a new model for the drying of droplets containing suspended solids n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
A new model for the drying of droplets containing suspended solids PowerPoint Presentation
Download Presentation
A new model for the drying of droplets containing suspended solids

Loading in 2 Seconds...

play fullscreen
1 / 31

A new model for the drying of droplets containing suspended solids - PowerPoint PPT Presentation


  • 309 Views
  • Uploaded on

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. outline. Motivation Industrial Application The Drying Process Model Description Results for a Sodium Sulphate Droplet. motivation - spray drying.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'A new model for the drying of droplets containing suspended solids' - remy


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
a new model for the drying of droplets containing suspended solids

A new model for the drying of droplets containing suspended solids

C.S. Handscomb, M. Kraft and A.E. Bayly

Wednesday 19th September, 2007

outline
outline
  • Motivation
    • Industrial Application
    • The Drying Process
  • Model Description
  • Results for a Sodium Sulphate Droplet
motivation spray drying
motivation - spray drying
  • 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 drying1
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

particle morphologies
particle morphologies

Solid Particle

Collapse

‘Puffed’ Particle

Re-inflation

‘Dry Shell’

High temperature

‘Wet Shell’

A. Cheyne, D. Wilson and D. Bridgwater, Spray Dried Detergent Particles, unpublished, 2003

A. Cheyne, D. Wilson and D. Bridgwater, Spray Dried Detergent Particle, unpublished, 2003

Internal Bubble Nucleation

Crust Formation

Saturated Surface Drying

Initial Droplet

Blistered (Burst) Particle

Shrivelled Particle

Inflated, Hollow Particle

particle morphologies1
particle morphologies

No particle formation

Solid Particle

Collapse

Low solids concentration <1%w/w

‘Puffed’ Particle

Re-inflation

‘Dry Shell’

High temperature

A. Lee and C.Law. ‘Gasification and shell characteristics in slurry droplet burning’ Combust. Flame,85(1): 77-93, 1991

‘Wet Shell’

Internal Bubble Nucleation

Crust Formation

Saturated Surface Drying

Initial Droplet

Tsapis et al. ‘Onset of buckling in Drying Droplets of Colloidal Suspensions’ Phys. Rev. Let. 94(1), 2005

Blistered (Burst) Particle

Shrivelled Particle

Inflated, Hollow Particle

particle morphologies2
Demonstrates the core features of the new modelparticle morphologies
  • Focus on drying prior to shell formation in this paper

Solid Particle

Collapse

‘Puffed’ Particle

Re-inflation

‘Dry Shell’

High temperature

‘Wet Shell’

Internal Bubble Nucleation

Crust Formation

Saturated Surface Drying

Initial Droplet

Blistered (Burst) Particle

Shrivelled Particle

Inflated, Hollow Particle

new drying model
new drying model
  • 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

Assumed ideal binary solution

discrete phase
discrete phase
  • Population balance for solids
  • Spherical symmetry  reduce to 1-D
  • One internal and one external coordinate

external coordinate

internal coordinate

diffusion term

advection term

  • Solve for the moments of this equation
discrete phase1
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
discrete phase2
discrete phase
  • Stokes-Einstein equation for solids diffusion coefficient
  • Moment evolution equation
  • Equation system is unclosed with size dependent diffusion coefficient

Particle nucleation rate per unit volume

discrete phase3
discrete phase
  • Moment hierarchy closed by linear extrapolation on a log-scale
  • 4 PDEs required to describe the discrete phase
continuous phase
continuous phase

Volume Averages

Superficial

Intrinsic

Total

  • Volume averaged equations for the continuous phase
  • Assume Fickian diffusion is primary transport mechanism

evolution

diffusion

crystallization

advection

continuous phase1
continuous phase
  • Advection velocity arises due to density difference between the solute and solvent
continuous phase2
continuous phase
  • Effective diffusion coefficient is a strong function of local solids fraction and solute mass fraction
  • Diffusion coefficient must be obtained from experiments
continuous phase3
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
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

boundary conditions
boundary conditions2
Droplet shrinkage rateboundary conditions

Solvent mass flux to the bulk calculated using standard correlations based on a partial pressure driving force

boundary conditions3
Population balance boundary condition…

…which gives BCs for the moments

Solids remain wetted and are drawn inwards by capillary forces between particles

boundary conditions

;

numerical implementation
numerical implementation
  • Apply coordinate transformation to all equations
  • Time derivatives are transformed according to

A virtual flux is introduced into all evolution equations

sodium sulphate droplet
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
sodium sulphate droplet1
sodium sulphate droplet
  • Crystallisation kinetics

D. Rosenblatt, S. Marks and R. Pigford ‘Kinetics of phase transitions in the system sodium sulfate-water’ Ind Eng Chem23(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

sodium sulphate droplet2
sodium sulphate droplet

Experimental data taken from: S. Nesic and J. Vodnik. ‘Kinetics of droplet evaporation’ Chem Eng Sci,46(2): 527-537, 1991

sodium sulphate droplet3
sodium sulphate droplet
  • Radial solute profiles

Profiles plotted at 5s intervals

Saturated solute mass fraction = 0.34

sodium sulphate droplet4
sodium sulphate droplet
  • Integrated moments
sodium sulphate droplet5
sodium sulphate droplet
  • Spatially resolved particle number density

Profiles plotted at 5s intervals

sodium sulphate droplet6
sodium sulphate droplet
  • Spatially resolved solids volume fraction

Profiles plotted at 1s intervals

conclusions
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