modelling shell formation when drying droplets containing suspended solids

modelling shell formation when drying droplets containing suspended solids Christopher Handscomb 19th April 2007

point of for the talk • ‘Know your audience’…

outline of the talk Introduction to droplet drying Shell formation Models for shell growth Conclusions and ‘further work’ (problems!)

droplet drying Consider droplet drying in a spray dryer Population balance for solids • Droplets contain suspended solids • Droplets dry by atomisation and contact with hot drying air Volume-averaged transport equations for the continuous phase • Consider a single droplet

drying behaviour • Consider only low temperature drying • Initially ideal shrinkage • Droplet radius decreases as particles are free to move • At some point, shell formation occurs

first drying period • Several papers only consider drying prior to shell formation • Liang et al. (2001) • Shabde et al. (2005) • Useful to determine final particle size (sometimes!) • Can be successfully simulated using my model

shell formation Questions • When does the shell form? • What is (are) the mechanism(s) of shell formation? • What is the nature of the shell? • How does shell growth occur?

when does the shell form? • a critical solids volume fraction • particle average • e.g., Elperin and Krasovitov, (1994); Kadja and Bergeles, (2003) • local at the surface • e.g., Seydel et al., (2006) • critical moisture content • e.g.,Cheong et al., (1986) • critical (saturated) solute content • e.g., Nešić and Vodnik (1990)

mechanism of shell formation Solidification of spray dried lactose droplet on a slide Solidification of mannitol droplet on a slide • Closely related to the question of when the shell forms • e.g., critical solids fraction → ‘locking’ • Experimental studies focus on ‘simpler’ systems: • Droplets on a slide (~2D) • Liquid bridge between slides Farber et al. (2003) Evolution and structure of drying material bridges of pharmaceutical excipients: studies on a microscope slide

particle drying with a shell r R S R(t) S(t) t Shell formation R Ideal Shrinkage: r2at • Shrinkage stops upon shell formation • Shell ‘grows’ inwards

nature of the shell • The nature of the shell determines: • Subsequent drying behaviour; • Final particle structure; • Consider moisture removal once the shell has formed…

drying after shell formation • Moisture is still being removed… • …but the volume of the droplet isn’t changing. → vapour must exist somewhere • Where is this vapour located?

drying after shell formation • The vapour could be located: • in the shell region → Dry Shell • In a bubble(s) somewhere→Wet Shell • A different approach required for each • The scenario which occurs dictates the final particle morphology

which mode? Solid Particle Dry Shell How do we know which mode? Hollow Shell Crumpled Shell ‘Buckling’ Wet Shell

dry shell model • A ‘shrinking core’ model’ • Shell region defined by the dry zone • variable solids vol. frac. in the shell • Heat transfer limited

precedents in the literature • Dry Shell • Audu and Jeffreys (1975); • Cheong et al. (1986); • Nešić and Vodnik (1990); • Elperin and Krasovitov (1995); • Kadja and Bergeles (2003); • Seydel et al. (2006); • Dalmaz et al. (2007);

wet shell model • Wet Shell models in the literature • Sano and Keey (1982); • Etzel (1995); • Kadja and Bergeles (2003); • Lee and Law (1991); • Less common than the dry shell approach… • …but expected morphologies are observed experimentally!

wet shell Hollow Shell Crumpled Shell ‘Buckling’ Lee and Law. (1991) Combustion and Flame Tsapis et al. (2005) Physical Review Letters

wet shell model • Assume the continuous phase wets the solids at all times • Single, centrally located ‘bubble’ • Shell region defined by region with critical solids volume fraction • Shell region grows by solids migration mechanism

mechanisms of shell growth • Consider the inner shell boundary • Model as a sink in the solids population balance

mechanisms of shell growth • Is this physical?

mechanisms of shell growth • Solute flux conservation across boundary • Odd behaviour… (mistake?!)

mechanisms of shell growth Solute Mass Fraction Profiles before shell formation mass fraction just after shell formation radial coordinate/m

mechanisms of shell growth Solute Mass Fraction in the Shell Solute Mass Fraction in the Wet Kernel mass fraction mass fraction radial coordinate/m radial coordinate/m Profiles at 50s intervals after shell formation

conclusions • Shells are formed when drying droplets containing suspended particles • Different types of shell are possible • Wet Shell • Dry Shell • Work currently underway to model formation and growth of both shell types

modelling shell formation when drying droplets containing suspended solids