Bubble swarm velocities in a flotation column.

摘要

A new fast response conductivity meter was developed and tested. The "five time constant" of the meter is 0.08 s which meets the requirement for measurements under the dynamic conditions relevant to this work.; In a laboratory column, a bubble interface was created by introducing a step change of gas flow, and the rising velocity of this interface, {dollar}usb{lcub}in{rcub},{dollar} was measured using a conductivity method with the new conductivity meter. A measurement of the three-dimensional bubble swarm velocity in the column was obtained by interpolation from the {dollar}usb{lcub}in{rcub}{dollar} measured as a function of {dollar}Jsb{lcub}g2{rcub}vert Jsb{lcub}g{rcub}sb1 ,{dollar} where {dollar}Jsb{lcub}g{rcub}sb1{dollar} and {dollar}Jsb{lcub}g{rcub}sb2{dollar} are the superficial gas velocities before and after a step change of gas flowrate, respectively. This velocity was referred to as the hindered velocity, {dollar}usb{lcub}h{rcub}.{dollar} The buoyancy velocity, {dollar}usb0 ,{dollar} was readily determined by switching off the gas, i.e. {dollar}usb0 = usb{lcub}in{rcub}{dollar} at {dollar}Jsb{lcub}g{rcub}sb2 = 0.{dollar}; The average gas velocity, {dollar}usb{lcub}g{rcub},{dollar} was corrected to the local average gas velocity, {dollar}usb{lcub}g,loc{rcub},{dollar} to obtain the average gas velocity under the local pressure conditions at a given vertical position in the column. The experimental results showed that {dollar}usb{lcub}h{rcub}{dollar} was significantly less than {dollar}usb{lcub}g,loc{rcub}{dollar} (and {dollar}usb{lcub}g{rcub}).{dollar} This is because the {dollar}usb{lcub}h{rcub}{dollar} is the three-dimensional bubble swarm velocity and {dollar}usb{lcub}g,loc{rcub}{dollar} is the one-dimensional bubble swarm velocity. Unlike {dollar}usb{lcub}g,loc{rcub},{dollar} the {dollar}usb{lcub}h{rcub}{dollar} was constant along the column, which was supported by theoretical momentum analysis. The {dollar}usb{lcub}h{rcub}{dollar} is proposed as the key characteristic swarm velocity of the system.; For the air-water only system in the two-dimensional domain, using parabolic models for gas holdup and liquid circulation velocity profiles over the cross section of the column, the {dollar}usb{lcub}h{rcub}{dollar} could be fitted to the experimental data. For the air-water-frother system, the {dollar}usb{lcub}h{rcub}{dollar} could not be fitted to the experimental data which is attributed to the air bubbles adopting a circulatory flow pattern.; In the air-water only system under batch operation, Nicklin's derivation (1962), i.e. {dollar}usb{lcub}g{rcub} = usb0 + Jsb{lcub}g{rcub},{dollar} was supported only under restrictive conditions, namely {dollar}usb{lcub}g{rcub}{dollar} and {dollar}Jsb{lcub}g{rcub}{dollar} must be measured at atmospheric pressure. Considering the local values, the experiments showed that {dollar}usb{lcub}g,loc{rcub}{dollar} was not equal to {dollar}usb0 + Jsb{lcub}g,loc{rcub}.{dollar} In the presence of frothers under batch or countercurrent operation, the experiments showed that Nicklin's derivation was not applicable even if atmospheric values of {dollar}usb{lcub}g{rcub}{dollar} and {dollar}Jsb{lcub}g{rcub}{dollar} were used.