Abstract
The objective of this interdisciplinary project was to develop a continuous atmospheric freeze-drying process for the production of lyophilized powder aerosols as pulmonary drug delivery systems in cooperation between an experimental and formulation group at the University of Bonn and a modelling and imaging team at the University of Halle (Saale). Observation and simulation results indicated deficiencies in the initial concept, which were eliminated by stepwise modifications of the freezing and drying system. Collisions and coalescence of droplets in fast streams exiting from piezoelectric generators were recorded by high-speed imaging and analyzed. Both the mean and the spread of the particle size distributions were reduced by a novel vortex-jet freezing technique. The fine particle fraction of the powder, which is suited to alveolar deposition in lungs, was increased to more than 40 %. In spite of the small size and low density of spherical and highly porous particles, the flowability of the powders is very good. Besides the powder aerosols envisaged in the initial concept, the method can be adapted to the production of other pharmaceutical dosage forms and may contribute to lowering the expenses and energy requirements for the manufacture of freeze-dried parenteral products.
The aim of the theoretical and numerical part of the project was the support of the technical realization of a continuous atmospheric spray-freeze-drying chamber using the Euler/Lagrange approach for numerically calculating the entire process and providing strategies for the design of the equipment and the optimal operational conditions. Since models for the drag coefficient of porous particles and the sublimation (drying) of frozen solution droplets are not available, a multi-scale approach was adopted. This implies that first the flow about a dry single porous particle and porous particles where the pore structure is fully filled with ice was proposed to simulate by the Lattice–Boltzmann method (LBM). Therefrom, appropriate correlations for drag and sublimation models shall be developed. Consequently, the available in-house LBM-code had to be extended by the calculation of the temperature field, fully coupled with the flow field. Moreover, a tracking model for the retraction of the ice structure inside the porous particle was proposed.
In parallel a sublimation model for Lagrangian calculations of the frozen particle phase was implemented. In the literature, two approaches for atmospheric freeze-drying have been developed: experimental diffusion models and the uniformly retreating ice front (URIF) model. In the experimental diffusion models, multi-component vapour diffusion mechanisms are reflected by experimentally determined effective diffusivity and activation energy. The URIF model is based on the assumption of equilibrium at the ice front interface and was selected for the present application. Simultaneous heat and mass transfer can be calculated solving the conservation equations of mass and energy. Preliminary calculations for the drying of single iced particles were conducted for validation.
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Abbreviations
- \( f\left(\overrightarrow{\mathsf{x}},\overrightarrow{\xi},t\right) \) :
-
Distribution function in the LBM
- 1N:
-
Single fluid nozzle
- 2N:
-
Two fluid nozzle
- 3N:
-
Three fluid nozzle
- 4N:
-
Four fluid nozzle
- AES:
-
Area equivalent size
- A equi (m2):
-
Equivalent area
- AFD:
-
Atmospheric freeze-drying
- c D :
-
Drag coefficient
- CI:
-
Carr’s Index
- CT-DSG:
-
Capillary type droplet stream generator
- d aero (μm):
-
Aerodynamic diameter
- D AES (M):
-
Area equivalent diameter of porous particle or agglomerates
- D e (m2/s):
-
Effective diffusivity of water vapour in the dried product
- D f :
-
Fractal dimension
- d geo (μm):
-
Geometric diameter
- d p (m):
-
Particle diameter
- DSG:
-
Droplet stream generator
- D VES (m):
-
Volume equivalent diameter of porous particle or agglomerates
- f eq :
-
Equilibrium distribution function
- FPF (%):
-
Fine particle fraction
- G (kg/s):
-
Sublimation flow rate
- IgG:
-
Immunoglobulin G
- J w (kg/s m2):
-
Sublimation flux
- L 0 (m):
-
Initial characteristic dimension of the product
- L dried (m):
-
Characteristic dimension of the dried product
- LED:
-
Light emitting diode
- LN2 :
-
Liquid nitrogen
- M w (kg/kmol):
-
Water molecular weight
- NGI:
-
Next-Generation Impactor
- n pp :
-
Number of particles
- p *w (Pa):
-
Water vapour partial pressure at the external surface of the product
- PT-DSG:
-
Pinhole type droplet stream generator
- p w (Pa):
-
Water vapour partial pressure
- p w,c (Pa):
-
Water vapour partial pressure in the drying chamber
- p w,i (Pa):
-
Water vapour partial pressure at the sublimation interface
- Q (W):
-
Heat flow rate
- R (J/kmol K):
-
Ideal gas constant
- r (m):
-
Radial coordinate
- rH (%):
-
Relative humidity
- S (m2):
-
Surface of the product
- s.c.:
-
Subcutaneous
- SD:
-
Spray drying
- SEC:
-
Size exclusion chromatography
- SEM:
-
Scanning electron microscopy
- SFD:
-
Spray-freeze-drying
- t (s):
-
Time
- T air (K):
-
Air temperature
- T i (K):
-
Temperature of the sublimation interface
- U air (m/s):
-
Air velocity
- V dried (m3):
-
Volume of the dried product
- W (kgwater/kgdry matter):
-
Water content in the product at the end of the drying process
- W 0 (kgwater/kgdry matter):
-
Water content in the product at the beginning of the drying process
- ×10 (μm):
-
Volumetric tenth percentile diameter
- ×50 (μm):
-
Volumetric median diameter
- ×90 (μm):
-
Volumetric ninetieth percentile diameter
- α (m/s):
-
Mass transfer coefficient
- β (W/m2⋅K):
-
Heat transfer coefficient
- ΔH s (J/kg):
-
Heat of sublimation
- ε :
-
Gas volume fraction or void fraction
- λ dried (W/m K):
-
Thermal conductivity of the dried product
- μ (Pa ⋅ s):
-
Dynamic viscosity
- ρ (kg/m3):
-
Gas density
- ρ dried (kg/m3):
-
Density of the dried product
- σ :
-
Indicator for velocity direction
- τ :
-
Relaxation parameter
- φ p :
-
Particle or solids volume fraction
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Acknowledgements
The financial support by the German Research Council (DFG: Deutsche Forschungsgemeinschaft) through the grants LA 1362-2/1-3 and SO 204-36/1-3 in the frame of the SPP 1423 is gratefully acknowledged. The authors would also like to thank all cooperating teams within the framework of the SPP 1423, Sören Höhn (Frauenhofer IKTS, Dresden) for the ion-beam section of particles and SEM imaging, Franz–Josef Willems and Thomas Vidua for technical assistance.
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Wanning, S. et al. (2016). Droplet-Stream Freeze-Drying for the Production of Protein Formulations: From Simulation to Production. In: Fritsching, U. (eds) Process-Spray. Springer, Cham. https://doi.org/10.1007/978-3-319-32370-1_10
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