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

Christopher Handscomb point of for the talk ‘Know your audience’…

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

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

Christopher Handscomb 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

Christopher Handscomb 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

Christopher Handscomb 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?

Christopher Handscomb 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)

Christopher Handscomb mechanism of shell formation 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 Solidification of spray dried lactose droplet on a slide Solidification of mannitol droplet on a slide

Christopher Handscomb particle drying with a shell R r t Ideal Shrinkage: r 2  t R Shell formation S Shrinkage stops upon shell formation R(t) S(t) Shell ‘grows’ inwards

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

Christopher Handscomb 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?

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

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

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

Christopher Handscomb 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);

Christopher Handscomb 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!

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

Christopher Handscomb 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

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

Christopher Handscomb mechanisms of shell growth Is this physical?

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

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

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

Christopher Handscomb 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