A Kinetic Model for Spray-Freezing of Pharmaceuticals

Published:December 02, 2020DOI:


      Spray freeze-drying (SFD), which includes spray-freezing into droplets and dynamic vacuum drying, presents a promising alternative approach to manufacture dried pharmaceuticals more efficiently than conventional vial freeze-drying. Without reliable predictive models for the SFD conditions of interest, any respective process development still relies on empirical approaches. In this work, we propose an improved modeling framework to describe the fast freezing (<1 s) that sub-millimeter droplets undergo in the present SFD process. The modeled freezing rate accounts for both the kinetics of ice growth and droplet heat transfer mechanisms. Computational fluid dynamics (CFD) simulations and experiments on bulk spray-freezing are combined to refine and validate the proposed reduced-order model. While this study is limited to water-sucrose solutions, the present modeling approach can be extended to other pharmaceutical excipients. For the cooling rates of interest, model results indicate that droplets with initial sucrose concentration higher than 20% w/w will transit to a glassy state before completion of crystallization and, consequently, devitrification is expected during post spray-freezing manipulation of the bulk material. In practice, such compact model does not only allow quantification of process parameters that cannot be measured in real time but also enable the choice of optimal spraying conditions for production of free-flowing, high-quality frozen droplets that meet the target product profile.


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        • Pikal M.
        Freeze drying.
        in: Swarbrick J. Encyclopedia of Pharmaceutical Technology. Informa Healthcare, USA2006: 1807-1833
        • LyoHub
        Lyophilization technology roadmap.
        (Available at:)
        Date: 2017
        Date accessed: May 27, 2020
        • Renteria Gamiz A.G.
        • Van Bockstal P.-J.
        • De Meester S.
        • De Beer T.
        • Corver J.
        • Dewulf J.
        Analysis of a pharmaceutical batch freeze dryer: resource consumption, hotspots, and factors for potential improvement.
        Dry Technol. 2019; 37: 1563-1582
        • Tchessalov S.
        Exploring new opportunities beyond vial freeze-drying: aseptic spray freeze drying and foam drying of complex biologics.
        in: Freeze-Drying Pharmaceutical and Biologicals Conference. Garmisch-Partenkirchen, Germany2018
        • Luy B.
        • Stamato H.
        Spray freeze drying.
        in: Drying Technologies for Biotechnology and Pharmaceutical Applications. 2020: 217-237
        • Meridion
        MERIDION Technologies: processes from lab to productions scale.
        (Available at:)
        Date: 2020
        Date accessed: May 27, 2020
        • IMA-Group
        LYNFINITY: continuous aseptic spray-freeze-drying.
        (Available at:)
        Date: 2020
        Date accessed: May 27, 2020
        • GMP-News
        New FDA guideline: quality aspects for continuous manufacturing.
        (Available at:)
        • Lowe D.
        • Mehta M.
        • Govindan G.
        Spray Freeze-Drying Technology: Enabling Flexibility of Supply Chain and Drug-Product Presentation for Biologics.
        BioProcess International, 2018
        • Clénet D.
        • Hourquet V.
        • Woinet B.
        • Ponceblanc H.
        • Vangelisti M.
        A spray freeze dried micropellet based formulation proof-of-concept for a yellow fever vaccine candidate.
        Eur J Pharm Biopharm. 2019; 142: 334-343
        • Adali M.B.
        • Barresi A.A.
        • Boccardo G.
        • Pisano R.
        Spray freeze-drying as a solution to continuous manufacturing of pharmaceutical products in bulk.
        Processes. 2020; 8: 709
        • Borges Sebastião I.
        • Robinson T.D.
        • Alexeenko A.
        Atmospheric spray freeze-drying: numerical modeling and comparison with experimental measurements.
        J Pharm Sci. 2017; 106: 183-192
        • Sebastião I.B.
        • Bhatnagar B.
        • Tchessalov S.
        • et al.
        Bulk dynamic spray freeze-drying Part 1: modeling of droplet cooling and phase change.
        J Pharm Sci. 2019; 108: 2063-2074
        • Sebastião I.B.
        • Bhatnagar B.
        • Tchessalov S.
        • et al.
        Bulk dynamic spray freeze-drying Part 2: model-based parametric study for spray-freezing process characterization.
        J Pharm Sci. 2019; 108: 2075-2085
        • Cheng N.-S.
        Comparison of formulas for drag coefficient and settling velocity of spherical particles.
        Powd Technol. 2009; 189: 395-398
        • Ranz W.
        • Marshall W.R.
        Evaporation from drops.
        J Chem Eng Prog. 1952; 48: 141-146
        • Downingm C.G.
        The evaporation of drops of pure liquids at elevated temperatures: rates of evaporation and wet-bulb temperatures.
        AIChE J. 1966; 12: 760-766
        • Bergman T.L.
        • Lavine A.S.
        • Incropera F.P.
        • DeWitt D.P.
        Fundamentals of Heat and Mass Transfer.
        John Wiley & Sons, 2011
        • Hill M.J.M.
        • Henrici O.M.F.E.
        VI. On a spherical vortex.
        Philos Trans R Soc Lond A. 1894; 185: 213-245
        • Wei Y.
        • Deng W.
        • Chen R.-H.
        Effects of internal circulation and particle mobility during nanofluid droplet evaporation.
        Int J Heat Mass Transf. 2016; 103: 1335-1347
        • Nakagawa K.
        • Hottot A.
        • Vessot S.
        • Andrieu J.
        Modeling of freezing step during freeze-drying of drugs in vials.
        AIChE J. 2007; 53: 1362-1372
        • Shampine L.F.
        • Gladwell I.
        • Thompson S.
        Solving ODEs with Matlab.
        Cambridge University Press, 2003
        • Weber C.
        Zum Zerfall eines Flüssigkeitsstrahles.
        Z Angew Math Mech. 1931; 11: 136-154
        • Brandenberger H.R.
        • Widmer F.
        Immobilization of highly concentrated cell suspensions using the laminar jet breakup technique.
        Biotechnol Prog. 1999; 15: 366-372
        • Brandenberger H.
        • Widmer F.
        A new multinozzle encapsulation/immobilisation system to produce uniform beads of alginate.
        J Biotechnol. 1998; 63: 73-80
        • Hindmarsh J.P.
        • Russell A.B.
        • Chen X.D.
        Observation of the surface and volume nucleation phenomena in undercooled sucrose solution droplets.
        J Phys Chem C. 2007; 111: 5977-5981
        • Bigg E.K.
        The supercooling of water.
        Proc Phys Soc B. 1953; 66: 688-694
        • Murray B.J.
        • Broadley S.L.
        • Wilson T.W.
        • et al.
        Kinetics of the homogeneous freezing of water.
        Phys Chem Chem Phys. 2010; 12: 10380-10387
        • Sikora A.
        • Dupanov V.O.
        • Kratochvíl J.
        • Zámečník J.
        Transitions in aqueous solutions of sucrose at subzero temperatures.
        J Macromol Sci B. 2007; 46: 71-85
        • Patel S.M.
        • Bhugra C.
        • Pikal M.J.
        Reduced pressure ice fog technique for controlled ice nucleation during freeze-drying.
        AAPS PharmSciTech. 2009; 10: 1406
        • Shaw R.A.
        • Durant A.J.
        • Mi Y.
        Heterogeneous surface crystallization observed in undercooled water.
        J Phys Chem B. 2005; 109: 9865-9868
        • Tabazadeh A.
        • Djikaev Y.S.
        • Hamill P.
        • Reiss H.
        Laboratory evidence for surface nucleation of solid polar stratospheric cloud particles.
        J Phys Chem A. 2002; 106: 10238-10246
        • Shibkov A.A.
        • Golovin Y.I.
        • Zheltov M.A.
        • Korolev A.A.
        • Leonov A.A.
        Morphology diagram of nonequilibrium patterns of ice crystals growing in supercooled water.
        Phys A Stat Mech Appl. 2003; 319: 65-79
        • Murh A.H.
        • Blandshard J.M.V.
        Effect of polysaccharide stabilizers on the rate of growth of ice.
        J Food Technol. 1986; 21: 683-710
        • Lusena C.V.
        Ice propagation in systems of biological interest. III. Effect of solutes on nucleation and growth of ice crystals.
        Arch Biochem Biophys. 1955; 57: 277-284
        • Hindmarsh J.P.
        • Russell A.B.
        • Chen X.D.
        Measuring dendritic growth in undercooled sucrose solution droplets.
        J Cryst Growth. 2005; 285: 236-248
        • Pruppacher H.R.
        • Klett J.D.
        Growth of ice particles by accretion and ice particle melting.
        in: Microphysics of Clouds and Precipitation. Springer Netherlands, Dordrecht2010: 659-699
        • Longinotti M.P.
        • Corti H.R.
        Viscosity of concentrated sucrose and trehalose aqueous solutions including the supercooled regime.
        J Phys Chem Ref Data. 2008; 37: 1503-1515
        • Kasper J.C.
        • Pikal M.J.
        • Friess W.
        Investigations on polyplex stability during the freezing step of lyophilization using controlled ice nucleation—the importance of residence time in the low-viscosity fluid state.
        J Pharm Sci. 2013; 102: 929-946
        • Hindmarsh J.P.
        • Russell A.B.
        • Chen X.D.
        Fundamentals of the spray freezing of foods—microstructure of frozen droplets.
        J Food Eng. 2007; 78: 136-150
      1. Siemens, P.L.M., Simcenter STAR-CCM+®Documentation User Guide Version 13.04 2018.

        • MacKenzie A.P.
        Non-equilibrium freezing behaviour of aqueous systems.
        Philos Trans R Soc Lond B Biol Sci. 1977; 278: 167-189
        • Macfarlane D.R.
        Devitrification in glass-forming aqueous solutions.
        Cryobiology. 1986; 23: 230-244
        • Sacha G.A.
        • Nail S.L.
        Thermal analysis of frozen solutions: multiple glass transitions in amorphous systems.
        J Pharm Sci. 2009; 98: 3397-3405
        • Meng Z.
        • Zhang P.
        Dynamic propagation of ice-water phase front in a supercooled water droplet.
        Int J Heat Mass Transf. 2020; 152: 119468

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