Size distribution of bubbles in agitated viscous Newtonian and non‐Newtonian solutions

Abstract

The effects of impeller type, Newtonian shear thinning liquid viscosities, and noncoalescing conditions on the impeller gas cavities, impeller power consumption, and Sauter mean bubble diameter (d 32 ) in a multiphase agitated vessel were systematically studied. An underwater recording technique was used to study gas cavities and bubble size in various operating and design conditions. The gas cavity images were used to relate d 32 to gas cavity structure. It was observed that d 32 values increase with an increase in Newtonian and shear thinning liquid viscosities. Results also indicate that impellers operating in shear thinning liquids consume higher gassed power at the same operating conditions compared with those in Newtonian fluids. In addition, the d 32 values in noncoalescing liquids are substantially smaller compared with those in coalescing solutions at the same P g /V. Mathematical correlations are proposed for estimating the d 32 in the impeller discharge stream and P g /V in viscous Newtonian and non-Newtonian solutions.KEYWORDS bubble size, gas cavities, gas-liquid hydrodynamics, mathematical correlations, non-Newtonian liquid, power consumption Nomenclature and symbols:Greek letters: σ, surface tension, N/m; η, microscale of turbulence, m; ρ L , liquid phase density, kg/m 3 ; μ L , liquid phase viscosity, Pa·s; μ G , gas phase viscosity, Pa·s; τ, torque, N·m; v, kinematic viscosity of liquid, m 2 /s Letters and subscripts: a G-L , gas-liquid interfacial area, m 2 /m 3 ; C, impeller clearance, m; Ca c , critical capillary number, dimensionless; D, impeller diameter, m; d, particle size, m; d max , maximum stable diameter, m; d 32 , Sauter mean diameter, m; d bi , average bubble diameter in Equation (2), m; ε, energy dissipation rate, W/kg; G, strength of the applied strain rate around the bubble, 1/s; g, gravitational acceleration, m/s 2 ; H, liquid height, m; k, impeller constant; L, scale of the main flow, m; M s , mass of solids, kg; N, impeller speed, rps; n i , number of bubbles in Equation (2); N jsg , impeller speed for complete off-bottom solids suspension in three-phase systems, rps; N js , impeller speed for complete off-bottom solids suspension in two phase systems, rps; N P , power number; P g , gassed power input, W; S, dimensional coefficient; Q g , gas flow rate, vvm; T, tank diameter, m; V, liquid volume, m 3 ; V S , superficial gas velocity, m/s; vvm, volumetric flow rate of gas per minute per volume of liquid in the tank; u 2 , mean square velocity difference, m 2 /s 2 ; X, solid loading ratio, kg/kg Abbreviations: CMC, carboxymethyl cellulose; MIBC, methyl isobutyl carbinol

Bubble size and liquid-side mass transfer coefficient measurements in aerated stirred tank reactors with non-Newtonian liquids

“…If non-Newtonian systems in stirred vessels are considered, available data is much more limited, and existing empirical correlations are derived from the-oretical considerations (Garcia-Ochoa and Gomez (2009)). As pointed out by Momiroski et al (2018), current techniques are not suitable to measure bubble size in highly viscous and opaque fluids in aerated stirred tanks. In their work, they measured the bubble size in the impeller discharge region in shear-thinning solutions; however, the maximum superficial gas velocity they investigated was relatively low, equaling 3 mm s −1 .…”

Gas Dispersion in Non-Newtonian Fluids with Mechanically Agitated Systems: A Review

“…Khalili et al [20] studied the agitation effect on the bubble diameter and observed that even though the impeller rotation affected the Sauter mean bubble diameter, it did not change the number of bubble classes in the mixing system. The bubble size distribution, in turn, depends on the cavity structure for a given impeller type, gas flow rate, and impeller speed, as presented by Momiroski et al [65]. Their results also indicated that hollow blade turbines (HBT) generated smaller mean bubble sizes compared to Rushton turbines (RT).…”

“…High mass transfer requires a large interfacial area that can be achieved by decreasing the bubble mean diameter. However, the determination of the bubble size distribution is complex, and it is even more challenging in the non-Newtonian media [65]. In this case, the shear rate variation throughout the mixing system promotes a non-uniform bubble size distribution in which lower bubble mean sizes are observed near the impeller region due to higher shear rate in this region [66].…”

“…Some of the experimental techniques for measuring the bubble size employ conductivity probes [67,68], imaging probes [65,69], suction probes [66,[70][71][72], particle image velocimetry [46], photography [51,73], laser-induced fluorescence [74], and gas disengagement technique [20,75]. The experimental techniques must be set accordingly to obtain the bubble size in different regions of the vessel to have a better representation of the wide bubble size distribution.…”

“…In addition, Garcia-Ochoa et al [14] estimated the bubble mean diameter in a rheologically evolving system, using a correlation that was originally proposed by Bhavaraju et al [77] for Newtonian fluids. Momiroski et al [65] obtained different proportionality constants for coalescing and non-coalescing systems with a pseudoplastic fluid for three impeller types. Bach et al [34], in turn, correlated the bubble size to the superficial gas velocity and specific gassed power uptake, applying a constant of proportionality that depends on the aeration rate.…”