Filament Capture Rate: Cross-Domain Analysis

• Filament capture rate is a measure quantifying the successful transition of a filament from free motion to a constrained state, conditioned by additional processes in mechanical, biochemical, and astrophysical domains.
• In extrusion additive manufacturing, capture rate reflects the maximum reliable feed governed by a nut-feed mechanism and thermal conditioning, enabling higher build rates with improved force capacity.
• In nanopore and protein–filament studies, capture rate emerges from stochastic and diffusion-driven processes, while in astrophysics it acts as an indirect proxy for gas accretion and dense structure formation.

Filament capture rate denotes a class of rate-like quantities that describe successful engagement with a filament or filament-associated target. In the recent literature, the term is not a single standardized observable. In desktop extrusion additive manufacturing, it refers to the maximum reliable feed rate at which a drive mechanism can engage and advance filament without slip or mechanical failure; in nanopore physics, it is the stochastic rate at which a polymer is captured for translocation; in cytoskeletal biophysics, it is an effective association rate to a filament tip generated by one-dimensional diffusion and end capture; and in studies of interstellar filaments it appears more indirectly through accretion diagnostics and dense-gas assembly measures rather than as a formally defined capture constant (Go et al., 2017, Seth et al., 2021, Reithmann et al., 2015, Gómez et al., 2021, Xu et al., 20 Feb 2026).

1. Scope and operational meanings

Across disciplines, the common element is that “capture” is not mere contact. It is a successful transition into a constrained state: a threaded filament engaged by a nut-drive, a DNA end or fold entering a nanopore, a protein reaching and remaining at a filament tip, or gas becoming concentrated into dense filamentary substructure. What differs is the operational observable used to quantify that transition.

Domain	Captured entity or process	Operational rate concept
FastFFF extrusion	Threaded polymer filament	Maximum reliable feed rate and supported build rate
Nanopore translocation	DNA entry into a solitary nanopore	$\lambda_{cap}$ in $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$
Protein–filament systems	Protein association to filament end	$$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$
Molecular-cloud filaments	Gas accretion traced chemically	Width ratios proposed as accretion-rate diagnostic
Dense-gas tomography	Assembly of dense sub-parsec structure	No explicit numerical capture rate derived

A recurrent misconception is to treat capture rate as a purely geometric or kinematic quantity. The cited works show that it is usually conditional on an additional process: heating in extrusion, field-driven conformational bias in nanopores, diffusion plus detachment competition on cytoskeletal filaments, or chemistry–flow competition in astrophysical filaments. This suggests that capture rates are best interpreted as coupled transport-to-engagement observables rather than as standalone speeds.

2. Positive mechanical capture in extrusion additive manufacturing

In FastFFF, the paper does not define a formal metric called filament capture rate, but the relevant quantity is the maximum controllable filament feed rate at which the drive can reliably engage the filament, keep it threaded, and push it through heating and the nozzle without loss of traction or mechanical failure (Go et al., 2017). The central design change is a nut-feed mechanism. The filament is custom-threaded with a standard 4-40 thread, and a rotating drive nut with matching internal threads pushes the filament forward. The nut is constrained so it can only rotate axially, while the filament is constrained by rollers so it can only translate linearly. Feed is governed by

$Z = P \dot{\theta},$

where $Z$ is the linear feed rate, $P$ is the thread pitch, and $\dot{\theta}$ is the angular velocity of the nut.

This arrangement replaces friction-limited pinch-wheel traction with near-circumferential thread engagement. The paper compares the force capacity of the threaded interface with conventional pinch-wheel drive by estimating a maximum axial force from thread shear area,

$F_{\max} \sim \tau_{\text{uts}} A_s.$

For ABS threaded filament, the illustrative single-thread engagement failure force is $109$ N for an engagement length $l_e = 0.64$ mm, measured over strain rates of $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$0–$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$1 mm/s; the estimated capacity from geometry and ABS tensile strength is $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$2 N. This is compared with a traditional pinch-wheel extruder maximum force of $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$3 N. The engineering significance is direct: the nut-feed mechanism improves the ability to capture and hold filament under load.

The practical limit is set not only by axial engagement but by torsional and frictional failure. At forces above $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$4 N, the filament failed in torsion due to frictional resistance in the nut-thread interface. The paper therefore identifies a tradeoff: larger thread engagement and finer pitch increase force capacity, but they also increase friction and required motor torque, which can drive torsional stress and failure. Filament capture rate in this sense is a bounded operating window rather than a monotone function of engagement strength.

FastFFF also shows that mechanical capture is inseparable from thermal conditioning. The printhead augments conduction heat transfer with a fiber-coupled diode laser, and the paper states that additional IR heating reduces the force required for a particular feed rate and increases the maximum achievable feed rate before filament failure. With IR laser preheating, the maximum extrusion rate is $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$5 with a $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$6 mm nozzle at a laser power equivalent of $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$7. Without the laser, the measured maxima are $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$8 for a $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$9 mm nozzle and $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$0 for a $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$1 mm nozzle, with force approaching $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$2 N before torsional failure. The paper’s conclusion is explicit: better filament handling alone is insufficient unless the thermoplastic is heated quickly enough to reduce extrusion force.

The feed rate sets system-level throughput through

$$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$3

where $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$4 is volumetric build rate, $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$5 is filament feed rate, and $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$6 mm for the 4-40 threaded ABS filament. The corresponding print speed relation is given as $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$7. The paper gives two examples: with $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$8 mm, $$k_{\mathrm{on}}^{\mathrm{eff}}=k_{\mathrm{on}}+k_{\mathrm{on}}^{D}$$9 mm, and $Z = P \dot{\theta},$0 mm/s, $Z = P \dot{\theta},$1 mm/s; with $Z = P \dot{\theta},$2 mm, $Z = P \dot{\theta},$3 mm, and $Z = P \dot{\theta},$4 mm/s, $Z = P \dot{\theta},$5 mm/s. The prototype achieved $Z = P \dot{\theta},$6 at $Z = P \dot{\theta},$7 and $Z = P \dot{\theta},$8 at $Z = P \dot{\theta},$9, corresponding to $Z$0 and $Z$1 the Stratasys Mojo’s $Z$2, while the printhead maximum of $Z$3 is about $Z$4 the Mojo’s directly measured infill rate. The paper frames these gains within a build-rate/resolution trade space and notes that high capture and deposition rates create additional challenges for toolpath optimization and real-time deposition control.

3. Stochastic capture before nanopore translocation

In solitary nanopore translocation, capture rate is treated as a property of the pre-translocation stage rather than the passage through the pore itself. The Brownian dynamics study defines capture probability for a polymer released from equipotential $Z$5 as

$Z$6

and, under a memoryless assumption, fits it by

$Z$7

where $Z$8 is the capture rate (Seth et al., 2021). Capture-time histograms are reported to be exponential, with mean and standard deviation approximately equal, consistent with a Poisson process.

A central methodological choice is that the polymer is not initialized at the pore. Equilibrated DNA is released from equipotential surfaces at vertical distances $Z$9, corresponding to $P$0 in MD units. The mean capture times are $P$1 for $P$2, and the corresponding rates are

$P$3

Best-fit rates from the exponential capture-probability fits, $P$4, are $P$5. The main trend is that the closer the polymer starts to the pore, the faster the capture and the higher the capture probability.

The paper’s mechanistic emphasis is that the extended electric field outside the pore drives capture well before entry. Far from the pore, the field is nearly concentric; near the pore, it becomes elliptical. As a polymer drifts inward, the field gradient elongates it and increases the chance of successful threading after multiple failed attempts. The work therefore rejects a one-step picture in which capture occurs only at the pore mouth. Instead, the chain can approach, partially enter, fail, and retreat, while the field keeps it near the pore and progressively compresses its configurational freedom.

This conformational bias is quantified through longitudinal and transverse components of the radius of gyration: $P$6 together with the ratio $P$7. Far from the pore, $P$8; closer to the pore, the chain becomes increasingly elongated along the translocation axis. The paper interprets this as a structural marker for the crossover from diffusion-dominated to drift-dominated approach.

Capture statistics also determine the distribution of post-capture conformations. The study distinguishes Type 1 single-file capture, Type 2-1 folded capture at a nonsymmetric internal position, and Type 2 symmetric folded capture. A superficially counterintuitive result is that starting farther away can yield a shorter overall translocation time, but the paper explains that this is caused by enrichment in folded captures, which translocate faster than true single-file events. When Type 1 and Type 2-1 events are separated, the contradiction disappears: Type 1 mean first passage times increase with release distance, whereas Type 2-1 and Type 2 are faster because both ends of a hairpin can thread simultaneously until the loop unfolds.

Polymer stiffness and end tagging further reshape capture rate and fidelity. With $P$9, corresponding to $\dot{\theta}$0, the paper finds that stiffening the chain suppresses hairpin capture and promotes single-file capture. It identifies $\dot{\theta}$1 as a critical point above which Type 1 capture becomes more probable than folded capture. A charged $\dot{\theta}$2 tag, implemented by making the last six monomers at that end three times more charged than a normal monomer, lowers scan time and its variability and increases the probability of uni-directional $\dot{\theta}$3 capture/translocation. Capture rate is therefore coupled to starting position, field geometry, conformational deformation, stiffness, and end asymmetry.

4. One-dimensional diffusion and capture at filament tips

For proteins that bind to microtubules or actin filaments, filament capture rate appears as an effective end-association rate generated by one-dimensional diffusion along the filament. The model treats the filament as a one-dimensional lattice of length $\dot{\theta}$4 with spacing $\dot{\theta}$5 nm. Proteins hop with rate $\dot{\theta}$6, so $\dot{\theta}$7; they bind and unbind in the bulk with rates $\dot{\theta}$8 and $\dot{\theta}$9; and the tip has direct association and dissociation rates $F_{\max} \sim \tau_{\text{uts}} A_s.$0 and $F_{\max} \sim \tau_{\text{uts}} A_s.$1. The defining capture condition is that proteins bound at the tip do not hop further along the lattice, although they may still detach to solution (Reithmann et al., 2015).

The central quantitative result is that tip binding can be described by an effective association rate

$F_{\max} \sim \tau_{\text{uts}} A_s.$2

where $F_{\max} \sim \tau_{\text{uts}} A_s.$3 is the contribution from one-dimensional diffusion and capture. Without diffusion-capture, tip occupancy follows the Langmuir isotherm

$F_{\max} \sim \tau_{\text{uts}} A_s.$4

With diffusion-capture, the same form is approximately retained with an effective dissociation constant

$F_{\max} \sim \tau_{\text{uts}} A_s.$5

The diffusive contribution is defined through a conditional current to an unoccupied tip,

$F_{\max} \sim \tau_{\text{uts}} A_s.$6

and over a broad concentration range this current is approximately first order in concentration,

$F_{\max} \sim \tau_{\text{uts}} A_s.$7

The derived analytical expression is

$F_{\max} \sim \tau_{\text{uts}} A_s.$8

The numerator reflects entry onto the filament followed by one-dimensional diffusion; the denominator reflects competition between detachment and the ability to reach the tip before detaching. This makes capture rate here an emergent kinetic parameter of a search-and-retention process.

The model further maps tip-mediated catalysis onto Michaelis–Menten kinetics. If a tip-bound protein catalyzes a reaction at rate $F_{\max} \sim \tau_{\text{uts}} A_s.$9, then

$109$0

so that $109$1 and $109$2. The paper describes this as a single-molecule Michaelis–Menten framework in which enzyme concentration $109$3 acts as the substrate-like variable in the effective expression. It also reports that for the proteins examined, $109$4 to $109$5 of tip binding can occur via one-dimensional diffusion, and that for XMAP215 the effective affinity satisfies $109$6, i.e. roughly a $109$7-fold enhancement due to diffusion-capture. The broader conclusion is that one-dimensional diffusion plus capture can bypass the three-dimensional Smoluchowski diffusion limit for association to filament ends.

5. Filamentary accretion, chemical lag, and dense-gas assembly

In interstellar-filament studies, the relevant quantity is usually an accretion rate onto the filament rather than a formally defined filament capture rate. One paper proposes that widths measured in different molecular tracers can diagnose the accretion rate because chemistry responds on finite timescales as gas parcels fall into a filament and experience changing density, temperature, and extinction (Gómez et al., 2021). In the nominal model, density rises from about $109$8 to $109$9, temperature drops from about $l_e = 0.64$0 K to $l_e = 0.64$1 K, and extinction rises to $l_e = 0.64$2 mag at the filament center. The key competition is between chemical timescale and accretion or flow timescale.

The width definition is observationally motivated: the paper uses the full width at half maximum of the projected column density distribution of each species after Gaussian convolution with a width of $l_e = 0.64$3 in the model units. The nominal accretion rate is

$l_e = 0.64$4

and the study also considers half the nominal rate, twice the nominal rate, and a static non-accreting case. The most sensitive species are C$l_e = 0.64$5H, CO, CN, CS, and C$l_e = 0.64$6H$l_e = 0.64$7; the least sensitive are N$l_e = 0.64$8H$l_e = 0.64$9, NH$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$00, H$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$01CO, HNC, and CH$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$02OH. The proposed observational diagnostic is to use width ratios such as CN/CS, C$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$03H/CS, CO/CS, N$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$04H$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$05/CO, and NH$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$06/CS. The paper presents this as a first-order estimate of accretion rate rather than a universal calibration and explicitly notes model dependence, sensitivity to radiation field, optical-depth effects, and the lack of a fully self-consistent chemo-hydrodynamical treatment.

A second astrophysical example clarifies the boundary of the term. The LANCET study of the 14-pc filament G316.8 does not explicitly derive a filament mass inflow rate or a numerical “capture rate” in the sense of $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$07. Instead, it quantifies dense-gas assembly through fragment masses, dense-gas mass fraction, column-density PDFs, and $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$08-variance analysis (Xu et al., 20 Feb 2026). Dense-gas fraction is defined as

$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$09

and rises from $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$10 in the young region to $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$11 in the intermediate region and $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$12 in the evolved region. The maximum fragment mass increases from $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$13 to $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$14 and then $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$15. The $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$16-variance slopes flatten from $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$17 in the young region to $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$18 in the intermediate region and $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$19 in the evolved region, which the paper interprets as increasing small-scale structure. The study supports progressive dense-gas assembly but explicitly leaves kinematic determination of gas flows to future line observations.

These two astrophysical uses are important because they separate a true rate estimate from a structural proxy. In the chemical-width paper, tracer widths are proposed as a tool to estimate accretion rate onto the filament. In LANCET, by contrast, no direct numerical inflow or capture rate is claimed. This distinction guards against the common misuse of “capture rate” as a synonym for any monotonic increase in filament-associated mass.

6. Instrumentation, control, and cross-domain methodology

The engineering literature also treats filament capture and production rates as quantities that can be monitored and regulated. An open-source camera-based 3-D filament diameter sensor was developed for recycling, winding, and additive manufacturing systems to measure diameter, ovality, surface irregularities, and the location of defective regions along the spool (Petsiuk et al., 2020). The paper gives a spool-winding relation in which total wound length depends on spool radius $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$20, number of filament layers $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$21, number of filament diameters $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$22, and filament diameter $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$23, and states explicitly that the length of wound filament and thus spooling speed directly depend on diameter $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$24. The sensor records $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$25 RGB images at $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$26 frame per second, uses main and mirrored views to obtain three projections, and each frame yields $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$27 diameter measurements when each of the three regions of interest has width $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$28. Commercial filament measurements stayed within $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$29 mm tolerance, and the system is described as a basis for feedback control of puller speed, motor parameters, or printer extrusion rate.

A related control problem appears in screw extrusion-based polymer 3D printing, where filament production rate is represented through the motion of the solid–liquid interface $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$30 rather than by a separate algebraic throughput formula (Koga et al., 2019). The process is modeled as a two-phase Stefan problem on a time-varying domain. The interface satisfies

$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$31

so the rate of interface motion is driven by the heat-flux difference at the phase-change front. The control objective is to regulate $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$32, since interface position determines how much polymer is molten and ready for deposition. The observer-based output-feedback design uses measurements

$P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$33

with inlet cooling $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$34 as the actuator. Simulations at screw speeds $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$35, $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$36, and $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$37 mm/s show convergence of the interface to the setpoint, while PI control does not robustly stabilize the interface and can violate the condition $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$38. In the fast mode $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$39 mm/s, the estimated temperature profile becomes very close to the true profile by about $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$40 s, and the paper states that observer convergence is roughly $P_{cap}(\Phi,t)=1-\exp(-\lambda_{cap} t)$41 times faster than interface convergence in that example.

Taken together, these results suggest a general methodological principle. Filament capture rate is rarely a primitive quantity measured in isolation. It is usually inferred or stabilized through a coupled state variable: thread engagement and extrusion force in FastFFF, waiting-time statistics in nanopores, conditional end flux on cytoskeletal filaments, tracer-width ratios in filament accretion studies, diameter history in winding systems, or phase-front position in screw extrusion. A plausible implication is that cross-domain comparisons are most meaningful when they preserve this coupling structure rather than equating all “capture rates” to simple counts per unit time.