❄️ Freeze Drying Sublimation (Pikal Lyophilization)

Simulate pharmaceutical primary freeze-drying sublimation cycle times, moving ice front temperature, dry cake vapor resistance (Rp), and vial heat flux.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 43

⚡ Calculs faits 33

💾 Téléchargements 397 📦 Code Fortran 6.4 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

❄️ Pharmaceutical Vial Sublimation Front Progression & Vapor Flow

Real-time visual simulation of ice sublimation interface descending through porous cake under chamber vacuum

📝 Configuration & Presets

💉 Biopharma mAb (6R Vial) 🧪 Vaccine mRNA LNP (-33°C) 💊 Antibiotic Cake (10R) 🔬 Diagnostic Enzyme

🧪 Vial Formulation & Geometry

Vial Fill Volume [mL]:

Vial Base Area A_v [cm²]: 2R: ~2.0 cm², 6R: ~3.8 cm², 10R: ~5.5 cm²

Formulation Solids Content [%]:

Collapse Limit Temp T_c [°C]:

❄️ Lyophilizer Operating Conditions

Chamber Vacuum P_ch [mTorr]: 100 mTorr = 0.133 mbar = 13.3 Pa

Shelf Temperature T_shelf [°C]:

Vial Heat Transfer Coeff K_v [W/(m²·K)]:

Base Cake Resistance R_p0 [Torr·hr·cm²/g]:

Pikal Lyophilization Formulations:
• Sublimation Mass Flux: ṁ_sub = (P_sat(T_ice) − P_ch) / R_p [g/(cm²·h)]
• Shelf Heat Flux: q̇ = K_v · (T_shelf − T_bottom) = ṁ_sub · ΔH_sub
• Primary Drying Time: t_p = ∫ [ ρ_ice (1 − c_s) / ṁ_sub ] dL_dry
• Collapse Constraint: T_ice < T_collapse

📊 Primary Drying Results

📊 Output Summary
💾 Fortran Source

Primary Drying Cycle Duration

t_primary = 13.0 hours

Ice Front Temperature: -38.0 °C (✅ SAFE (No Product Collapse))

L₀ = 5.0 mm

Ice Sublimation Vapor Pressure 121 mTorr Chamber: 60 mTorr

Average Sublimation Flux 0.035 g/(cm²·h) 0.4 kg/(m²·h)

Shelf-to-Vial Heat Flux 396.0 W/m² K_v = 22 W/(m²·K)

Safety Margin to Collapse 5.0 °C Limit: -33.0 °C

📈 Sublimation Front Depth L_dry (mm) vs Drying Time (h)

📉 Primary Drying Duration (hours) vs Shelf Temp (°C)

=================================================================
 THERMOFLUIDCALC — PHARMACEUTICAL LYOPHILIZATION REPORT
=================================================================
Case Title                 : Viral Vaccine / mRNA LNP Nanoparticle Lyophilization
Vial Geometry              : 1.00 mL fill in 2.00 cm2 base (Cake Depth = 5.00 mm)
Formulation Solids Content : 4.0 wt% (Collapse limit = -33.0 °C)
Chamber Vacuum / Shelf T   : 60.0 mTorr / -20.0 °C
-----------------------------------------------------------------
PRIMARY DRYING DURATION    : 13.03 hours
Ice Interface Temperature  : -38.00 °C
Cake Structural Integrity  : ✅ SAFE (No Product Collapse)
Ice Saturation Vapor P     : 120.8 mTorr
Average Sublimation Flux   : 0.0352 g/(cm2.h)
Shelf-to-Vial Heat Flux    : 396.00 W/m2
=================================================================

📘 Calculation Methodology & Pikal Lyophilization Standards

Pikal Coupled Heat & Mass Balance

During primary drying, latent heat of ice sublimation ($\Delta H_{sub} = 2835\,\text{J/g}$) supplied by shelf conduction must equal the vapor sublimation mass transfer:

                    Kv(Tshelf − Tbottom) = ΔHsub · [ (Psat(Tice) − Pch) / Rp ]
                

Micro-Collapse Prevention

If the ice sublimation interface exceeds the glass transition temperature $T_g'$ or collapse temperature $T_{collapse}$, the porous cake collapses, resulting in product degradation.

Key Engineering Assumptions

Planar 1D moving sublimation front progressing from top to bottom.
Vapor transport governed by dry cake Knudsen & viscous resistance $R_p$.
Equilibrium Clausius-Clapeyron ice vapor pressure.

ThermoFluidCalc Engineering Report