Intrusive measurements for particulate flows

Objectives

• Decide between intrusive and non-intrusive techniques
• Risks in sampling
• Some common techniques
  • Filters
  • Optical Particle Counters
  • Differential Mobility analyzers
• Calibration techniques

Reference material

Aerosol Measurement: Principles, Techniques, and Applications, Third Edition (Kulkarni et al.)

Aerosol measurements

Image source: AiirSource Military

What to measure

• Particle size
• Particle shape
• Mass and number concentration
• Size distributions
• Chemical and physical properties
• Flow properties

Intrusive vs non-intrusive

Intrusive vs non-intrusive

Intrusive vs non-intrusive

Averaged information about the particles

$↔$

Instantaneous information about particles and their motion in a flow

Steps in the measurement process

Original aerosol

Steps in the measurement process

After sampling

Steps in the measurement process

After internal losses

Steps in the measurement process

After sensor response

Steps in the measurement process

After processing

Steps in the measurement process

1. Original aerosol
2. After sampling
3. After internal losses
4. After sensor response
5. After processing

Ref: Kulkarni, Baron and Willeke, 2011

Sampling

Representative sampling

Causes for loss

• Aspiration effects
• Particle deposition
• Coagulation, condensation, evaporation
• Inhomogeneities in the aerosol cloud
• Inhomogeneities in the inlet
• Clogging of the inlet
• Particle resuspension

Efficiencies

Aspiration efficiency

$η_\mathrm{asp} = \frac{c_\mathrm{in}}{c_\mathrm{aerosol}}$

Efficiencies

Transmission efficiency

$η_\mathrm{trans} ≡ \frac{c_\mathrm{out}}{c_\mathrm{in}}$

Efficiencies

Inlet efficiency

$η_\mathrm{inlet} ≡ η_\mathrm{asp} η_\mathrm{trans}$

• Inlet efficiency depends on
  • Particle size (or St)
  • Flow conditions

Sampling in a flow

Isokinetic

Sampling in a flow

Super-isokinetic

Sampling in a flow

Sub-isokinetic

Isoaxial aspiration efficiency

Rader & Marple, 1987:

$η_\mathrm{asp} = 1+\left(\frac{u_0}{u} - 1\right) \left(1 - \frac{1}{1+3.77 \mathrm{St}^{0.883}}\right)$

• Maximum error 5 % if:
  • $0.005 < \mathrm{St} < 10$
  • $0.5 < \frac{u_0}{u} < 5$
• Note: $\mathrm{St} ≡ \frac{τu_0}{d}$

Isoaxial aspiration efficiency

$η_\mathrm{asp} = 1+\left(\color{red}{\frac{u_0}{u}} - 1\right) \left(1 - \frac{1}{1+3.77 \color{red}{\mathrm{St}}^{0.883}}\right)$

Anisoaxial sampling

Sampling in calm air

\begin{equation} η_\mathrm{asp} = \color{red}{\frac{v_{ts}}{u}} \cos{\color{red}{φ}} + \exp\left(-\frac{4\color{red}{\mathrm{St}}^{\left(1+\sqrt{\color{red}{\frac{v_{ts}}{u}}}\right)}}{1+2\color{red}{\mathrm{St}}}\right) \end{equation}

Ref: Grinshpun, Willeke & Kalatoor, 1993

Transmission efficiency

$η_\mathrm{trans} ≡ \frac{c_\mathrm{out}}{c_\mathrm{in}}$

Transmission losses

Loss due to inertia

Transmission losses

Loss due to gravity

Transmission losses

Loss due to brownian motion

Transmission losses

Loss due to turbophoresis

Transmission losses

Loss due to thermophoresis

Transmission losses

Loss due to electrophoresis

Dilution

$DR = \frac{Q_t}{Q_s} = \frac{Q_d + Q_s}{Q_s} = \frac{Q_t}{Q_t-Q_d}$

Measure $Q_t$ and $Q_s$ ($DR = \frac{Q_t}{Q_s}$)

\begin{eqnarray} (Δ DR)^2 &=& \left(\frac{∂ DR}{∂Q_t}\right)^2 (ΔQ_t)^2 + \left(\frac{∂ DR}{∂Q_s}\right)^2 (ΔQ_s)^2\\ &=& \frac{1}{Q_s^2} (ΔQ_t)^2 + \frac{Q_t^2}{Q_s^4} (ΔQ_t)^2\\ &=& \frac{Q_t^2}{Q_s^2} \left(\frac{ΔQ_t}{Q_t}\right)^2 + \frac{Q_t^2}{Q_s^2} \left(\frac{ΔQ_s}{Q_s}\right)^2 \end{eqnarray}

$⇒ Δ_\% DR = \sqrt{\left(\Delta_\% Q_t\right)^2 + \left(\Delta_\% Q_s\right)^2}$

Measure $Q_d$ and $Q_s$ ($DR = \frac{Q_d + Q_s}{Q_s}$)

\begin{eqnarray} (Δ DR)^2 &=& \frac{1}{Q_s^2} (ΔQ_d)^2 + \frac{Q_d^2}{Q_s^4} (ΔQ_s)^2\\ &=& \frac{Q_d^2}{Q_s^2} (Δ_\%Q_d)^2 + \frac{Q_d^2}{Q_s^2} (Δ_\%Q_s)^2\\ &=& (DR-1)^2\left((Δ_\%Q_d)^2 + (Δ_\%Q_s)^2\right)\\ \end{eqnarray}

$⇒ Δ_\% DR = \left(1-\frac{1}{DR}\right)\sqrt{(\Delta_\% Q_d)^2 + (\Delta_\% Q_s)^2}$

Measure $Q_d$ and $Q_t$ ($DR = \frac{Q_t}{Q_t-Q_d}$)

\begin{eqnarray} (Δ DR)^2 &=& \frac{Q_t^2}{(Q_t - Q_d)^4} (ΔQ_d)^2 + \frac{Q_d^2}{(Q_t - Q_d)^4} (ΔQ_t)^2\\ &=& \left(\frac{Q_d}{Q_t-Q_d}DR\right)^2\left((Δ_\%Q_d)^2 + (Δ_\%Q_t)^2\right)\\ &=& ((DR-1)DR)^2\left((Δ_\%Q_d)^2 + (Δ_\%Q_t)^2\right)\\ \end{eqnarray}

$⇒ Δ_\% DR = \left(DR-1\right)\sqrt{(\Delta_\% Q_d)^2 + (\Delta_\% Q_t)^2}$

Dilution ratio error

Sampling using filters

Sampling chain

Figure: Aerosol Measurement: Principles, Techniques, and Applications, Third Edition

Filter principles

Figure: AFPRO Filters

Filter principles

Figure: AFPRO Filters

Filter principles

Figure: AFPRO Filters

Filter principles

Figure: AFPRO Filters

Filter principles

Figure: AFPRO Filters

Filter types

PTFE membrane filter

Analysis methods

• Gravimetric analysis
• Microscopy
• Chemical
• Biological

Artifacts

• Moisture
• Vapor adsorption
• Volatilization
• Particle bounce

Optical particle counters

Image: GRIMM Aerosol Technik

Image: Palas

Physical principle: light scattering

Image: Sharayanan, CC BY-SA 3.0

Mie theory

Particle size influence

Single wavelength, forward scattering ($θ = 0$)

Wavelength influence

Forward scattering ($θ = 0$)

Index of refraction influence

Forward scattering ($θ = 0$)

Optical particle counter layout

Schematic: Wikipedia

Response function

Graph: Heim et al.

Sources for errors

• Inlet losses
• Coincidence
• Wrong index of refraction
• Particle shape
• Recirculation
• Border zone illumination

Concentration limits

• Upper limit
  • Limited by coincidence and recovery time
  • Limit sample flow rate
  • Dilute inlet
• Lower limit
  • Depends on number of "noise pulses"
  • Lower limit = 1 order above noise count
  • Might be leaks or recirculation

Size limits

• Lower limit
  • Detector limit
  • Gradual decrease in the sub-μm range
  • Increase lightsource power
  • Problem: Rayleigh-scattering of air (1 mm³ = 0.2 μm)
  • Not always 50 % efficiency for lower limit!
• Lower limit
  • Depends on number of "noise pulses"
  • Lower limit = 1 order above noise count

Differential Mobility Analyzer

Differential Mobility Analyzer

Graph: Flagan, 2008

Differential Mobility Analyzer

Image: Knutson & Whitby, 1975

DMA properties

• Can classify down to the nm range
• Quite slow to operate
• Radioactive source required for particle charging
• Detector: typically CPC

Calibration

Size calibration

Monodisperse reference

Photo: Polysciences

Size calibration

Size calibration

Size calibration

Atomization

Pitfalls

• Polydispersity
• Surfactant
• Agglomeration
• Difference in composition vs. application
• Health hazards

Particle counter example

Known polydisperse source

• DEHS oil droplet aerosol generator
• Pass through charge neutralizer
• Classify using Differential Mobility Analyzer
• Calibrate

Ref: Heim et al.

Index of refraction correction

Ref: Bundke et al.

Mass concentration correction

• Particle counter: mass based on assumed density
• Correct with known density
• Weighing of filter
• Different index of refraction ⇒ non-linear