Classical first-order flotation kinetics assume all mineral particles float with an identical rate constant k. In real ore flotation, however, particle size distribution, liberation degree, and surface collector coverage create heterogeneous floatability. Kelsall's two-rate model divides the floatable valuable mineral into a fast-floating fraction (1 - Phi_slow) with rate constant k_fast (typically well-liberated, fine-to-medium particles) and a slow-floating fraction Phi_slow with rate constant k_slow (locked composite grains or coarse particles). This dual-rate distribution accurately fits laboratory batch kinetics and reliably predicts bank recovery across rougher, scavenger, and cleaner stages.

Mechanical flotation cells introduce pressurized or self-aspirated air at superficial gas velocities (Jg) between 0.5 and 2.5 cm/s, creating a continuous dispersed bubble swarm. This gas occupies between 10% and 20% of the active cell volume (gas holdup, epsilon_g). True liquid-solid pulp residence time tau is governed by the net slurry volume: V_slurry = V_cell * (1 - epsilon_g). Ignoring gas holdup overestimates available residence time by 15% to 25%, resulting in undersized flotation tanks, inadequate mineral-bubble collision opportunities, and unrecovered valuable minerals in tailings.

A bank of N identical agitated flotation cells operating in continuous mode behaves hydrodynamically as N continuous stirred-tank reactors (CSTRs) in series. For a component with kinetic rate k and mean residence time per cell tau_c, the continuous bank recovery is given by R_bank = 1 - 1 / (1 + k * tau_c)^N. Due to backmixing and RTD dispersion, continuous cells require 1.3 to 1.8 times the nominal batch flotation residence time (the "scale-up factor") to reach equivalent metallurgical recovery.

By combining the overall mass balance (F = C + T) with the component balance (F * f = C * c + T * t), the concentrate mass pull percentage (Y = 100 * C / F) is derived as Y = 100 * (f - t) / (c - t). The fractional recovery R is (C * c) / (F * f) = (c / f) * ((f - t) / (c - t)). In reverse, when bank recovery R is calculated from flotation kinetics, the resulting tailings grade is t = f * (1 - R) / (1 - Y) and concentrate pull is Y = 100 * R * (f / c).

Rougher banks operate at high throughput to maximize initial recovery of fully liberated fast-floating minerals. Scavenger banks receive rougher tailings to recover difficult slow-floating particles and composite grains, requiring longer residence times, higher collector dosing, and elevated power inputs. Cleaner banks receive rougher/scavenger concentrates to reject entrained gangue and elevate product grade, operating at lower pulp densities (15-22% solids) with deep froth beds and wash-water addition.