutional neural operators for robust and accurate learning of pdes, 2023

    Bogdan Raonić, Roberto Molinaro, Tim De Ryck, Tobias Rohner, Francesca Bartolucci, Rima Alaifari, Siddhartha Mishra, and Emmanuel de Bézenac. Convolutional neural operators for robust and accurate learning of pdes, 2023

    2023

  36. [45]

    Challenges in training pinns: A loss landscape perspective

    Pratik Rathore, Weimu Lei, Zachary Frangella, Lu Lu, and Madeleine Udell. Challenges in training pinns: A loss landscape perspective. arXiv preprint arXiv:2402.01868, 2024

    2024 arXiv

  37. [46]

    Sukop, and Haibao Hu

    Feng Ren, Baowei Song, Michael C. Sukop, and Haibao Hu. Improved lattice boltzmann modeling of binary flow based on the conservative allen-cahn equation. Phys. Rev. E, 94: 0 023311, Aug 2016. doi:10.1103/PhysRevE.94.023311. URL https://link.aps.org/doi/10.1103/PhysRevE.94.023311

    2016 doi

  38. [47]

    U-net: Convolutional networks for biomedical image segmentation

    Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical image computing and computer-assisted intervention--MICCAI 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part...

    2015

  39. [48]

    Multiphase flow in microfluidics: From droplets and bubbles to the encapsulated structures

    Amirmohammad Sattari, Pedram Hanafizadeh, and Mina Hoorfar. Multiphase flow in microfluidics: From droplets and bubbles to the encapsulated structures. Advances in Colloid and Interface Science, 282: 0 102208, 2020

    2020

  40. [49]

    A modular microfluid system with an integrated micromixer

    Norbert Schwesinger, Thomas Frank, and Helmut Wurmus. A modular microfluid system with an integrated micromixer. Journal of Micromechanics and Microengineering, 6 0 (1): 0 99, 1996

    1996

  41. [50]

    Droplet impingement on a surface at low reynolds numbers

    Drue Seksinsky and Jeffrey S Marshall. Droplet impingement on a surface at low reynolds numbers. Journal of Fluids Engineering, 143 0 (2): 0 021304, 2021

    2021

  42. [51]

    Role of atwood number on flow morphology of a planar shock-accelerated square bubble: A numerical study

    Satyvir Singh. Role of atwood number on flow morphology of a planar shock-accelerated square bubble: A numerical study. Physics of Fluids, 32 0 (12), 2020

    2020

  43. [52]

    Chaotic mixer for microchannels

    Abraham D Stroock, Stephan KW Dertinger, Armand Ajdari, Igor Mezic, Howard A Stone, and George M Whitesides. Chaotic mixer for microchannels. Science, 295 0 (5555): 0 647--651, 2002

    2002

  44. [53]

    Sukop and Daniel T

    Michael C. Sukop and Daniel T. Thorne. Lattice boltzmann modeling: An introduction for geoscientists and engineers . Springer Berlin Heidelberg, 2006. ISBN 3540279814. doi:10.1007/978-3-540-27982-2. URL http://link.springer.com/10.1007/978-3-540-27982-2

    2006 doi

  45. [54]

    Flowbench: A large scale benchmark for flow simulation over complex geometries

    Ronak Tali, Ali Rabeh, Cheng-Hau Yang, Mehdi Shadkhah, Samundra Karki, Abhisek Upadhyaya, Suriya Dhakshinamoorthy, Marjan Saadati, Soumik Sarkar, Adarsh Krishnamurthy, et al. Flowbench: A large scale benchmark for flow simulation over complex geometries. arXiv preprint arXiv:2...

    2024 arXiv

  46. [55]

    Dynamic pattern formation in a vesicle-generating microfluidic device

    Todd Thorsen, Richard W Roberts, Frances H Arnold, and Stephen R Quake. Dynamic pattern formation in a vesicle-generating microfluidic device. Physical review letters, 86 0 (18): 0 4163, 2001

    2001

  47. [56]

    Formation of droplets and mixing in multiphase microfluidics at low values of the reynolds and the capillary numbers

    Joshua D Tice, Helen Song, Adam D Lyon, and Rustem F Ismagilov. Formation of droplets and mixing in multiphase microfluidics at low values of the reynolds and the capillary numbers. Langmuir, 19 0 (22): 0 9127--9133, 2003

    2003

  48. [57]

    Microconfined equiviscous droplet deformation: Comparison of experimental and numerical results

    Anja Vananroye, Pieter JA Janssen, Patrick D Anderson, Peter Van Puyvelde, and Paula Moldenaers. Microconfined equiviscous droplet deformation: Comparison of experimental and numerical results. Physics of Fluids, 20 0 (1), 2008

    2008

  49. [58]

    Droplet impact on suspended metallic meshes: Effects of wettability, reynolds and weber numbers

    Konstantinos Vontas, Cristina Boscariol, Manolia Andredaki, Anastasios Georgoulas, Cyril Crua, Jens Honor \'e Walther, and Marco Marengo. Droplet impact on suspended metallic meshes: Effects of wettability, reynolds and weber numbers. Fluids, 5 0 (2): 0 81, 2020

    2020

  50. [59]

    Droplet deformation and breakup in shear flow of air

    Zhikun Xu, Tianyou Wang, and Zhizhao Che. Droplet deformation and breakup in shear flow of air. Physics of Fluids, 32 0 (5), 2020

    2020

  51. [60]

    Y. Y. Yan and Y. Q. Zu. A lattice Boltzmann method for incompressible two-phase flows on partial wetting surface with large density ratio . Journal of Computational Physics, 227 0 (1): 0 763--775, nov 2007. ISSN 10902716. doi:10.1016/j.jcp.2007.08.010. URL https://linkinghub.e...

    2007 doi

  52. [61]

    A fast and practical adaptive finite difference method for the conservative allen–cahn model in two-phase flow system

    Junxiang Yang, Darae Jeong, and Junseok Kim. A fast and practical adaptive finite difference method for the conservative allen–cahn model in two-phase flow system. International Journal of Multiphase Flow, 137: 0 103561, 2021. ISSN 0301-9322. doi:https://doi.org/10.1016/j.ijmu...

    2021

  53. [62]

    H. Z. Yuan, Z. Chen, C. Shu, Y. Wang, X. D. Niu, and S. Shu. A free energy-based surface tension force model for simulation of multiphase flows by level-set method . Journal of Computational Physics, 345: 0 404--426, 2017. ISSN 10902716. doi:10.1016/j.jcp.2017.05.020

    2017 doi

  54. [63]

    Y. Q. Zu and S. He. Phase-field-based lattice boltzmann model for incompressible binary fluid systems with density and viscosity contrasts. Phys. Rev. E, 87: 0 043301, Apr 2013. doi:10.1103/PhysRevE.87.043301. URL https://link.aps.org/doi/10.1103/PhysRevE.87.043301

    2013 doi

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.