{"id":"6d0a850a-8cbc-493d-8f41-61d4ae5a2a62","arxiv_id":"2606.08575","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"DNS of moderate-viscosity-ratio droplets reveals regimes initiated by internal m=2 instability, progressing to biplanar wakes, oblique paths, rotating waves, and chaotic motion with multistability.","lead":"Numerical simulations of toluene droplets rising in water identify a sequence of regimes as size increases, beginning with steady rise then shifting due to internal flow instabilities to oblique, rotating, and chaotic paths. A smart generalist might read it to see how fluid motion inside droplets controls their external behavior in processes like chemical separation.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"DNS fidelity for internal m=2 instability initiation (vs. wake or interface artifacts) is the load-bearing assumption for the central claim.","rationale":"The reader's weakest_assumption directly identifies the numerical fidelity issue that must hold for the internal-initiation claim to be accepted. No other internal inconsistency appears from the abstract or the described results; the concern is therefore the same one already flagged.","tokens_in":1815,"tokens_out":303,"duration_ms":14353,"concrete_test":"Re-run the axisymmetric-to-3D transition case at the smallest R where m=2 appears, using at least two additional grid resolutions (e.g., double the radial points inside the droplet) and a second interface-capturing scheme; if the critical radius or the internal m=2 growth rate shifts by >10%, the initiation sequence is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The strongest claim requires that axisymmetry breaking begins inside the droplet via the m=2 mode before wake effects dominate. This sequence is observed in the DNS, but the paper's methods section (grid, interface treatment, time-stepping, and any artificial viscosity or surface-tension regularization) must ensure that internal-flow growth rates are not altered by numerical diffusion or spurious currents at the interface. If the discretization damps or excites azimuthal modes differently inside versus outside, the reported order of instabilities and multistable regimes could be an artifact rather than physical.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript uses direct numerical simulations to study the rise of toluene droplets (viscosity ratio μ*=0.62) in water for radii 0.5–3 mm. It reports a sequence of regimes beginning with steady axisymmetric rise, followed by an internal m=2 azimuthal instability that produces a biplanar-symmetric wake and reduced terminal speed, then an oblique regime with coexisting m=1 and m=2 modes, a nearly vertical path, an m=2 rotating-wave regime, and finally chaotic paths with shape oscillations and vortex shedding. Multistable terminal states are identified depending on initial conditions. The central claim is that, unlike bubbles or solid particles, axisymmetry breaking is initiated inside the droplet by the internal flow instability.","tokens_in":1927,"tokens_out":498,"duration_ms":17323,"significance":"If the reported internal m=2 instability sequence is free of numerical artifacts, the work would be significant for multiphase flow dynamics by demonstrating the dominant role of internal circulation in shaping wake structure, rise speed, and path for moderate viscosity ratios. The identification of multistable regimes and the use of both axisymmetric and fully 3D simulations are strengths that could guide future modeling of droplet transport.","major_comments":[{"comment":"Numerical Methods (and associated results sections): The claim that axisymmetry breaking originates inside the droplet via the m=2 mode before wake effects dominate (Abstract and main text) is load-bearing and requires explicit demonstration that internal-flow growth rates are not altered by interface regularization, spurious currents, or differential numerical diffusion inside versus outside the droplet. Grid-convergence checks focused on azimuthal mode amplitudes and growth rates within the droplet, together with validation against experimental terminal velocities for comparable μ* and Re, are needed to support the reported instability sequence and multistable states.","section":"Numerical Methods"}],"minor_comments":[{"comment":"The transition radii or equivalent dimensionless numbers (Re, Bo, etc.) between the reported regimes are not quantified in the abstract or early sections, making it difficult to compare with prior bubble and particle studies.","section":null},{"comment":"Figure captions and text should explicitly state the grid resolution inside the droplet and the interface-capturing scheme parameters to allow assessment of internal-flow fidelity.","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We appreciate the referee's detailed review and the emphasis on numerical validation for our central claim regarding the internal origin of the instability. We provide a point-by-point response below and will incorporate revisions as indicated.","responses":[{"response":"We thank the referee for this important comment. To address the concern about potential numerical artifacts affecting the internal m=2 instability, we will perform and report additional tests in the revised manuscript. Specifically, we will conduct grid-convergence studies with a focus on the growth rates and amplitudes of the m=2 mode inside the droplet, using multiple resolutions. We will also examine the sensitivity of these growth rates to the interface regularization parameters and the level of spurious currents. Furthermore, we will include a validation section comparing our simulated terminal velocities against available experimental data for droplets with similar viscosity ratios and Reynolds numbers. These revisions will provide stronger support for the claim that the axisymmetry breaking is initiated by the internal flow.","revision_made":"yes","referee_comment":"[Numerical Methods] Numerical Methods (and associated results sections): The claim that axisymmetry breaking originates inside the droplet via the m=2 mode before wake effects dominate (Abstract and main text) is load-bearing and requires explicit demonstration that internal-flow growth rates are not altered by interface regularization, spurious currents, or differential numerical diffusion inside versus outside the droplet. Grid-convergence checks focused on azimuthal mode amplitudes and growth rates within the droplet, together with validation against experimental terminal velocities for comparable μ* and Re, are needed to support the reported instability sequence and multistable states."}],"tokens_in":1490,"tokens_out":337,"duration_ms":21869,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing here is that for toluene droplets in water at μ*=0.62 the simulations show axisymmetry breaking starting inside the droplet with an m=2 mode, followed by m=1 coexistence, a rotating wave state, and multistable ranges, which the authors say differs from the usual bubble and particle sequences.\n\nThey ran axisymmetric and 3D DNS across radii from 0.5 to 3 mm and tracked the progression from steady vertical rise to biplanar wake with reduced speed, then oblique paths, azimuthal drift, and finally chaotic motion with shape oscillations. The multistability findings from different initial conditions are a concrete addition.\n\nWhat the work does reasonably well is lay out this specific sequence and point to the internal flow as the driver for most of the regimes. That focus on the droplet interior rather than just the wake is a useful distinction for this viscosity ratio.\n\nThe soft spot is the missing numerical detail. The abstract mentions no grid sizes, convergence tests, interface resolution, or comparisons to experiments, so the claim that the m=2 mode originates inside and is not a discretization or spurious-current effect rests on unshown evidence. The stress-test concern about whether the internal instability growth rates are faithfully captured versus altered by the scheme is worth pressing in review.\n\nThis is for people who model or simulate droplet rise in multiphase flows and want a regime map at moderate viscosity ratios. A reader already working in that subfield can extract the sequence and multistability observations even if the numerics require extra scrutiny.\n\nIt deserves peer review so the methods can be examined directly; the topic fills a gap but the central ordering of instabilities needs confirmation that it is not numerical.","headline":"The paper gives a regime map for rising droplets at viscosity ratio 0.62 where internal m=2 instability leads the symmetry breaking, but the DNS methods need close checking for artifacts.","tokens_in":2410,"tokens_out":426,"would_cite":false,"duration_ms":17561,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Moderate-viscosity droplets initiate axisymmetry breaking from internal flow instability.","keywords":["rising droplets","path instability","viscosity ratio","direct numerical simulations","axisymmetry breaking","internal flow","wake dynamics","multistable regimes"],"falsifier":"An experiment that measures the velocity field inside the rising droplet and shows whether the m=2 azimuthal mode develops prior to any external wake asymmetry would confirm or refute the internal initiation of instability.","tokens_in":2723,"feed_emoji":"💧","tokens_out":617,"duration_ms":24285,"temperature":0.7,"pith_summary":"This paper studies the rise of freely buoyant droplets with moderate viscosity ratio using direct numerical simulations. It identifies a series of regimes as droplet size grows, starting from steady vertical rise, then internal instability with m=2 mode, oblique paths, rotating waves, and chaotic motion. The key finding is that axisymmetry breaking starts inside the droplet, shaping the wake and dynamics differently than for bubbles or particles. This distinction matters for accurately modeling droplet motion in liquids.","feed_headline":"Droplet rise instability begins inside the droplet","feed_subtitle":"Moderate viscosity ratio causes internal m=2 mode to break axisymmetry first, changing wake and speed before external modes act.","key_machinery":"Internal flow instability with azimuthal mode m=2 that initiates axisymmetry breaking","core_discovery":"As the droplet radius increases, the system undergoes a sequence of rise regimes beginning with steady axisymmetric rise, followed by an internal flow instability of azimuthal mode m=2 leading to biplanar-symmetric wake and reduced speed, then a steady oblique regime with coexisting m=1 and m=2 modes, an m=2 rotating-wave regime, and finally chaotic paths with shape oscillations and vortex shedding. Multistable states exist in certain size ranges. This demonstrates that axisymmetry breaking is initiated within the droplet due to internal flow instability, fundamentally differing from bubbles and solid particles.","pith_inferences":["Models of droplet dynamics in engineering applications may need to prioritize internal circulation effects over wake dynamics alone.","Similar internal instabilities could appear in other immiscible liquid systems with comparable viscosity ratios.","Experiments could test this by seeding the droplet with tracers to visualize internal flow patterns before wake asymmetry develops."],"forward_implications":["Reduced terminal rise speed accompanies the biplanar-symmetric wake state.","The oblique regime features coexistence of m=1 and m=2 modes.","Multistable terminal states coexist in certain radius ranges depending on initial conditions.","The rotating-wave regime has the wake drifting azimuthally at constant angular velocity.","Chaotic paths emerge at larger sizes from persistent shape oscillations and vortex shedding."],"fun_headline_variants":["Internal flow instability initiates droplet axisymmetry break","m=2 mode causes biplanar wake before oblique droplet rise","Moderate ratio droplets enter rotating wave then chaos","Distinct terminal states coexist in droplet size ranges","Droplet dynamics driven by internal not external modes"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"Direct numerical simulations accurately capture the physical internal flow instability sequence without significant numerical or modeling artifacts.","fun_headline_variants_meta":{"raw":{"variants":["Internal flow instability initiates droplet axisymmetry break","m=2 mode causes biplanar wake before oblique droplet rise","Moderate ratio droplets enter rotating wave then chaos","Distinct terminal states coexist in droplet size ranges","Droplet dynamics driven by internal not external modes"]},"model":"grok-4.3","cost_usd":0.009264,"raw_usage":{"total_tokens":4208,"prompt_tokens":790,"num_sources_used":0,"completion_tokens":69,"cost_in_usd_ticks":92637000,"prompt_tokens_details":{"text_tokens":790,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3349,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":790,"tokens_out":69,"duration_ms":22395,"temperature":1.0,"reasoning_tokens":3349,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T18:07:16.776336+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An experiment that measures the velocity field inside the rising droplet and shows whether the m=2 azimuthal mode develops prior to any external wake asymmetry would confirm or refute the internal initiation of instability.","supporting_citations":[],"review_version":1}