{"id":"079d522c-dc27-4abb-b13b-1e73c664d093","arxiv_id":"2507.06800","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For inlet velocities just above the dripping-jetting threshold, a nozzle drips for tens of droplets before reaching steady jetting, and inlet velocity perturbations can accelerate or suppress the transition.","lead":"This paper reports that near the dripping-to-jetting transition in a Newtonian fluid faucet, the system keeps dripping for many droplets before the jet finally forms, and that small flow perturbations can switch between regimes. It combines high-speed experiments, a simplified jet model, and full two-phase simulations to characterize when this delayed transition happens.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The experimental delayed-jetting observation requires that the inlet Weber number is truly stepped to its final value; the pump's flow-rate transient is never measured, and the time origin is defined inconsistently between the figure caption and the text.","rationale":"The reader's weakest assumption correctly identifies the syringe-pump transient as the load-bearing point, and my reading confirms it. The delayed-jetting observation is meaningful only if the Weber number is fixed throughout the transient; otherwise the experiment measures a response to a slowly increasing control parameter rather than an intrinsic history-dependent transition. The manuscript provides no measurement of the actual inlet flow-rate time history, and the inconsistent statement of the t/tc=0 origin in Figure 2 versus Section II makes the problem concrete rather than hypothetical. I do not escalate beyond CONDITIONAL because the numerical simulations with an ideal step velocity show the same qualitative behavior, giving independent support that the phenomenon can exist at fixed parameters; the absence of a direct experiment-simulation comparison at the transition, however, means the experimental evidence remains vulnerable. If the proposed flow-transient measurement shows that the pump reaches setpoint within one capillary time, the central claim would be substantially strengthened. If it shows a slow ramp, the experimental claim would need to be revised, although the computational result could still stand as a theoretical prediction about transient dynamics from an idealized startup.","tokens_in":16114,"tokens_out":7565,"duration_ms":91438,"concrete_test":"Measure the time-resolved inlet velocity during step startup, either by high-speed imaging of the meniscus inside or immediately downstream of the nozzle or by a fast inline flow sensor, and compare the time to reach 95% of the programmed Um with the first pinch-off time. If the ramp time is a substantial fraction of the droplet period or of the observed delay, repeat the experiment using a constant-pressure reservoir with a fast solenoid valve that opens within a few tc, so that the velocity step is genuinely abrupt; if the number of transient dripping droplets before jetting remains O(10-50) at the same Ka, Bo, and We, the pump ramp is not the cause. Also reconcile the t/tc=0 definition between the Figure 2 caption and Section II before counting droplets.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that, at a fixed inlet velocity above the steady-state dripping-to-jetting threshold, the system forms several droplets in the dripping regime before switching to jetting. This interpretation requires the control parameter to reach its final value essentially instantaneously, so that every recorded pinch-off occurs at the stated Weber number. The paper never characterizes the actual flow rate delivered to the nozzle during startup. A NE-1000 syringe pump has a motor ramp, mechanical leadscrew compliance, tubing elasticity, and possible trapped air, all of which can make the nozzle inlet velocity rise over a finite time comparable to the first few pinch-off intervals. The capillary time here is about 1.9 ms, and a syringe-pump settling time of even 0.1-1 s spans many droplet periods. If the delivered Weber number crosses the transition threshold only after several droplets, the observed 'transient' is a quasi-static ramp response rather than an intrinsic fixed-We transient. The inconsistency in the time origin strengthens the concern: the Figure 2 caption says t/tc=0 is pump switch-on, while the Section II text says the timeline starts at the first pinch-off event. The numerical simulations impose an ideal velocity step and do show a delayed jet, which supports the intrinsic-transient reading; however, those simulations are validated against low-We dripping cases (Figure 8 and Appendix A, Figure 15c,d), not against the transition transient itself, and they start from a hemispherical initial condition rather than the measured experimental startup state. The experimental pillar of the central claim therefore rests on an uncharacterized control-parameter time trace.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports experiments and simulations of the dripping-to-jetting transition in Newtonian fluids and argues that, at a fixed inlet velocity above the steady-state critical Weber number, the system first produces several droplets in the dripping regime before switching to jetting. The authors support this with high-speed shadowgraphy of several fluids, a 1D slender-jet model, and Gerris volume-of-fluid simulations. They also show that superposed inlet-velocity perturbations can suppress or accelerate the transition. The central claim is that the transition is a history-dependent transient process rather than an instantaneous switch at a critical Weber number.","tokens_in":16393,"tokens_out":5153,"duration_ms":62158,"significance":"If the central claim holds, it refines the standard quasi-steady dripping-jetting phase diagram by identifying a transient transition band in which the number of pre-transition droplets depends on Weber number and fluid properties. This is practically relevant for drop-on-demand and jetting applications where startup transients determine the first produced droplets. A clear strength is that the 1D simulations use standard slender-jet equations with stated initial and boundary conditions and do not fit parameters to produce the phase diagrams; the low-Weber-number comparison in Fig. 8 is also a genuine validation. However, the experimental support is weakened by uncharacterized pump startup and by the absence of trial counts and error bars, and the numerical support is not validated against the transition transient itself. The result is plausible but not yet established at the level claimed.","major_comments":[{"comment":"The interpretation of the delayed transition as an intrinsic fixed-Weber-number transient requires the inlet velocity to reach its final value on a time scale much shorter than the droplet period. The Fig. 2 caption states that t/tc = 0 is when the syringe pump is switched on, while the text says the timeline starts at the first pinch-off; moreover, the paper nowhere reports the measured flow-rate transient, tubing compliance, or motor ramp of the NE-1000 pump. Because tc is about 2 ms for this system, a pump settling time of even 0.1 s spans many droplet periods, and if the delivered Weber number crosses the transition threshold only after several pinch-offs, the observed sequence is a quasi-static ramp response rather than a transient at fixed We. Please measure the delivered flow rate at the nozzle (or otherwise characterize the startup transient) and reconcile the time-origin definitions.","section":"Section II, Fig. 2"},{"comment":"The central quantitative claim of 'number of droplets before jetting' is presented without trial counts, error bars, or a statement of how many experimental repetitions each data point represents. Figures 3a and 4 show single representative runs, and the kernel density estimates in Fig. 6 do not report the number of droplets used. Given that the dripping regime is chaotic, a single run cannot establish the mean or the variability of the pre-transition droplet count. Please report repeated runs and the resulting spread, at least for the cases used to define W ed−j and the transition band.","section":"Section II, Figs. 3 and 7e"},{"comment":"The numerical evidence for the delayed transition is not validated against the transient regime it is meant to explain. Fig. 8 validates the 1D model at We = 0.0019, deep in the dripping regime, and Appendix A validates Gerris against P1 and P2 regimes; neither checks the predicted number of pre-transition droplets or the time evolution of L/Rn in the D-J transition band. Because the simulations are the primary evidence that the delay is intrinsic to an ideal velocity step, please compare simulated L/Rn(t) and droplet counts with the experimental transition traces at matched Ka and Bo, for example the Um = 0.88 case of Fig. 3a.","section":"Section III, Figs. 8, 10, and 11"},{"comment":"The perturbation frequencies are inconsistent between text and captions. The text says 'two frequencies ω = 1.38 and ω = 3.342' and 'For a frequency ω = 1.38 (Figure 12a)', but the Fig. 12 caption labels the panels '(a) ω = 0.342 (b) ω = 1.38', and the later discussion refers to 'ǫ = 0.2, ω = 0.342' and 'ǫ = 0.7, ω = 1.38'. This prevents the reader from reproducing the perturbation phase diagram in Fig. 14 and from assigning regimes correctly. Please correct the labels and ensure the text, captions, and figure axes agree.","section":"Section III, Figs. 12 and 14"}],"minor_comments":[{"comment":"The panel labels in the Fig. 3 caption repeat '(c)' for the Poincare maps, and the Fig. 7 caption repeats '(c)' for the P2 and jetting panels; please renumber them so that each panel is uniquely identified.","section":"Section II, Figs. 3 and 7"},{"comment":"There are several typographical errors: 'Kaptiza number' should be 'Kapitza number', 'For instant' should be 'For instance', 'vis-a-versa' should be 'vice versa', and in Appendix B 'Desnsity' and 'kernal' should be 'Density' and 'kernel'.","section":"Throughout"},{"comment":"The notation for the transition threshold is inconsistent: the abstract and text use U_{m−d_j}, while the figures and later text use W e_{d−j} or W e_{D−J}. Please define all symbols once and use them uniformly.","section":"Section II"},{"comment":"The perturbed inlet condition is written as a(0,t)=1 and u(0,t)=sqrt(We)+epsilon sin(omega t), but the frequency ranges in Fig. 14 are not stated on the axis labels. Please add explicit axis labels and, if possible, a dimensional or dimensionless frequency axis so the reader can connect Fig. 14 to the examples in Fig. 12.","section":"Section III, Eq. (4)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper has a genuinely new observation — at fixed flow rate near the dripping-jetting threshold, the system spends dozens of droplets in the dripping regime before switching to a jet — and it supports that observation with both experiments and slender-jet simulations that use the same ideal inlet step. The main soft spot is the uncharacterized syringe-pump transient and an internal inconsistency about when t=0 is set. Those are fixable, and the numerical pillar partly covers the experimental hole. I'd send it to review.\n\nWhat's new: previous work mapped the steady-state hysteresis and critical Weber scalings; nobody, as far as the cited literature goes, explicitly characterized the many-droplet transient path or showed that inlet perturbations can switch the regime around the transition. The 1D model is the standard Eggers slender-jet equations, no fitted parameters, and the phase diagrams are honest. The Gerris validation against P1/P2 is a plus.\n\nSoft spots, in order:\n- The time origin: Fig 2 caption says t/tc=0 is pump switch-on; Section II says it's the first pinch-off. That's a real contradiction and must be fixed. It also bears directly on the pump-transient concern.\n- The pump ramp: a NE-1000 has finite motor and compliance dynamics. The capillary time is ~1.9 ms; even a 0.1 s settling time spans many droplet periods. So the experimental delayed jetting could partly reflect a slowly rising We. The 1D simulations, though, impose an ideal velocity step and also show delayed jetting, so the phenomenon is not purely an artifact of the pump. The catch is that these simulations are validated on low-We dripping and P1/P2, not on the transition transient itself, and they start from a hemispherical initial condition. Measuring the actual flow rate at the nozzle, or at least checking the pump's step response, would close the gap.\n- No error bars or trial counts for the transition times and droplet counts. For a paper with mostly qualitative claims that's a moderate issue, not a fatal one.\n- The perturbation figure: text says ω=3.342 in one place, caption says 0.342. Given the phase plot, it's almost certainly 0.342, but the inconsistency is confusing.\n\nOverall: the central claim is plausible and the two pillars point the same way. With the time-origin fix and a pump characterization, this would be a solid contribution. For a journal, I'd send it to a referee who knows syringe pumps and dripping transients. As a reading group pick, it's worth a look but not a must-read.","headline":"A genuinely new transient-dripping observation, supported by both experiments and ideal-step simulations, but the pump-start transient and a time-origin inconsistency need to be addressed before I'd trust the experimental numbers.","tokens_in":16917,"tokens_out":3318,"would_cite":true,"duration_ms":37313,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"At a critical flow rate, dripping faucets keep dripping for dozens of pinch-off events before the jet finally appears.","keywords":["dripping-jetting transition","dripping faucet","transient dynamics","Weber number","Kapitza number","slender-jet equations","droplet pinch-off","flow-rate perturbation"],"falsifier":"Measure the time-resolved inlet velocity during pump startup, for example by imaging the meniscus in a transparent inlet line or placing a flow meter between the pump and nozzle, and repeat the $U_m = 0.88$ experiment with a pump that reaches its set flow rate in a time much shorter than the capillary time $t_c$. If the delay to jetting disappears or changes dramatically, the many-droplet transient is an artifact of the ramp; if a near-step inlet reproduces the same count of pinch-offs, the transient is intrinsic to the dripping-jetting transition.","tokens_in":15915,"feed_emoji":"💧","tokens_out":10506,"duration_ms":100079,"temperature":0.7,"pith_summary":"This paper asks what actually happens when the flow through a nozzle is increased past the point where the dripping-to-jetting transition is expected. The authors find that the transition is not an abrupt switch: at a critical inlet velocity the liquid column keeps pinching off droplets in the dripping mode for many events, and only after several to dozens of droplets does the system settle into a jet. The number of preliminary droplets grows as the Weber number approaches the threshold from above and depends on the Kapitza number and the Bond number, so the dripping-jetting boundary names a transient band rather than a single control value. Inlet-velocity perturbations can shift the system across that band, changing whether the final state is dripping or jetting. That matters for applications in which droplet size and formation timing near the transition have to be controlled.","feed_headline":"Dripping-to-jetting switch is a slow transient, not a flip","feed_subtitle":"New flow-rate experiments show the jet emerges only after many pinch-offs, and perturbations can advance or delay it.","key_machinery":"The load-bearing tool is the one-dimensional slender-jet formulation: a reduced model for an axisymmetric liquid column described by a radius $h(z,t)$ and a mean axial velocity $v_0(z,t)$, with inertia, viscosity, capillarity, and gravity represented through the Ohnesorge number, Bond number, and Weber number. To integrate through pinch-off the authors switch variables to $a = h^2$, which regularizes the thinning neck. The argument's mechanical core is the escape pinch-off process: after each breakup the column retracts and capillary waves travel upstream; prolate-oblate oscillations of the pendant drop coarsen the neck and delay the pinch-off, so the next droplet forms from a slightly longer column, and this ratcheting elongation eventually lets the tip outrun the recoil and establishes a jet. The same equations, with the inlet condition $a(0,t) = 1$ and $u(0,t) = \\sqrt{We} + \\epsilon \\sin(\\omega t)$, are used to show that inlet perturbations can suppress or accelerate the transition.","core_discovery":"The central discovery is a time-resolved picture of the dripping-jetting transition in Newtonian fluids. For inlet velocities just above the steady-state critical value, the system starts in dripping and repeatedly pinches off droplets while the liquid column attached to the nozzle grows a little after each breakup; eventually the tip velocity of the column exceeds the inlet velocity, the column stops fully recoiling, and the jet appears. In experiments with Kapitza number 0.181 and Bond number 0.067, a dimensionless inlet velocity $U_m = 0.88$ produced roughly fifty dripping pinch-offs before jetting, whereas $U_m = 1.5$ needed only about ten and reached the jet at $t/t_c = 312$ rather than $t/t_c = 888$. The same progressive elongation is reproduced by the slender-jet equations and by full two-phase Navier-Stokes simulations, including the asymmetry of the hysteresis loop: jetting-to-dripping upon reducing flow is a sudden drop rather than a long transient. The paper therefore claims that the quasi-steady phase boundary should be split into two Weber numbers: the lowest Weber number at which jetting eventually appears after a transient, and the higher Weber number at which jetting begins immediately.","pith_inferences":["Editorial extension: if the transition is a slow trajectory on the system's phase space, the number of pre-jetting droplets likely follows a scaling law in the distance from the threshold, such as a power of $(We - We_{d-j})$; the paper reports the trend but does not derive such a law, so this is a testable quantitative prediction.","Editorial extension: the escape-pinch-off ratchet should also operate in non-Newtonian or viscoelastic fluids, where delayed necking is stronger; repeating the same startup protocol with such fluids would test whether the transient band widens or narrows with relaxation time.","Editorial extension: in printing and spraying, a controller that perturbs the nozzle near the droplet formation frequency could use the transient band to switch between dripping and jetting on demand; the paper's perturbation phase plots are the raw material for such a control strategy."],"forward_implications":["The critical Weber number reported for dripping-to-jetting is observation-time dependent; two experiments at the same flow rate can be classified as dripping or jetting depending on whether the recording lasts long enough to include the transient.","The transient band is wider at low Kapitza numbers and narrows with increasing viscosity, so fluid properties set not only the boundary location but also the delay needed to reach it.","At the same nominal flow rate the system can display dripping, a mixed regime, or jetting depending on flow history, so the hysteresis in this transition has a temporal dimension, not just a static one.","Inlet forcing in the dripping-to-jetting band can move the system into either the dripping or the jetting branch, meaning perturbations of suitable amplitude and frequency can stabilize a desired breakup mode."],"supporting_citations":[{"why":"Supplies the Ohnesorge-number scaling for the steady-state dripping-jetting Weber number that defines the threshold from which the transient departs.","marker":"[8]"},{"why":"Establishes the quasi-steady dripping-jetting phase behavior and hysteresis that the present transient picture extends.","marker":"[5]"},{"why":"Provides experimental dependence of the critical Weber number on viscosity and Bond number, used for comparison with the new transient measurements.","marker":"[6]"},{"why":"Supplies the slender-jet equations used for the one-dimensional simulations of the transition.","marker":"[18]"},{"why":"Provides the numerical method and perturbation-forcing approach for controlling breakup on which the inlet-velocity perturbation study is built.","marker":"[19]"},{"why":"Supplies experimental validation cases, the P1 and P2 regimes, for both the slender-jet and volume-of-fluid simulations.","marker":"[10]"},{"why":"Describes the recoil and escape-pinch-off dynamics invoked to explain the progressive column elongation between droplets.","marker":"[17]"}],"fun_headline_variants":["Dripping to jetting: a slow transient, not a sudden flip","Jetting emerges after dozens of drips, not instantly","Slow transient governs the dripping-jetting transition","Drip-jet transition takes time: up to 50 pinch-offs","Jet appears late: transient dynamics decide the switch"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The experiments assume that switching on the syringe pump is an instantaneous step in inlet velocity at $t/t_c = 0$, but the pump's flow-rate ramp, tubing compliance, and motor transient are never characterized; if the pump approaches the set flow rate slowly, the observed delay in jetting could be a response to a gradually rising Weber number rather than an intrinsic many-droplet transient at fixed control conditions.","fun_headline_variants_meta":{"raw":{"variants":["Dripping to jetting: a slow transient, not a sudden flip","Jetting emerges after dozens of drips, not instantly","Slow transient governs the dripping-jetting transition","Drip-jet transition takes time: up to 50 pinch-offs","Jet appears late: transient dynamics decide the switch"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000147,"raw_usage":{"total_tokens":1233,"prompt_tokens":1037,"completion_tokens":196,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":653,"completion_tokens_details":{"reasoning_tokens":112}},"tokens_in":653,"tokens_out":196,"duration_ms":52171,"temperature":1.0,"reasoning_tokens":112,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T18:54:05.853460+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the time-resolved inlet velocity during pump startup, for example by imaging the meniscus in a transparent inlet line or placing a flow meter between the pump and nozzle, and repeat the $U_m = 0.88$ experiment with a pump that reaches its set flow rate in a time much shorter than the capillary time $t_c$. If the delay to jetting disappears or changes dramatically, the many-droplet transient is an artifact of the ramp; if a near-step inlet reproduces the same count of pinch-offs, the transient is intrinsic to the dripping-jetting transition.","supporting_citations":[{"cited_title":"Ambravaneswaran, H","cited_arxiv_id":null,"evidence_quote":"Supplies the Ohnesorge-number scaling for the steady-state dripping-jetting Weber number that defines the threshold from which the transient departs."},{"cited_title":"Clanet and J","cited_arxiv_id":null,"evidence_quote":"Establishes the quasi-steady dripping-jetting phase behavior and hysteresis that the present transient picture extends."},{"cited_title":"Rubio-Rubio, P","cited_arxiv_id":null,"evidence_quote":"Provides experimental dependence of the critical Weber number on viscosity and Bond number, used for comparison with the new transient measurements."},{"cited_title":"Eggers and T","cited_arxiv_id":null,"evidence_quote":"Supplies the slender-jet equations used for the one-dimensional simulations of the transition."},{"cited_title":"Shukla and F","cited_arxiv_id":null,"evidence_quote":"Provides the numerical method and perturbation-forcing approach for controlling breakup on which the inlet-velocity perturbation study is built."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies experimental validation cases, the P1 and P2 regimes, for both the slender-jet and volume-of-fluid simulations."},{"cited_title":"Hoepffner and G","cited_arxiv_id":null,"evidence_quote":"Describes the recoil and escape-pinch-off dynamics invoked to explain the progressive column elongation between droplets."}],"review_version":1}