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 for precise resuspension assessment.

¡Hola! ¿En qué cálculo, conversión o pregunta puedo ayudarte?

Pensando ...

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 particle resuspension in HVAC ducts based on airflow velocity and surface roughness.
Model resuspension of sediment particles in riverbeds during flood events.

Comprehensive Tables of Common Values in Resuspension Calculations

Parameter	Symbol	Typical Range	Units	Description
Particle Diameter	d_p	0.1 – 100	μm	Size of suspended particles, critical for aerodynamic behavior
Particle Density	ρ_p	1000 – 8000	kg/m³	Density of particles, varies by material (e.g., dust, soil, metal)
Air Density	ρ_a	1.2 – 1.3	kg/m³	Density of air at standard conditions
Dynamic Viscosity of Air	μ	1.7 × 10^-5	Pa·s	Viscosity affecting particle drag forces
Friction Velocity	u_*	0.1 – 1.0	m/s	Velocity scale representing shear stress at the surface
Surface Roughness Length	z₀	0.001 – 0.1	m	Characteristic length scale of surface irregularities
Resuspension Rate	R	10^-6 – 10^-2	s^-1	Rate at which particles detach from surfaces
Adhesion Force	F_a	10^-9 – 10^-6	N	Force binding particles to surfaces
Gravitational Acceleration	g	9.81	m/s²	Acceleration due to gravity
Particle Mass	m_p	Variable	kg	Mass of individual particle

Fundamental Formulas for Calculation of Resuspension

The calculation of resuspension involves quantifying the detachment of particles from surfaces due to aerodynamic forces overcoming adhesion. The primary parameters include particle properties, surface characteristics, and fluid dynamics.

1. Resuspension Rate (R)

The resuspension rate is often modeled as a function of friction velocity and adhesion forces:

R = A × exp(−B × (Fa / (ρa × u*2 × dp2)))

R: Resuspension rate (s^-1)
A: Empirical constant (typically 10^-3 to 10^-1)
B: Empirical constant (dimensionless, often between 1 and 10)
F_a: Adhesion force (N)
ρ_a: Air density (kg/m³)
u_*: Friction velocity (m/s)
d_p: Particle diameter (m)

This exponential relationship captures the sensitivity of resuspension to the ratio of adhesion to aerodynamic forces.

2. Adhesion Force (F_a)

Adhesion force between a particle and surface can be estimated using the Derjaguin-Muller-Toporov (DMT) model:

Fa = 4πγrpcos(θ)

γ: Surface energy (J/m²)
r_p: Particle radius (m)
θ: Contact angle (degrees)

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

3. Friction Velocity (u_*)

Friction velocity relates to shear stress at the surface:

u* = √(τ / ρa)

τ: Shear stress (Pa)
ρ_a: Air density (kg/m³)

Shear stress can be derived from wind velocity profiles near the surface.

4. Particle Mass (m_p)

Particle mass is essential for gravitational force calculations:

mp = (4/3)πrp3ρp

r_p: Particle radius (m)
ρ_p: Particle density (kg/m³)

5. Resuspension Flux (J)

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

J = R × Cs

J: Resuspension flux (particles/m²·s)
R: Resuspension rate (s^-1)
C_s: Surface concentration of particles (particles/m²)

This formula links the rate of detachment to the available particle reservoir on the surface.

Detailed Explanation of Variables and Their Typical Values

Particle Diameter (d_p): Influences aerodynamic drag and adhesion. Fine particles (<1 μm) are more easily resuspended.
Particle Density (ρ_p): Heavier particles require greater aerodynamic forces to resuspend.
Air Density (ρ_a): Slightly varies with altitude and temperature; affects drag forces.
Dynamic Viscosity (μ): Governs fluid resistance; standard air viscosity is ~1.7×10^-5 Pa·s.
Friction Velocity (u_*): Key parameter derived from wind shear; higher values increase resuspension.
Adhesion Force (F_a): Depends on surface energy and particle size; critical threshold for detachment.
Surface Concentration (C_s): Number of particles per unit area; varies widely by environment.

Real-World Applications and Case Studies

Case Study 1: Resuspension of Radioactive Particles from Contaminated Soil

Following a nuclear incident, understanding the resuspension of radioactive particles is vital for public safety and remediation efforts. Consider a contaminated soil surface with particles averaging 10 μm diameter and density 2500 kg/m³. The surface concentration is 1×10⁸ particles/m². Wind conditions produce a friction velocity of 0.3 m/s.

Given:

d_p = 10 × 10^-6 m
ρ_p = 2500 kg/m³
ρ_a = 1.225 kg/m³
u_* = 0.3 m/s
C_s = 1×10⁸ particles/m²
Surface energy γ = 0.05 J/m²
Contact angle θ = 60°

Step 1: Calculate particle radius:

rp = dp / 2 = 5 × 10-6 m

Step 2: Calculate adhesion force:

Fa = 4π × 0.05 × 5 × 10-6 × cos(60°) = 1.57 × 10-6 N

Step 3: Calculate resuspension rate using empirical constants A=0.01, B=5:

R = 0.01 × exp(−5 × (1.57 × 10-6 / (1.225 × 0.32 × (10 × 10-6)2)))

Calculate denominator:

1.225 × 0.09 × 1 × 10-10 = 1.1025 × 10-11

Ratio:

1.57 × 10-6 / 1.1025 × 10-11 ≈ 142,400

Exponent:

−5 × 142,400 = −712,000

Since exp(−712,000) ≈ 0, the resuspension rate is effectively zero under these conditions, indicating strong adhesion preventing particle detachment.

Step 4: Calculate resuspension flux:

J = R × Cs ≈ 0 × 1×108 = 0 particles/m²·s

This result suggests negligible resuspension at the given friction velocity, highlighting the importance of wind speed thresholds in contamination risk assessments.

Case Study 2: Dust Resuspension in an Industrial Warehouse

In an industrial warehouse, dust accumulation on floors poses respiratory hazards. Estimating resuspension helps design ventilation and cleaning protocols. Assume dust particles with diameter 5 μm, density 2000 kg/m³, surface concentration 5×10⁷ particles/m², and friction velocity induced by ventilation fans at 0.5 m/s.

Given:

d_p = 5 × 10^-6 m
ρ_p = 2000 kg/m³
ρ_a = 1.2 kg/m³
u_* = 0.5 m/s
C_s = 5×10⁷ particles/m²
Surface energy γ = 0.03 J/m²
Contact angle θ = 45°

Step 1: Calculate particle radius:

rp = 2.5 × 10-6 m

Step 2: Calculate adhesion force:

Fa = 4π × 0.03 × 2.5 × 10-6 × cos(45°) ≈ 2.65 × 10-7 N

Step 3: Calculate resuspension rate with A=0.02, B=4:

R = 0.02 × exp(−4 × (2.65 × 10-7 / (1.2 × 0.52 × (5 × 10-6)2)))

Calculate denominator:

1.2 × 0.25 × 2.5 × 10-11 = 7.5 × 10-12

Ratio:

2.65 × 10-7 / 7.5 × 10-12 ≈ 35,333

Exponent:

−4 × 35,333 = −141,332

Again, exp(−141,332) ≈ 0, indicating very low resuspension rate at this friction velocity.

Step 4: Resuspension flux:

J = R × Cs ≈ 0 × 5×107 = 0 particles/m²·s

This suggests that under normal ventilation, dust resuspension is minimal, but higher airflow or mechanical disturbance could increase rates significantly.

Additional Considerations and Advanced Modeling Approaches

While the exponential model provides a first-order approximation, advanced models incorporate stochastic particle detachment, surface heterogeneity, and transient wind conditions. Computational Fluid Dynamics (CFD) coupled with Discrete Element Method (DEM) simulations enable detailed prediction of resuspension in complex environments.

Surface Roughness Effects: Rough surfaces increase turbulence and local shear, enhancing resuspension.
Humidity and Electrostatic Forces: Moisture can increase adhesion, reducing resuspension; electrostatic charges may either attract or repel particles.
Particle Shape and Aggregation: Non-spherical particles and agglomerates exhibit different aerodynamic and adhesion properties.
Time-Dependent Resuspension: Continuous exposure to wind or mechanical forces can lead to cumulative resuspension effects.

Incorporating these factors requires experimental calibration and site-specific data to refine predictive accuracy.