Filament Drying Time and Re-Wetting Calculator

The strand is an effectively infinite circular cylinder with initially uniform moisture, constant surface equilibrium and spatially uniform diffusivity. Its normalized mean remaining water is

where $\alpha_j$ are zeros of $J_0$. Thirty modes are used above Fo = 0.003. Earlier times use the cylinder heat-content expansion

The radial profile uses a short-time expansion derived here from the Laplace-domain surface-step solution $I_0(\rho\sqrt{s})/[sI_0(\sqrt{s})]$, with $\rho=r/R$. The large-argument expansion of $I_0$ is given in NIST DLMF §10.40.1 (attached link s5). With $x=1-\rho$, $E=\operatorname{erfc}(x/(2\sqrt{\mathrm{Fo}}))$, $G=\sqrt{\mathrm{Fo}/\pi}\exp[-x^2/(4\mathrm{Fo})]$, the absorbed fraction is approximated by

This is used only at Fo ≤ 0.003 and $\rho\ge0.5$; the inner half-radius remains at its initial value at these short times, with an omitted change below $2\times10^{-10}$. Above that dose, the radial solution uses 30 Bessel modes. No clipping is used to conceal oscillations. The 201-point radial grid is concentrated near the surface. The Bessel basis is cached independently of animation time; a frame evaluates a matrix-vector product or the short-time expression.

Spool heat-up uses $C=m_f c_f+m_s c_s$, $\tau=C/(UA)$ and $T=T_d-(T_d-T_r)e^{-t/\tau}$. Arrhenius scaling is $D=D_r\exp[(E_a/\mathcal R)(1/T_r-1/T)]$, with absolute temperatures. Four-point Gauss–Legendre quadrature integrates $D/D_\mathrm{hot}$ directly in normalized time $u=t/\tau$. Completed 0.1-wide intervals are cached up to $u=20$; each query integrates its current partial interval directly. This avoids early-time interpolation bias and cancellation from subtracting nearly equal heat-up losses. After $u=20$, diffusivity is taken as its hot value. A cached 0.05-wide grid checks convergence over very short and long exposures. Bisection finds the target time. Equilibrium moisture is $w_e=a(\mathrm{RH}/100)^n$, using local RH at the stated air temperature.

For storage, the remaining radial gradient is retained by superposition:

Room-temperature diffusivity gives $\mathrm{Fo}_s$. The first threshold crossing is solved by bisection. If final equilibrium is below the limit, a logarithmic scan and peak refinement first check for transient overshoot. A missing time means no finite crossing under maintained conditions, or an unreachable drying target; read the interpretation card.

Scale calibration converts $(m_j-m_\infty)/(m_0-m_\infty)$ to Fo and fits Fo versus equivalent hot exposure by a least-squares slope through zero. Only drying diffusivity is multiplied by this fit. Before accepting a log, its total plateau weight must include the dry polymer and empty spool tare, allowing two scale divisions for measurement rounding. The largest remaining-water fraction residual is reported in the calculation steps.

• Parameter provenance: see the evidence column of the material selector. Polymers 2023, Tables 2–3 (attached source s1, pp. 8–10) provides grade-specific room-temperature sorption data. Tough PLA, Nylon PA6/66 and PC use the tabulated constant diffusivities.
• PETG uses an effective 0.0034 mm²/h inferred from the independently tabulated approximately 125 h to 80% uptake for 2.8 mm filament. Its printed Table 3 trendline has a negative diffusion offset inconsistent with positive diffusivity over the stated moisture range, so that trendline is not implemented. The inference is disclosed, and PETG's uptake timing is not reused as an independent validation case.
• The negative initial-mass offsets in Table 2 are omitted to construct dry-origin isotherms, as illustrated in s1 Figure 6. This is an estimate of absolute water content, not an absolute-moisture measurement. The same isotherm is used at room and dryer temperatures. Low-RH and heated use are extrapolations.
• Editable estimates: 25 °C as the numerical meaning of the source's unspecified room temperature; 50 kJ/mol activation energy; 1.5 and 1.2 J/(g·K) specific heats; and 0.45 W/K effective core conductance. These are scenario assumptions, not published measurements for the preset grades.
• Uniform core temperature is an effective approximation. Winding contact and restricted vapor flow are not separately solved. Changing filament mass changes thermal capacity, not intrinsic strand diffusivity.
• Constant RH and temperature, no surface transfer resistance, no desiccant exhaustion, no cooling transient, no crystallization or hydrolysis. Storage starts immediately at room temperature. Polymer moisture is on a dry-mass basis; spool mass is excluded.
• The half/double diffusivity times are sensitivity scenarios only. Parameter errors, especially activation energy and equilibrium moisture, may exceed this range.

Use for planning vapor sorption and desorption of 1–3.5 mm solid filament; the main source measured nominal 2.8 mm strands over 16–97% RH at room temperature. The defaults use 1.75 mm and extrapolate to heated, low-RH drying. Do not interpret a minute-level result as measured accuracy. Low-RH absolute equilibrium and Arrhenius drying predictions require grade-specific calibration.

The two literature reference cases compare the isothermal cylinder model with independently tabulated PLA and PC uptake timings; they do not validate heated spool drying. A separate 160-cell finite-volume scratch cross-check agrees with the mean cylinder series within 0.00018 remaining fraction over Fo = 0.001–0.3. An additional independent adaptive-integration case checks short drying during very slow heat-up. Cached checks cover heat-grid convergence, radial monotonicity, radial bounds, and agreement of the area-integrated profile with the mean over Fo = 0 to 10. The short-time radial approximation agrees with an independent 400-mode SciPy solution within 5×10⁻⁷ of the initial-to-surface moisture difference over the tested overlap range.

Wang et al. (BioResources 2025) dried one PETG sample at 70 °C for 8 h after humid conditioning; its initial reference weight was not proven anhydrous. This observation is context, not a universal drying endpoint. The UT Austin-hosted SFF 2022 study concerns OVERTURE Easy Nylon and demonstrates strong uptake at 40 °C / 80% RH; it does not supply parameters transferable to every nylon. Polymers 2025, 2938 uses printed coupon immersion for its water-absorption tests (s4 pp. 5–6); those results are not used as vapor diffusivities.

Scale fits require a water-only mass change, an independently measured same-condition plateau and stable readings. Cardboard spools, additives, scale drift and unknown initial gradients can defeat the fit. An effective fitted coefficient is specific to that dryer, mass, temperature and humidity. A dry box prediction holds only while its measured RH is maintained. Confirm the filament maker's temperature and moisture limits; drying cannot reverse chemical damage.