Filling, Overflowing, and Circulating System (FOC)

• FOC is a dual-context concept that maps observed microcavity filling and overflowing regimes in lab-on-a-chip experiments and informs large-scale liquid handling in JUNO.
• In microfluidics, FOC delineates filling versus overflowing states by examining interface pinning, capillary forces, and transient dynamics using advanced imaging and simulations.
• In JUNO, the FOC system integrates precise detector filling, overflow buffering, and optional circulation to meet stringent radiopurity and hydrostatic control requirements.

Searching arXiv for the cited FOC-related papers to ground the article in current sources. {"query":"arXiv (Nagel et al., 2024) Experimental and Numerical Study of Microcavity Filling Regimes for Lab-on-a-Chip Applications", "max_results": 5} Searching arXiv for the microcavity filling paper. {"query":"Experimental and Numerical Study of Microcavity Filling Regimes for Lab-on-a-Chip Applications", "max_results": 10} Filling, Overflowing, and Circulating System (FOC) is a designation used in recent literature for two distinct but thematically related technical objects. In microfluidics, it serves as a mapping from observed microcavity-interface states to the labels Filling and Overflowing, while a distinct Circulating regime was not identified under the low-$Re$, capillary-dominated conditions studied (Nagel et al., 2024). In the Jiangmen Underground Neutrino Observatory (JUNO), FOC denotes the liquid-handling subsystem responsible for detector filling, overflow management, and optional circulation for re-purification of liquid scintillator (LS) and water (Li et al., 12 Jul 2025, Li et al., 16 Dec 2025). In both contexts, the term centers on controlled management of interfaces, inventories, and transients under strong geometric and safety constraints.

1. Terminological scope and domain-specific meanings

The acronym is not used uniformly across domains. The microcavity study defines experimentally observed filling states and then maps them onto the Filling, Overflowing, and Circulating notion, with explicit caution that sustained in-cavity recirculation eddies were not observed as a regime (Nagel et al., 2024). By contrast, JUNO uses FOC as the name of a process plant and control system; the nomenclature varies slightly between publications, appearing as “Filling, Overflowing, and Circulating System” and as “Filling, Overflow, and Circulation (FOC) system” (Li et al., 12 Jul 2025, Li et al., 16 Dec 2025).

Usage	Filling / Overflowing	Circulating
Microcavity flow	Filling: cavity invasion after pinning; Overflowing: interface skims over cavities leaving an air cushion or bubble	Not identified as a distinct regime
JUNO liquid handling	Filling: water fill and LS exchange; Overflowing: passive and active accommodation of thermal volume changes	Optional online extraction, purification, and reinjection

In the microcavity context, Filling means that all cavities are invaded, either voidlessly or with only tiny trapped bubbles at the cavity bottom. Overflowing means that the interface pins at cavity edges, detaches, and passes over the cavities without complete filling, leaving an air cushion or bubble below the liquid. The paper also defines a Partially Filled state, but reports that it is not repeatable across replicates (Nagel et al., 2024).

In JUNO, Filling refers to commissioning operations such as synchronous water filling of the Central Detector (CD) and Water Pool (WP), and later water-to-LS exchange. Overflowing refers to the buffering of LS thermal volume changes via passive overflow tanks and active transfers with a storage tank. Circulation refers to optional extraction from the detector bottom, external re-purification, and reinjection at the top (Li et al., 16 Dec 2025).

2. Microcavity FOC regimes in capillary-dominated flow

The microcavity study investigates a moving liquid-air interface over a $3\times 3$ array of cylindrical cavities in a rectangular microchannel under lab-on-a-chip conditions. Two cavity depths were tested, $d = 0.07\ \mathrm{mm}$ and $d = 0.14\ \mathrm{mm}$. The cavities were patterned into a PMMA slide with micromilled roughness $\le 5\times 10^{-6}\ \mathrm{m}$, sealed by a smooth transparent Zeonex lid. Top-down high-speed imaging with $3\ \mu\mathrm{m}$ pixel size and grayscale-based edge detection was used to track the interface (Nagel et al., 2024).

Three fluids were examined at $20^\circ\mathrm{C}$: water, a $0.1\%$ aqueous Tween-80 solution, and Novec-7500. Their wetting properties differ strongly. Water and Tween exhibit partial wetting on PMMA/Zeonex, whereas Novec is reported as perfectly wetting on PMMA and Zeonex with $\theta_{eq}=0^\circ$. Static Zeonex contact angles from droplet tests were $94\pm 5^\circ$ for water, $3\times 3$0 for Tween, and $3\times 3$1 for Novec. The experimentally achieved capillary-number ranges were $3\times 3$2, $3\times 3$3, and $3\times 3$4 for water; $3\times 3$5, $3\times 3$6, and $3\times 3$7 for Tween; and $3\times 3$8 and $3\times 3$9 for Novec (Nagel et al., 2024).

The regime logic is governed by pinning, depinning, wetting, and viscous forcing. Filling occurs when the interface pins at upstream cavity edges and subsequently advances through the cavity volume. The mechanism is described as low apparent dynamic contact angle $d = 0.07\ \mathrm{mm}$0, strong capillary suction relative to imposed viscous drag, and pinning that precedes invasion. Near-wall cavities often invade first because of rivulets and local curvature, followed by center cavities. Overflowing also begins with pinning, but pinning is then insufficient to promote snap-through; the interface detaches and skims over the cavities, leaving an air cushion or bubble. Partial filling is attributed to sensitivity to local roughness, transient surfactant distribution, and subtle contact-angle hysteresis, producing stochastic pinning and depinning (Nagel et al., 2024).

The principal parametric trends are discrete rather than threshold-fitted. Novec exhibits Filling across all tested capillary numbers and both tested depths. Tween depends on capillary number and depth: at $d = 0.07\ \mathrm{mm}$1, Overflowing occurs, while lower $d = 0.07\ \mathrm{mm}$2 and shallower cavities increase the probability of Filling. Water is predominantly Overflowing; Partial filling was observed only at $d = 0.07\ \mathrm{mm}$3 in shallow cavities, while all higher tested $d = 0.07\ \mathrm{mm}$4 values yielded Overflowing. The study reports that apparent dynamic contact angles measured upstream of the array increase by more than $d = 0.07\ \mathrm{mm}$5 across the tested $d = 0.07\ \mathrm{mm}$6 range for each fluid, and that deeper cavities are harder to fill (Nagel et al., 2024).

The relevant dimensionless and capillary relations are given explicitly. The capillary number is

$d = 0.07\ \mathrm{mm}$7

the Reynolds number is

$d = 0.07\ \mathrm{mm}$8

the Bond number is

$d = 0.07\ \mathrm{mm}$9

and the Young-Laplace capillary pressure is

$d = 0.14\ \mathrm{mm}$0

A Cox-Voinov-type relation is cited as a common reference model,

$d = 0.14\ \mathrm{mm}$1

but the study does not fit a specific $d = 0.14\ \mathrm{mm}$2 law (Nagel et al., 2024).

3. Interface transients, numerical reconstruction, and the non-observation of a microcavity circulating regime

The microcavity work combines experiments with $d = 0.14\ \mathrm{mm}$3D Volume-of-Fluid simulations using plicRDF-isoAdvection on unstructured meshes. The solver is interFlow in OpenFOAM v2212 within the TwoPhaseFlow framework. A baseline mesh resolution of $d = 0.14\ \mathrm{mm}$4 was used, with refinement tests at $d = 0.14\ \mathrm{mm}$5 and $d = 0.14\ \mathrm{mm}$6; these showed negligible change in interface progression relative to regime differences. The timestep obeyed a capillary-wave restriction,

$d = 0.14\ \mathrm{mm}$7

Boundary conditions were constant inlet velocity and zero-pressure outlet, with partial-slip walls of slip length $d = 0.14\ \mathrm{mm}$8, an $d = 0.14\ \mathrm{mm}$9 symmetry plane, and constant wall contact angles taken from measured $\le 5\times 10^{-6}\ \mathrm{m}$0 medians. Stabilization used artificial interface viscosity $\le 5\times 10^{-6}\ \mathrm{m}$1 and wisp filtering tolerance $\le 5\times 10^{-6}\ \mathrm{m}$2 (Nagel et al., 2024).

The transient behavior clarifies how the observed regimes unfold. In a Novec Filling case at $\le 5\times 10^{-6}\ \mathrm{m}$3, the reported sequence is pinning at first-row edges at $\le 5\times 10^{-6}\ \mathrm{m}$4, rapid filling of near-wall cavities over $\le 5\times 10^{-6}\ \mathrm{m}$5 at $\le 5\times 10^{-6}\ \mathrm{m}$6, strong pinning at the center cavity at $\le 5\times 10^{-6}\ \mathrm{m}$7, and snap-through with traversal at $\le 5\times 10^{-6}\ \mathrm{m}$8. Position-versus-time curves exhibit “kinks” that coincide with pinning and filling events. In a Tween Overflowing case at $\le 5\times 10^{-6}\ \mathrm{m}$9, the first row shows pinning at $3\ \mu\mathrm{m}$0, center-cavity detachment at $3\ \mu\mathrm{m}$1, and wall-adjacent detachment at $3\ \mu\mathrm{m}$2, followed by repetition at the second row around $3\ \mu\mathrm{m}$3 (Nagel et al., 2024).

Agreement between experiments and simulations is reported as strong for most Filling-versus-Overflowing cases and for the timing of pinning, detachment, and traversal kinks. Partial filling was not reproduced; in marginal cases, simulations tended to predict Overflowing. The authors characterize this as conservative for void-free design. Near-wall rivulet morphology remains harder to reproduce exactly, and for Novec the effective contact-angle calibration depended on capillary number: $3\ \mu\mathrm{m}$4 at $3\ \mu\mathrm{m}$5 and $3\ \mu\mathrm{m}$6 at $3\ \mu\mathrm{m}$7 gave the best matches among tested values (Nagel et al., 2024).

The status of “Circulating” in this microfluidic usage is therefore negative rather than positive: it is not identified as a distinct regime. No sustained in-cavity recirculation eddies are reported by either experiments or simulations under the tested low-$3\ \mu\mathrm{m}$8 conditions. The imaging is top-down, intra-cavity flow fields were not resolved, and the modeling focuses on interface pinning, invasion, and skimming rather than on cavity-resolved vortical structures. The paper explicitly states that design implications for inducing or suppressing recirculation are extrapolations and should be tested separately. A plausible implication is that, in this parameter space, interfacial wetting barriers dominate more strongly than intra-cavity inertial recirculation (Nagel et al., 2024).

For practical diagnosis, the study recommends observing the pinning-depinning sequence at cavity edges, identifying interface kinks in position-time curves when rows are crossed, measuring upstream $3\ \mu\mathrm{m}$9, and using simulations with calibrated $20^\circ\mathrm{C}$0 to predict regime and transients. The associated data and code are publicly available through Bosch Research GitHub and the TUDatalib repository (Nagel et al., 2024).

4. JUNO FOC as a large-scale detector liquid-handling and control subsystem

In JUNO, the FOC system is a plant-scale subsystem engineered to safely deliver, maintain, and re-purify the $20^\circ\mathrm{C}$1-kiloton LS inventory of the Central Detector while preserving $20^\circ\mathrm{C}$2 energy resolution at $20^\circ\mathrm{C}$3 and low radioactive background. The control objectives include protection of the $20^\circ\mathrm{C}$4-m-diameter acrylic sphere and its chimneys during filling and exchange, stable detector internal pressure during operation, liquid-level excursions limited to $20^\circ\mathrm{C}$5, automatic overflow and refill, and online LS circulation for re-purification. Purity constraints include avoidance of oxygen, moisture, dust, radon, and rare-gas ingress, leakage rate $20^\circ\mathrm{C}$6, optical attenuation length $20^\circ\mathrm{C}$7, and dust $20^\circ\mathrm{C}$8. Reliability targets include sensor accuracy typically $20^\circ\mathrm{C}$9 FS, closed-loop deviation $0.1\%$0, pump speed stability within $0.1\%$1 of setpoint, on-off valve response $0.1\%$2, regulating-valve positioning accuracy $0.1\%$3, and extensive redundancy with fail-safe behavior (Li et al., 12 Jul 2025).

The hardware core is a Siemens S7-300 PLC with one CPU and one interface module, six $0.1\%$4-channel AI modules, two $0.1\%$5-channel AO modules, and three digital I/O modules. The PLC cabinet includes an industrial audible/visual alarm device and a physical emergency stop. Instrumentation is dominated by Endress+Hauser devices. For the CD, the system includes four electronic remote differential-pressure level gauges in two redundant pairs at $0.1\%$6 FS, one laser level gauge at $0.1\%$7 FS, and two differential-pressure gauges on the upper chimney at $0.1\%$8 FS. WP level uses five static pressure level gauges at $0.1\%$9 FS. Tank instrumentation combines differential-pressure gauges and radar wave level gauges at $\theta_{eq}=0^\circ$0 FS. Flow is measured by Coriolis and vortex meters, and pressure by gas-space and pump-discharge transmitters (Li et al., 12 Jul 2025).

Actuation is provided by SED regulating and on-off valves and by CDR electromagnetic pumps together with Yamei vacuum self-priming pumps. Eight pump units are included in total. Electromagnetic pumps are configured one-operating/one-standby. The process also contains a storage tank, two overflow tanks, top and bottom chimneys, a nitrogen cover-gas system, and filtration monitored by differential pressure. The software stack is built in Siemens TIA Portal and implements PID control, sequential or state-machine control, interlocks, split-range control, and selective control. EPICS is used for live monitoring, historical queries, and data caching across JUNO subsystems, with a heartbeat program supervising PLC status. Alarm management spans cabinet sirens, HMI alarms, and emergency stop, while historian functionality uses dual storage with local disk and synchronized Detector Control System (DCS) storage (Li et al., 12 Jul 2025).

The control methods are described in operational rather than formal-model terms. Ziegler-Nichols rules supply initial $\theta_{eq}=0^\circ$1, $\theta_{eq}=0^\circ$2, and $\theta_{eq}=0^\circ$3, followed by empirical refinement for minimal overshoot and fast settling. Signal preprocessing includes arithmetic mean filtering, which reduced radar level-gauge noise from about $\theta_{eq}=0^\circ$4 to about $\theta_{eq}=0^\circ$5, and time-hysteresis filtering to reduce transient false trips. Split-range control is used, for example, when a single flow controller drives two regulating valves during water filling. Selective control prioritizes the most critical constraint, such as pressure or level, when limits are approached. Safety logic is independent of normal control; critical sensors are separated in safety interlocks, and fail-safe defaults close valves and stop pumps upon anomaly detection or signal loss (Li et al., 12 Jul 2025).

5. Filling, overflow, and circulation operations in JUNO

The FOC system spans commissioning and long-term operation. During commissioning, water filling synchronously fills the CD and WP to displace air, rinse the acrylic inner surface, and establish a safe hydrostatic environment before LS exchange. LS filling then injects purified LS from the top chimney while draining water from the bottom. During long-term operation, overflow tanks buffer thermal volume changes and circulation supports optional online purification (Li et al., 16 Dec 2025).

Water filling handled approximately $\theta_{eq}=0^\circ$6 in $\theta_{eq}=0^\circ$7 days. The reported average flow calculation is

$\theta_{eq}=0^\circ$8

Operationally, the total available flow was about $\theta_{eq}=0^\circ$9, with Stage-2 and Stage-3 setpoints around $94\pm 5^\circ$0, punctuated by daily pauses and slow on-off top-up bursts. The WP served as the primary level reference, and the differential level $94\pm 5^\circ$1 was held within a fraction, $94\pm 5^\circ$2, of the FEA design limit, with on-off interlocks if exceeded. Because the acrylic sphere tolerates higher external than internal pressure, a slightly higher WP level was preferred. Pure-water system tests reported two PID-controlled streams reaching about $94\pm 5^\circ$3 on the WP pipeline and about $94\pm 5^\circ$4 on the CD pipeline in about $94\pm 5^\circ$5 minutes, then holding with $94\pm 5^\circ$6 uncertainty (Li et al., 16 Dec 2025, Li et al., 12 Jul 2025).

The tall risers imposed a vertical static head of about $94\pm 5^\circ$7, creating risk of vapor cavity formation and water hammer. Vacuum-break valves on WP lines and a $94\pm 5^\circ$8 nitrogen buffer on CD lines prevented sub-atmospheric pressures without air ingress. A typical purge flow of about $94\pm 5^\circ$9 is reported for sensitive operations (Li et al., 16 Dec 2025).

LS filling handled approximately $3\times 3$00 in $3\times 3$01 days, corresponding to an average of

$3\times 3$02

The nominal LS production rate was $3\times 3$03. Before exchange, the CD was purged with ultra-pure nitrogen at $3\times 3$04. Startup injected an initial $3\times 3$05 LS batch and held for several days for OSIRIS radiopurity verification and radon decay stabilization. Continuous filling then ramped from $3\times 3$06-$3\times 3$07 to $3\times 3$08, with top injection and bottom water drainage. After completion, about $3\times 3$09 was drained from the CD bottom to remove the earliest batch, which had the longest contact with residual water and particulates. Internal FOC tests also demonstrated LS flow regulation to $3\times 3$10 through a regulating valve, Coriolis meter, and filter with PID feedback, reaching $3\times 3$11 accuracy after about $3\times 3$12 minutes (Li et al., 16 Dec 2025, Li et al., 12 Jul 2025).

Hydrostatic management is central during LS exchange because $3\times 3$13 and $3\times 3$14. The governing hydrostatic relation is

$3\times 3$15

To balance the denser external water, the LS free surface must be higher than the WP level. The reported illustrative balance is

$3\times 3$16

giving

$3\times 3$17

For $3\times 3$18, this implies $3\times 3$19, which is consistent with the final LS level near $3\times 3$20. Achieved LS level precision was $3\times 3$21, and flow regulation was within $3\times 3$22 of setpoints (Li et al., 16 Dec 2025).

Overflow management combines passive and active modes. Two $3\times 3$23 overflow tanks connected to the top chimney absorb small thermal swings by gravity flow. For larger temperature steps, transfers occur between storage and overflow or CD via pumps under PLC control. With the operational CD level stabilized at about $3\times 3$24, passive overflow capacity is reduced to about $3\times 3$25 of nominal, so the PLC maintains CD level within $3\times 3$26 through small active transfers in addition to passive buffering. The thermal-volume estimate

$3\times 3$27

with $3\times 3$28 and $3\times 3$29 yields $3\times 3$30, which is consistent with the reported buffering demand (Li et al., 16 Dec 2025).

Circulation extracts LS from the detector bottom, routes it through water extraction and gas stripping, and reinjects it at the top. The nominal circulation setpoint is $3\times 3$31, corresponding to a nominal full-volume turnover time of about $3\times 3$32 days. CFD results cited in the operational paper indicate that a single-volume exchange removes about $3\times 3$33 of bulk impurities without temperature offset, while heating the injected LS by about $3\times 3$34 improves circulation efficiency to about $3\times 3$35 by suppressing convective short-circuiting (Li et al., 16 Dec 2025).

6. Purity assurance, operational limitations, and broader significance

For JUNO, FOC performance is inseparable from radiopurity and cleanliness control. All wetted components are specified as low-radioactivity stainless steel with $3\times 3$36, electropolished inner roughness $3\times 3$37 and typically $3\times 3$38-$3\times 3$39, helium leak-rate goals of $3\times 3$40 for components and $3\times 3$41 for assembled systems or critical flanges, and nitrogen inerting over LS-contacted gas spaces. Cleaning is specified as detergent degrease, dilute $3\times 3$42 pickling, $3\times 3$43 passivation, UPW rinse, and nitrogen drying, with acceptance by MIL-STD-1246C particle-density criteria and final-rinse $3\times 3$44 (Li et al., 16 Dec 2025).

The achieved radiopurity metrics during LS filling were $3\times 3$45, below the stated requirement of $3\times 3$46, and bulk $3\times 3$47 by ICP-MS. An initial $3\times 3$48 rate of about $3\times 3$49 after fill is reported. Monitoring used in-situ $3\times 3$50-$3\times 3$51 tagging for radon, periodic $3\times 3$52-$3\times 3$53 OSIRIS batch assays, and ICP-MS on prepared LS samples with ultra-clean labware. The radon-decay relation

$3\times 3$54

with $3\times 3$55, is used to illustrate why the initial $3\times 3$56 hold stabilizes nonequilibrium radon before continuous fill (Li et al., 16 Dec 2025).

Both domains also report limitations. In the microcavity study, top-down imaging does not resolve intra-cavity flow fields, surfactant transport is not modeled, the dynamic contact angle is imposed as a constant apparent $3\times 3$57 rather than through a fitted $3\times 3$58 law, and stochastic Partial filling linked to roughness and adsorption is not reproduced numerically. The absence of a distinct Circulating regime is therefore an observation specific to the studied low-$3\times 3$59, capillary-dominated parameter range rather than a universal exclusion of cavity recirculation (Nagel et al., 2024).

In JUNO, instrumentation tests revealed a $3\times 3$60-$3\times 3$61 dead zone for some differential-pressure level gauges due to installation constraints and about a $3\times 3$62 dead zone with response lag for radar gauges in horizontal tanks. An overflow-line airlock was encountered after filling and was mitigated by repurposing the LS fill line, sustaining overflow above $3\times 3$63. Raw LAB supply intermittency and scheduled maintenance caused short pauses during LS filling. Structural loads remained within design, although a few rods reached about $3\times 3$64 above FEA predictions and were reported as under investigation. ICS cybersecurity specifics, line sizes, and some gas-handling details are not publicly specified in the paper set (Li et al., 12 Jul 2025, Li et al., 16 Dec 2025).

The broader significance differs by scale but converges methodologically. In microfluidics, FOC language organizes how wetting, pinning, and capillary suction determine whether cavity invasion is achieved or bypassed. In JUNO, FOC integrates hydraulics, automation, leak-tight engineering, nitrogen protection, and radiopurity assurance into a subsystem that filled the world’s largest LS detector with verified $3\times 3$65 level precision and $3\times 3$66 flow regulation during LS operations (Li et al., 16 Dec 2025). JUNO explicitly situates this approach in conceptual continuity with Borexino and KamLAND—nitrogen blanketing, ultra-clean materials, distillation, stripping, water extraction, leak-tight assembly, and online radiopurity assay—while emphasizing the scale-driven advances required for a $3\times 3$67 sphere, synchronized WP-CD hydrostatic control, and overflow handling for thermal swings of about $3\times 3$68 (Li et al., 16 Dec 2025).