Centrifuge Sizing Calculator

Centrifugal Separation Fundamentals

Centrifuges separate particles from liquids by applying centrifugal force many times greater than gravity. This accelerated "settling" allows separation of particles that would take hours under gravity to occur in seconds or minutes.

• Separation Driving Force: Density difference between particle and fluid (Delta-rho)
• Resistance Force: Viscous drag from the continuous phase
• Particle Size Effect: Settling velocity increases with diameter squared
• G-Force Amplification: Centrifugal acceleration = omega^2 * r (can exceed 100,000 G)

Stokes Settling Law

Stokes law describes particle settling velocity in the laminar flow regime (Re < 0.1). For a particle settling in a centrifugal field:

v_s = d^2 * (rho_p - rho_f) * omega^2 * r / (18 * mu)

• d = Particle diameter (m)
• rho_p = Particle density (kg/m3)
• rho_f = Fluid density (kg/m3)
• omega = Angular velocity (rad/s)
• r = Radial position (m)
• mu = Dynamic viscosity (Pa.s)

Key Insight: Doubling particle diameter quadruples settling velocity. This is why centrifuges struggle with very fine particles.

Sigma Factor (Equivalent Settling Area)

Sigma (capital-sigma) represents the equivalent gravitational settling area of a centrifuge. It allows direct comparison between centrifuges of different sizes and types:

Sigma = (pi * L * omega^2 / g) * (3*r2^2 + r1^2) / 4 (simplified for tubular bowl)

For disc stack centrifuges:

Sigma = (2 * pi * n * omega^2 / (3 * g)) * (r2^3 - r1^3) * cot(theta)

• Physical Meaning: A centrifuge with Sigma = 1000 m^2 separates as well as a 1000 m^2 gravity settler
• Scale-up Rule: Q1/Sigma1 = Q2/Sigma2 for equivalent separation
• Typical Values: Lab centrifuge ~10 m^2, Industrial disc stack ~50,000 m^2

Residence Time

Residence time is how long fluid spends in the separation zone. Particles must settle to the wall within this time:

t_res = V_bowl / Q

For complete separation, residence time must exceed settling time:

t_settle = (r2 - r1) / v_s

• Critical Particle Size: Smallest particle that settles completely at given flow rate
• Cut Size (d50): Particle size with 50% separation efficiency
• Design Margin: Typically size for 2-3x required residence time

Centrifuge Types Comparison

• Tubular Bowl: Highest G-force (up to 60,000 G), small capacity, batch operation. Best for fine particles, lab scale, and clarification.
• Disc Stack: High G-force (5,000-15,000 G), continuous operation, self-cleaning. Ideal for liquid-liquid separation and dairy/beverage industry.
• Decanter (Scroll): Moderate G-force (1,500-4,000 G), handles high solids, continuous discharge. Used in wastewater, drilling mud, and food processing.
• Basket/Peeler: Lower G-force (500-2,500 G), filtering centrifuge, batch operation. Best for crystalline products and dewatering.

Separation Efficiency Factors

• Hindered Settling: High solids concentration reduces settling velocity (use Richardson-Zaki correlation)
• Non-Spherical Particles: Apply shape factor (typically 0.6-0.9 for irregular particles)
• Flocculation: Can dramatically improve separation by increasing effective particle size
• Temperature Effects: Higher temperature reduces viscosity, improves separation
• Feed Distribution: Poor feed distribution can cause short-circuiting and reduced efficiency