Calculation of Resuspension

Understanding the Calculation of Resuspension: A Technical Deep Dive

Resuspension calculation quantifies particle detachment from surfaces into the air. It is critical in environmental and industrial applications.

This article explores detailed formulas, variable definitions, and real-world examples of resuspension calculation methods.

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  • Calculate resuspension rate for dust particles on industrial floors under varying wind speeds.
  • Determine resuspension flux of radioactive particles from contaminated soil after rainfall.
  • Estimate resuspension factor for PM10 particles in urban street canyons during traffic peak hours.
  • Model resuspension velocity of sediment particles in a riverbed under fluctuating flow conditions.

Comprehensive Tables of Common Values in Resuspension Calculations

ParameterSymbolTypical RangeUnitsNotes
Resuspension RateR10-9 to 10-3m/sRate at which particles detach from surfaces
Resuspension FactorFr10-9 to 10-5m-1Ratio of airborne concentration to surface contamination
Particle Diameterdp0.1 to 100μmSize of suspended particles
Particle Densityρp1000 to 8000kg/m3Density of particulate matter
Surface Roughnessz00.001 to 0.1mCharacteristic roughness length of surface
Wind Shear Velocityu*0.1 to 1.0m/sFriction velocity influencing particle detachment
Adhesion ForceFa10-9 to 10-6NForce binding particles to surfaces
Gravitational Accelerationg9.81m/s2Standard gravity
Air Densityρa1.2kg/m3Density of ambient air at sea level
Dynamic Viscosity of Airμ1.8 Ɨ 10-5PaĀ·sViscosity affecting particle motion

Fundamental Formulas for Calculation of Resuspension

The calculation of resuspension involves several key formulas that describe the physical processes governing particle detachment and entrainment. Below are the primary equations used in the field, along with detailed explanations of each variable and typical values.

1. Resuspension Rate (R)

The resuspension rate quantifies the velocity at which particles are lifted from a surface into the air:

R = A Ɨ u*n
  • R: Resuspension rate (m/s)
  • A: Empirical coefficient (typically 10-7 to 10-3)
  • u*: Wind shear velocity (m/s)
  • n: Exponent, usually between 2 and 4 depending on surface and particle type

This formula is empirical and derived from experimental data. The coefficient A and exponent n depend on surface roughness, particle adhesion, and environmental conditions.

2. Resuspension Factor (Fr)

The resuspension factor relates airborne particle concentration to surface contamination:

Fr = Ca / Cs
  • Fr: Resuspension factor (m-1)
  • Ca: Airborne particle concentration (Bq/m3 or μg/m3)
  • Cs: Surface contamination concentration (Bq/m2 or μg/m2)

This factor is crucial in radiological assessments and air quality modeling, providing a direct link between surface contamination and airborne exposure.

3. Critical Shear Velocity for Particle Detachment (u*c)

The minimum friction velocity required to initiate particle resuspension is given by:

u*c = √(Fa / (ρa Ɨ dp))
  • u*c: Critical shear velocity (m/s)
  • Fa: Adhesion force between particle and surface (N)
  • ρa: Air density (kg/m3)
  • dp: Particle diameter (m)

This formula assumes a balance between aerodynamic forces and adhesion forces holding the particle to the surface.

4. Adhesion Force (Fa)

Adhesion force can be estimated using the Derjaguin-Muller-Toporov (DMT) model for elastic contact:

Fa = 4πγr
  • γ: Surface energy per unit area (J/m2)
  • r: Particle radius (m)

Typical surface energy values range from 0.01 to 0.1 J/m2 depending on material composition.

5. Resuspension Flux (J)

The flux of particles resuspended per unit area and time is:

J = R Ɨ Cs
  • J: Resuspension flux (particles/m2/s)
  • R: Resuspension rate (m/s)
  • Cs: Surface concentration (particles/m3)

This equation links the resuspension rate with the available surface contamination to estimate airborne particle generation.

Detailed Explanation of Variables and Typical Values

  • Wind Shear Velocity (u*): Represents the friction velocity near the surface, influenced by wind speed and surface roughness. Typical values range from 0.1 m/s (calm conditions) to 1.0 m/s (strong winds).
  • Particle Diameter (dp): Particle size significantly affects resuspension. Fine particles (50 μm).
  • Adhesion Force (Fa): Depends on particle and surface material properties, humidity, and electrostatic effects. Lower adhesion forces facilitate resuspension.
  • Surface Roughness (z0): Rougher surfaces increase turbulence and can either enhance or inhibit resuspension depending on particle trapping.
  • Surface Concentration (Cs): The amount of particulate matter deposited on surfaces, often measured in Bq/m2 for radioactive particles or μg/m2 for dust.

Real-World Applications of Resuspension Calculations

Case Study 1: Resuspension of Radioactive Particles from Contaminated Soil

Following a nuclear accident, soil surfaces become contaminated with radionuclides. Estimating airborne radioactive particle concentrations due to resuspension is critical for public health risk assessments.

Scenario: A contaminated site has a surface activity concentration of 1 Ɨ 106 Bq/m2. The wind shear velocity is measured at 0.3 m/s. The particle diameter is 20 μm, and the adhesion force is estimated at 5 Ɨ 10-8 N.

Step 1: Calculate the critical shear velocity:

u*c = √(Fa / (ρa Ɨ dp)) = √(5 Ɨ 10-8 / (1.2 Ɨ 20 Ɨ 10-6)) ā‰ˆ 0.045 m/s

Since the actual wind shear velocity (0.3 m/s) exceeds u*c, resuspension occurs.

Step 2: Estimate resuspension rate using empirical coefficient A = 1 Ɨ 10-5 and exponent n = 3:

R = 1 Ɨ 10-5 Ɨ (0.3)3 = 1 Ɨ 10-5 Ɨ 0.027 = 2.7 Ɨ 10-7 m/s

Step 3: Calculate resuspension flux:

J = R Ɨ Cs = 2.7 Ɨ 10-7 Ɨ 1 Ɨ 106 = 0.27 Bq/m2/s

This flux indicates the rate at which radioactive particles become airborne, informing exposure models and remediation strategies.

Case Study 2: Dust Resuspension in an Industrial Warehouse

In a warehouse storing fine powders, dust resuspension can affect worker health and product quality. Calculating resuspension rates helps design ventilation and cleaning protocols.

Scenario: Surface dust concentration is 500 μg/m2, particle diameter is 5 μm, wind shear velocity from ventilation fans is 0.5 m/s, and adhesion force is 1 Ɨ 10-8 N.

Step 1: Calculate critical shear velocity:

u*c = √(1 Ɨ 10-8 / (1.2 Ɨ 5 Ɨ 10-6)) ā‰ˆ 0.041 m/s

Since 0.5 m/s > 0.041 m/s, resuspension is expected.

Step 2: Using A = 5 Ɨ 10-6 and n = 3:

R = 5 Ɨ 10-6 Ɨ (0.5)3 = 5 Ɨ 10-6 Ɨ 0.125 = 6.25 Ɨ 10-7 m/s

Step 3: Calculate resuspension flux:

J = R Ɨ Cs = 6.25 Ɨ 10-7 Ɨ 500 = 3.13 Ɨ 10-4 μg/m2/s

This value guides ventilation design to maintain airborne dust below occupational exposure limits.

Additional Considerations and Advanced Topics

Resuspension is influenced by multiple environmental and material factors beyond the basic formulas. These include:

  • Humidity and Moisture: Increased moisture enhances adhesion forces, reducing resuspension rates.
  • Electrostatic Charges: Charged particles may adhere more strongly or repel, affecting detachment.
  • Surface Texture and Porosity: Porous surfaces can trap particles, lowering resuspension.
  • Particle Shape and Composition: Irregular shapes and heterogeneous materials alter aerodynamic behavior.
  • Temporal Variability: Resuspension rates fluctuate with diurnal wind patterns and human activity.

Advanced models incorporate Computational Fluid Dynamics (CFD) and stochastic processes to simulate complex resuspension scenarios, especially in urban or industrial environments.

Authoritative Resources for Further Study

Understanding and accurately calculating resuspension is essential for environmental safety, industrial hygiene, and regulatory compliance. The formulas and examples provided here offer a robust foundation for expert analysis and practical application.