Batch & Continuous Hindered Sedimentation, Kynch Slurry Settling Kinetics & Clarifier Sizing

Process apparatus & industrial sensors.

A reason behind every step.

Investigate batch hindered sedimentation kinetics for concentrated calcium carbonate (CaCO_3) slurries across suspension concentrations C_s from 10.0 to 60.0 g/L in a 1.0-meter graduated settling column, track interface subsidence rates, determine the Kynch hindered settling velocity slope S, evaluate free Stokes settling velocity v_0, and apply the Coe–Clevenger method to size an industrial continuous gravity thickener. Standardized parameter settings: 10.0, 20.0, 30.0, 40.0, 50.0, 60.0 g/L.

Process engineering background & physical principles.

Sedimentation and gravity clarification are foundational mechanical separation unit operations utilized extensively in chemical manufacturing, mineral beneficiation, hydrometallurgy, water clarification, and municipal wastewater treatment. In dilute suspensions (solids volume fraction φ < 0.005), individual spherical particles settle independently without hydrodynamic particle-particle interaction according to Stokes' law: v_0 = g · d_p^2 · (ρ_p - ρ_f) / (18 · μ). However, in concentrated industrial slurries (φ > 0.05), particles settle as a collective cloud or blanket with a sharp, visible interface between the descending clarified supernatant and the concentrated suspension—a phenomenon known as hindered settling or zone settling. According to the classical sedimentation theory formulated by George J. Kynch in 1952, the local settling velocity v_s of particles in a suspension depends solely on the local solids volume concentration: v_s = f(C_s). As solids concentration increases, the upward displacement velocity of displaced fluid through the narrowing interstitial pores increases, and viscous drag is amplified by surrounding particles, causing settling velocity to decrease sharply. In the moderate concentration regime (C_s = 10.0 to 60.0 g/L), the Kynch hindered settling velocity decreases linearly with solids concentration: v_s = v_0 - S · C_s, where v_0 = 120.0000 cm/min is the unhindered terminal velocity intercept and S = 1.8500 (cm/min)/(g/L) is the Kynch hindered settling slope. Alternatively, the non-linear relationship across wide concentration ranges is described by the Richardson–Zaki correlation: v_s = v_0 · ε^n = v_0 · (1 - φ)^n, where ε is suspension voidage and n is the Richardson–Zaki exponent (~4.65 in laminar creeping flow). In continuous industrial gravity thickeners, the solid flux method (Coe & Clevenger / Yoshioka analysis) utilizes these batch settling velocity curves to identify the critical solids handling capacity (minimum flux G_min) and determine the required cross-sectional clarifier area A = F_s / G_min. In this laboratory experiment, a 1.0-meter precision glass settling column equipped with automated optical array interface detection tracks suspension interface subsidence across CaCO_3 concentrations from 10.0 to 60.0 g/L to evaluate v_s, determine S = 1.8500 (cm/min)/(g/L), and calculate continuous thickener dimensions.

Evaluated using a 100.0 cm tall, 6.0 cm ID precision graduated glass settling column with automated optical photodiode array and constant-temperature jacket at 20.0 °C. Standardized calcium carbonate slurry (mean particle diameter d_p = 25.0 μm, true solids density ρ_p = 2710 kg/m^3) in deionized water (ρ_f = 998.2 kg/m^3, μ = 1.002 mPa·s).