| name | agitator-design |
| description | Agitator/mixer design — impeller type selection, Power number/Flow number, Reynolds number for mixing, blend time, gas-liquid mixing, scale-up, baffles, ASME mixing vessel, Rushton turbine, pitched blade. |
| metadata | {"priority":7,"promptSignals":{"phrases":["agitator design","mixer design","impeller selection","Power number mixing","blend time","mixing tank design","Rushton turbine"],"minScore":3}} |
Agitator/Mixer Design — Complete Skill
Impeller Types and Selection
| Impeller | Flow pattern | Np (turbulent) | Nq | Best use |
|---|
| Rushton disc turbine (RT) | Radial | 5.0 | 0.72 | Gas-liquid; high shear |
| Pitched blade turbine (PBT) | Axial/radial mix | 1.5–2.0 | 0.87 | Blending; solids suspension |
| Hydrofoil (HE-3, A310) | Axial | 0.3–0.6 | 0.55 | Blending; low viscosity |
| Anchor | Tangential | 0.4–1.0 | — | High viscosity (Re < 100) |
| Helical ribbon | Axial | 300/Re | — | Very high viscosity |
| Marine propeller | Axial | 0.3 | 0.5 | Low viscosity; bulk mixing |
Dimensionless Numbers
Reynolds number for mixing:
Re_mix = ρ × N × D² / μ
N = rotational speed [rev/s]; D = impeller diameter [m]; ρ = fluid density [kg/m³]; μ = dynamic viscosity [Pa·s]
Turbulent: Re > 10,000 (Np = constant)
Transitional: 10 < Re < 10,000
Laminar: Re < 10 (Np = K_p/Re; K_p depends on impeller)
Power number Np:
P = Np × ρ × N³ × D⁵ [W; P = agitator shaft power]
Np from impeller data at given Re and baffle configuration
Flow number Nq:
Q_pumped = Nq × N × D³ [m³/s; impeller pumping rate]
Blend number Nθ (blending):
t_blend = Nθ / N [s; Nθ typically 30–60 for turbulent mixing]
Tank Geometry and Baffles
Standard geometry ratios:
T = tank diameter; H = liquid height; D = impeller diameter
H/T = 1.0 (standard); D/T = 0.3–0.4 (turbines); D/T = 0.5–0.6 (hydrofoil low power)
Bottom clearance: C = T/4 to T/3
Baffles:
Standard: 4 baffles; width W_b = T/12 to T/10; installed vertical, near wall
Without baffles: swirling vortex; poor mixing; power draw lower
With baffles: turbulent; Np = full (Table above)
Multiple impellers:
For H/T > 1.2: add second (upper) impeller
Impeller spacing: S = 0.8–1.2 D between impellers
Power Calculation
Agitator power:
P = Np × ρ × N³ × D⁵ [W]
Motor power:
P_motor = P / (η_motor × η_gearbox) × service_factor
η_motor = 0.92–0.96; η_gearbox = 0.94–0.97; service factor = 1.25
Example — Rushton turbine:
D = 0.5 m; N = 3 rev/s; ρ = 1000 kg/m³; Np = 5.0 (turbulent)
P = 5.0 × 1000 × 3³ × 0.5⁵ = 5.0 × 1000 × 27 × 0.03125 = 4219 W ≈ 4.2 kW
Blend Time Correlations
Turbulent blend time (Nienow, Ruszkowski):
t_mix = (T/D)^2.43 × (T/H)^0.5 × (5.9/N) × (T/D) [simplified; check specific correlation]
More accurate (Grenville & Nienow 2004):
N × t_blend = C₁ × (T/D)^α × (H/T)^β [correlation constants from literature]
Conservative estimate:
t_blend = (4–5) × circulation_time = (4–5) × V_tank / Q_pumped
For blending miscible liquids:
t_blend (95% uniformity) ≈ 20–30 circulation times (laminar); 5–10 (turbulent)
Gas-Liquid Mixing
Gas dispersion power:
P_gassed / P_ungassed = f(FlG) [gassed power fraction depends on gas flow number]
Gas flow number: FlG = Q_gas / (N × D³) [Q_gas = volumetric gas flow at tank conditions]
Nienow correlation:
P_g/P = 0.1 × (N² D³ / (g × V_L^(1/3) × Q_g^(2/3)))^(-0.5) [approximation; use chart for accuracy]
For Rushton: P_g/P ≈ 0.5 at FlG = 0.04
Superficial gas velocity:
U_g = Q_gas / A_tank [m/s]
Minimum for gas distribution: U_g ≥ 0.01–0.02 m/s
Flooding (gas not dispersed):
Flooding FlG > FlG_flood = 30/(Np)^0.5 × (D/T)^3.5 [at flooding; impeller overwhelmed]
k_L a (volumetric mass transfer coefficient):
k_L a = C × (P_g/V_L)^α × U_g^β
C, α, β from Higbie penetration theory or empirical (Van't Riet correlation):
k_L a = 0.026 × (P_g/V_L)^0.4 × U_g^0.5 [s⁻¹; P_g/V_L in W/m³; U_g in m/s]
Solids Suspension
Zwietering correlation (just-suspended speed N_JS):
N_JS = S × ν^0.1 × d_p^0.2 × [(g(ρ_s - ρ_L)/ρ_L)^0.45] × (C_s/D)^0.13 / D^0.85
S = Zwietering parameter (from impeller/geometry table; 4–8 for turbines)
ν = kinematic viscosity [m²/s]; d_p = particle diameter [m]; C_s = solids loading [kg_solid/m³_liquid]
Rule: design for 1.1–1.2 × N_JS to ensure all solids in suspension
Scale-Up Criteria
Equal power per unit volume (P/V = const):
N_scale = N_lab × (D_lab/D_scale)^(2/3) [most common for mixing]
P/V constant; blend time increases with scale (t_blend ∝ D^(2/3))
Equal tip speed (V_tip = π N D = const):
N_scale = N_lab × (D_lab/D_scale)
Better for shear-sensitive processes (cells, crystals)
Equal blend time: N_scale = N_lab → P/V increases (expensive at scale)
Equal Froude number (surface behavior):
Fr = N² D / g = const → N ∝ D^(-0.5)
Use for surface aeration or vortex formation
Output
Provide: impeller type, diameter D [m] and T/D ratio, speed N [RPM], Power number Np, shaft power P [kW] and motor power [kW], pumping rate Q [m³/s], blend time t_blend [s], gas flow number FlG (if gas-liquid), k_L a [s⁻¹] (if mass transfer), just-suspended speed N_JS [RPM] (if solids), baffle specification, scale-up basis and governing criterion, and applicable reference (ASME mixing design guides; Handbook of Industrial Mixing).
