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A new model for the drying of droplets containing suspended solids C.S. Handscomb, M. Kraft and A.E. Bayly Wednesday 19 th September, 2007

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Christopher Handscomb (csh33@cam.ac.uk) outline Motivation –Industrial Application –The Drying Process Model Description Results for a Sodium Sulphate Droplet

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Christopher Handscomb (csh33@cam.ac.uk) An important technology in industry Used to produce, for example: –Pharmaceuticals –Food stuffs (e.g. milk powder and coffee) –Detergents Unique drying technology combining moisture removal and particle formation motivation - spray drying

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Christopher Handscomb (csh33@cam.ac.uk) motivation – spray drying Consider droplet drying in a spray dryer Droplets dry by atomisation and contact with hot drying air Consider a single droplet Droplets contain suspended solids Continuous phase may be either single- or multi- component

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Christopher Handscomb (csh33@cam.ac.uk) particle morphologies Initial Droplet No particle formation Low solids concentration <1%w/w Saturated Surface Drying ‘Puffed’ Particle High temperature Crust Formation Internal Bubble Nucleation ‘Dry Shell’ Solid Particle ‘Wet Shell’ Inflated, Hollow Particle Blistered (Burst) Particle Shrivelled Particle Collapse Re-inflation A. Cheyne, D. Wilson and D. Bridgwater, Spray Dried Detergent Particle, unpublished, 2003 A. Cheyne, D. Wilson and D. Bridgwater, Spray Dried Detergent Particles, unpublished, 2003

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Christopher Handscomb (csh33@cam.ac.uk) particle morphologies Initial Droplet Saturated Surface Drying ‘Puffed’ Particle High temperature Crust Formation Internal Bubble Nucleation ‘Dry Shell’ Solid Particle ‘Wet Shell’ Inflated, Hollow Particle Blistered (Burst) Particle Shrivelled Particle Collapse Re-inflation A. Cheyne, D. Wilson and D. Bridgwater, Spray Dried Detergent Particle, unpublished, 2003 A. Cheyne, D. Wilson and D. Bridgwater, Spray Dried Detergent Particles, unpublished, 2003

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Christopher Handscomb (csh33@cam.ac.uk) particle morphologies Initial Droplet No particle formation Low solids concentration <1%w/w Saturated Surface Drying ‘Puffed’ Particle High temperature Crust Formation Internal Bubble Nucleation ‘Dry Shell’ Solid Particle ‘Wet Shell’ Inflated, Hollow Particle Blistered (Burst) Particle Shrivelled Particle Collapse Re-inflation A. Lee and C.Law. ‘Gasification and shell characteristics in slurry droplet burning’ Combust. Flame, 85(1): 77-93, 1991 Tsapis et al. ‘Onset of buckling in Drying Droplets of Colloidal Suspensions’ Phys. Rev. Let. 94(1), 2005

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Christopher Handscomb (csh33@cam.ac.uk) particle morphologies Initial Droplet Saturated Surface Drying ‘Puffed’ Particle High temperature Crust Formation Internal Bubble Nucleation ‘Dry Shell’ Solid Particle ‘Wet Shell’ Inflated, Hollow Particle Blistered (Burst) Particle Shrivelled Particle Collapse Re-inflation Focus on drying prior to shell formation in this paper Demonstrates the core features of the new model

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Christopher Handscomb (csh33@cam.ac.uk) 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

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Christopher Handscomb (csh33@cam.ac.uk) wet shell Buckled Shell Tsapis et al. (2005) Physical Review Letters Lee and Law. (1991) Combustion and Flame. Particles produced by burning coal slurries Hollow Shell Burst Shell

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Christopher Handscomb (csh33@cam.ac.uk) Assumptions in the present model: –Three component system: A – solvent; B – solute; D – solid –Spherical particles, 1D model –Small Biot number uniform particle temperature –Allow for a single centrally located bubble new drying model Assumed ideal binary solution

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Christopher Handscomb (csh33@cam.ac.uk) discrete phase Spherical symmetry reduce to 1-D One internal and one external coordinate Solve for the moments of this equation Population balance for solids advection term diffusion term external coordinate internal coordinate

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Christopher Handscomb (csh33@cam.ac.uk) discrete phase Principle variable of interest is solids volume fraction Related to the moments of the population balance equation by: Integer moments of the internal coordinate

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Christopher Handscomb (csh33@cam.ac.uk) discrete phase Stokes-Einstein equation for solids diffusion coefficient Moment evolution equation Particle nucleation rate per unit volume Equation system is unclosed with size dependent diffusion coefficient

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Christopher Handscomb (csh33@cam.ac.uk) discrete phase Moment hierarchy closed by linear extrapolation on a log-scale 4 PDEs required to describe the discrete phase

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Christopher Handscomb (csh33@cam.ac.uk) continuous phase Volume averaged equations for the continuous phase Assume Fickian diffusion is primary transport mechanism crystallization diffusion evolution advection Volume Averages Superficial Intrinsic Total

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Christopher Handscomb (csh33@cam.ac.uk) continuous phase Advection velocity arises due to density difference between the solute and solvent

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Christopher Handscomb (csh33@cam.ac.uk) continuous phase Effective diffusion coefficient is a strong function of local solids fraction and solute mass fraction Diffusion coefficient must be obtained from experiments

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Christopher Handscomb (csh33@cam.ac.uk) continuous phase Continuous phase equation coupled to the population balance through the last term 1 PDE required to describe the continuous phase 5 coupled PDEs in total

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Christopher Handscomb (csh33@cam.ac.uk) continuous phase

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Christopher Handscomb (csh33@cam.ac.uk) boundary conditions Consider only low temperature drying Initially ideal shrinkage –Droplet radius decreases as particles are free to move At some point, shell formation occurs

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Christopher Handscomb (csh33@cam.ac.uk) boundary conditions Zero solute mass flux following receding interface External solute boundary condition

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Christopher Handscomb (csh33@cam.ac.uk) boundary conditions Droplet shrinkage rate Solvent mass flux to the bulk calculated using standard correlations based on a partial pressure driving force

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Christopher Handscomb (csh33@cam.ac.uk) boundary conditions Population balance boundary condition… …which gives BCs for the moments Solids remain wetted and are drawn inwards by capillary forces between particles ;

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Christopher Handscomb (csh33@cam.ac.uk) numerical implementation Apply coordinate transformation to all equations Time derivatives are transformed according to A virtual flux is introduced into all evolution equations

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Christopher Handscomb (csh33@cam.ac.uk) sodium sulphate droplet Simulate the drying of a droplet of sodium sulphate solution Initial conditions: –Solute content: 14 wt% (near saturated) –Droplet temperature: 20 C –Solids volume fraction: 1.1 x 10 -12

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Christopher Handscomb (csh33@cam.ac.uk) sodium sulphate droplet Crystallisation kinetics D. Rosenblatt, S. Marks and R. Pigford ‘Kinetics of phase transitions in the system sodium sulfate-water’ Ind Eng Chem 23(2): 143-147, 1984 Nucleation kinetics (heterogeneous) J. Dirksen and T. Ring. ‘Fundamentals of crystallization: Kinetic effect on particle size distributions and morphology. Chem Eng Sci, 46(10): 2389-2427, 1991

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Christopher Handscomb (csh33@cam.ac.uk) sodium sulphate droplet Experimental data taken from: S. Nesic and J. Vodnik. ‘Kinetics of droplet evaporation’ Chem Eng Sci, 46(2): 527-537, 1991

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Christopher Handscomb (csh33@cam.ac.uk) sodium sulphate droplet Radial solute profiles Saturated solute mass fraction = 0.34 Profiles plotted at 5 s intervals

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Christopher Handscomb (csh33@cam.ac.uk) sodium sulphate droplet Integrated moments

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Christopher Handscomb (csh33@cam.ac.uk) sodium sulphate droplet Spatially resolved particle number density Profiles plotted at 5 s intervals

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Christopher Handscomb (csh33@cam.ac.uk) sodium sulphate droplet Spatially resolved solids volume fraction Profiles plotted at 1 s intervals

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Christopher Handscomb (csh33@cam.ac.uk) conclusions Spray dying to form particles is an important and complex industrial process Outlined droplet drying model incorporating a population balance to describe the solid phase New model capable of enhanced morphological prediction

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Christopher Handscomb (csh33@cam.ac.uk) acknowledgements

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