vapour bubble formation
water removed by evaporation
‘blown shell’
modelling shell formation when drying droplets containing suspended solids
Christopher Handscomb
19th April 2007
Christopher Handscomb([email protected])
outline of the talk
• Introduction to droplet drying
• Shell formation
• Models for shell growth
• Conclusions and ‘further work’ (problems!)
Christopher Handscomb([email protected])
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([email protected])
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([email protected])
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([email protected])
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([email protected])
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([email protected])
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([email protected])
particle drying with a shell
R
r
t
Ideal Shrinkage: r2t
R
Shell formation
S
• Shrinkage stops upon shell formation
R(t)
S(t)
• Shell ‘grows’ inwards
Christopher Handscomb([email protected])
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([email protected])
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([email protected])
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([email protected])
which mode?
Dry Shell
Wet Shell
Solid Particle
Hollow Shell
Crumpled Shell‘Buckling’
How do we know which mode?
Christopher Handscomb([email protected])
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([email protected])
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([email protected])
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([email protected])
wet shell
Hollow Shell
Crumpled Shell‘Buckling’
Tsapis et al. (2005) Physical Review Letters
Lee and Law. (1991) Combustion and Flame
Christopher Handscomb([email protected])
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([email protected])
mechanisms of shell growth
• Consider the inner shell boundary• Model as a sink in the solids population
balance
Christopher Handscomb([email protected])
mechanisms of shell growth
• Is this physical?
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10-4
0
0.1
0.2
0.3
0.4
0.5
0.6
Simulated Solids Volume Fraction in a Drying Droplet
Radial Position/mm
Sol
ids
Vol
ume
Fra
ctio
n [-
]
Profiles at 25s intervals
Christopher Handscomb([email protected])
mechanisms of shell growth
• Solute flux conservation across boundary
• Odd behaviour… (mistake?!)
Christopher Handscomb([email protected])
mechanisms of shell growth
0 1 2 3 4 5 6
x 10-4
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
0.56
0.58Solute Mass Fraction Profiles
radial coordinate/m
mass fraction
before shell formation
just after shell formation
4.82 4.83 4.84 4.85 4.86 4.87
x 10-4
0.4838
0.484
0.4842
0.4844
0.4846
0.4848
0.485
0.4852
0.4854
Christopher Handscomb([email protected])
mechanisms of shell growth
0 1 2 3 4 5 6
x 10-4
0.4
0.42
0.44
0.46
0.48
0.5
0.52
radial coordinate/m
mass fraction
4.72 4.74 4.76 4.78 4.8 4.82 4.84 4.86 4.88 4.9
x 10-4
0.8635
0.8636
0.8636
0.8637
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([email protected])
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