modelling shell formation when drying droplets containing suspended solids

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])

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

• 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


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

• 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


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


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

– 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


which mode?

Dry Shell

Wet Shell

Solid Particle

Hollow Shell

Crumpled Shell‘Buckling’

How do we know which mode?


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’

Tsapis et al. (2005) Physical Review Letters

Lee and Law. (1991) Combustion and Flame


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



• 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



• Solute flux conservation across boundary

• Odd behaviour… (mistake?!)



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



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


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

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