# ENTRAINMENT OF PARTICLES IN THE MECHANOBR LABORATORY FLOTATION MACHINE

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1 Prace Naukowe Instytutu Górnictwa Nr 16 Politechniki :URFáDZVNLHM Nr 16 6WXGLD L DWHULDá\ Nr DQ '5=<\$à\$ Edward HRYCYNA* flotation, mechanical carryover, flotometric equation, separation ENTRAINMENT OF PARTICLES IN THE MECHANOBR LABORATORY FLOTATION MACHINE Entrainment of hydrophilic particles during flotation is usually characterized by a function or parameter related to the recovery of water. In this work another approach for characterizing entrainment of hydrophilic particles was presented. It was adopted from a procedure developed for Hallimond tube micro-flotation and called the flotometry. It relies on performing batch-type mechanical carryover tests in the presence of a frother and different size fractions of various solids for several minutes until there is no more recovery of solids in the froth or a plateau on the recovery versus time curves is reached. This procedure allows elimination of time in the formulas characterizing entrainment of particles. The entrainment tests provided data on the mechanical carryover of each studied material in the form of separation curves (recovery of particles versus their size) having a characteristic point of d 5. The d 5 parameter is the size of particles for which the recovery due to entrainment after a long time of foam collection is 5%. The performed tests with solids of different densities ρ allowed to find an equation which describes the entrainment of the hydrophilic particles in the 2 cm 3 cell of the Mechanobr laboratory flotation machine in the presence of 12.5 mg/dm 3 of α-terpineol as a frother. The equation is: d 5 (ρ /ρ) 1.65 = L, where L is a constant equal to 9±9 (µm), when diameter of particles d is expressed in µm and their density in water ρ in g/cm 3 while ρ is density of water (1 g/cm 3 ). The proposed flotometric equation is useful for characterization and prediction of entrainment of different materials in the 2 cm 3 cell of Mechanobr laboratory flotation machine. INTRODUCTION Mechanical carryover of hydrophilic particles to the concentrate during flotation is harmful since it reduces the quality of the final products ([5] and quoted there papers on entrainment). Literature data on entrainment of hydrophilic particles indicate that entrainment is a complex phenomenon and depends on many parameters including particle size, particle density and the type of flotation cell [4]. 3ROLWHFKQLND :URFáDZVND,QVW\WXW *yuqlfwzd :URFáDZ SO7HDWUDOQ\

2 22 The entrainment in a Mechanobr flotation machine has not been studied extensively, therefore the aim of this paper is to evaluate the mechanical carryover of hydrophilic particles when only one sort of hydrophilic particles is present in the 2 cm 3 flotation cell of the laboratory Mechanobr flotation machine. The applied procedure is similar to that used for Hallimond tubes utilized for micro-scale flotation tests [2] which is called flotometry [1]. EXPERIMENTAL The entrainment tests were carried out in a Mechanobr laboratory flotation machine equipped with a Plexiglas cell shown in Fig. 1. The volume of the cell was 2 cm 3. The height of the cell measured from the bottom to the place of froth formation was 7.5 cm. A sample of a narrow size fraction of a material (either quartz, gypsum or sapropel coal) was placed in the cell, supplemented with distilled water to a level that the froth, created during the flotation test, was not running off the cell. In each test α-terpineol was used as a frother. Its concentration was 12.5 mg/dm 3. No other chemicals were used in the experiments. air Fig. 1. The cell of laboratory Mechanobr flotation machine used in the investigations 5\V 6FKHPDW FHOL IORWDF\MQHM ODERUDWRU\MQHM PDV]\QNL W\SX HFKDQREU X*\WHM Z EDGDQLDFK The mixture of particles, water and α-terpineol was being stirred for 3 s. Next, the air was admitted to the system by opening a valve of the sub-aerating rotor of the flotation machine. The air was dispersed into small bubbles and foam was formed. Its height was about 1 cm. The foam containing particles was collected in a graduated cylinder to measure the volume of water collected with the froth. The recovery of the solids with the froth was determined by separation of water from solids by filtration and drying. The time intervals of collection of the froth were usually 2, 6 and 12 (or 14) minutes.

3 recovery of solids, % Hryc2 23 RESULTS AND DISCUSSION The entrainment of hydrophilic particle in flotation machines depends on the machine and the system subjected to flotation. Typical tests to characterize an entrainment system rely on determination of a relationship between the recovery of the entrainment particles and the recovery of water. A careful analysis of the literature data indicates that there are three basic types of entrainment curves, which are shown schematically in Fig Type 3 3 Type 2 2 Type UHFRYHU\ RI ZDWHU, % Fig. 2. Types of relationships between recovery of water and recovery of entrained hydrophilic particles in mechanical carryover experiments 5\V 7\S\ ]DOH*QRFL SRPLG]\ X]\VNLHP ZRG\ L X]\VNLHP wynoszonych mechanicznie ziaren hydrofilnych The tests carried out in the Mechanobr.2 dm 3 laboratory flotation cell (Fig. 3) showed that there is a non-linear type 1 relationship between water and entrainment particles. In such a case, the entrainment of hydrophilic particles cannot be characterized by a constant (entrainment factor), which is defined as the slope of the entrainment line (type 2 in Fig. 2). For such the case some authors suggest using a function for the entrainment which is dependent on the amount of recovered water [3]. In this paper, we would like to propose another approach to characterize entrainment of particles valid for the case when the entrainment is of type 1. In this approach only the plateau level is taken into account.

4 recovery of solids, % Hryc coal.8-1. mm UHFRYHU\ RI ZDWHU, % Fig. 3. Typical relationship between recovery of water and hydrophilic particles during batch entrainment tests for sapropel coal, quartz, and gypsum in a Mechanobr.2 dm 3 laboratory flotation cell 5\V 7\SRZH ]DOH*QRFL SRPLG]\ X]\VNLHP ZRG\ L K\GURILOQ\FK ]LDUHQ SRGF]DV EDGD Z\QLHVLHQLD PHFKDQLF]QHJR ]LDUHQ ZJOD VDSURSHORZHJR NZDUFX RUD] JLSVX Z ODERUDWRU\MQHM PDV]\QFH IORWDF\MQHM o SRMHPQRFL NRPRU\ GP 3 The results of entrainment tests in the form of recovery of particles versus time of bubbling, carried for gypsum, sapropel coal and quartz are shown in Figs They all are of type 1. Since at the plateau the amount of recovered water does not influences the recovery of particles, time is no longer a useful parameter of the process. Therefore, the recovery of all particles or a class of particles becomes a measure of entrainment. It results from Fig. 4 6 that the entrainment-time curves for all solids and size fractions reach plateau when the flotation time is above about 12 min. The maximum entrainment can be used for plotting another graph relating the maximum recovery of particles as a function of particle size. Such relationships are plotted in Figs. 7, 8 and are known as the separation classification curves. They are S-shaped and can be used for determination of the so-called d 5 parameter, which is the most characteristic point of the separation curve. This is so because a particle having the size equal to d 5 has equal chance to be entrained or to sink. Parameter d 5 can be used for comparison of entrainment of particles of different materials. The values of d 5 for the investigated systems are given in Figs. 7, 8.

5 recovery of solids, % recovery of solids, % Hryc3 Hryc gypsum mm mm mm WLPH RI HQWUDLQPHQW, t, min Fig. 4. Results of entrainment as a function of time of bubbling for gypsum 5\V :\QLNL EDGD Z\QLHVLHQLD PHFKDQLF]QHJR MDNR IXQNFML F]DVX SU]HSXV]F]DQLD SFKHU]\NyZ SoZLHWU]D SU]H] ]DZLHVLQ ]LDUHQ JLSVRZ\FK 6 5 quartz mm mm mm WLPH RI HQWUDLQPHQW, t, min Fig. 5. Results of entrainment as a function of time of bubbling for quartz 5\V :\QLNL EDGD Z\QLHVLHQLD PHFKDQLF]QHJR MDNR IXQNFML F]DVX SU]HSXV]F]DQLD SFKHU]\NyZ SoZLHWU]D SU]H] ]DZLHVLQ ]LDUHQ NZDUFX

6 recovery of solids, % Hryc5 Hryc sapropel coal mm mm mm WLPH RI HQWUDLQPHQW, t, min Fig. 6. Results of entrainment as a function of time of bubbling for sapropel coal 5\V :\QLNL EDGD Z\QLHVLHQLD PHFKDQLF]QHJR MDNR IXQNFML F]DVX SU]HSXV]F]DQLD SFKHU]\NyZ SoZLHWU]D SU]H] ]DZLHVLQ ]LDUHQ ZJOD VDSURSHORZHJR solids recovery after long time of entrainment, % d5 sapropel coal SDUWLFOH VL]H, d, µm particle VL]H G P Fig. 7. Separation entrainment curve for sapropel coal 5\V.U]\ZH VHSDUDFML GOD ZJOD VDSURSHORZHJR

7 Hryc6 Hryc7 27 solids recovery after long time of entrainment, % gypsum d5 4 quartz d SDUWLFOH VL]H, d, µm Fig. 8. Separation entrainment curves for gypsum and quartz Rys. 8. Krzywe separacji dla gipsu i kwarcu 5 density of solids, ρ', g/cm 3 4 d 5 (ρ '/ρ)1.65 = 9±9µ m SDUWLFOH VL]H, d, µm particle VL]H G P Fig. 9. Flotometric equation for entrainment of various materials in the investigated flotation cell ρ sapropel coal = 1.3 g/cm 3, ρ sapropel coal =.3 g/cm 3, d 5, sapropel coal = 72 µm, ρ gypsum = 2.4 g/cm 3, ρ gypsum = 1.4 g/cm 3, d 5, gypsum = 46 µm, ρ quartz = 2.6 g/cm 3, ρ quartz = 1.6 g/cm 3, d 5, quartz = 43 µm, ρ = density of water = 1 g/cm 3 5\V =DOH*QRü IORWRPHWU\F]QD GOD Z\QLHVLHQLD PHFKDQLF]QHJR GOD Uy*Q\FK PDWHULDáyZ VWRVRZDQ\FK GR EDGD FHOL IORWDF\MQHM

8 28 Combining information about d 5 (in µm) and the density ρ of the tested minerals in water (in g/cm 3 ) provide a general equation relating entrainment of particles in the studied.2 dm 3 cell of the Mechanobr laboratory flotation machine: d 5 (ρ /ρ) 1.65 = L = 9±9 µm (1) where L is a constant (in µm) and ρ is the density of water (1 g/cm 3 ). Equation 1 is similar to that derived for the frothless microflotation cells called the Hallimond tubes. It is sometimes called the flotometric equation. On the basis Eq. 1 or its graphical form presented in Fig. 9, it is possible to predict the entrainment of other minerals in the tested flotation equipment. CONCLUSIONS On the basis of the entrainment tests carried out in a 2 cm 3 cell of the laboratory Mechanobr flotation machine it was found that entrainment of hydrophilic particles, which in a batch test have a plateau-type relationship between water and solids, in the presence of 12.5 mg/dm 3 of α-terpineol as a frother, and after prolonged time of froth collection can be described by the equation: d 5 (ρ /ρ) 1.65 = L = 9±9 µm where L is a constant and is equal to 9±9 µm when density of a particle in water (ρ = ρ particle ρ) is given in g/cm 3, density of water in g/cm 3, and particle size d 5 in micrometers. The proposed equation can be used for characterization and prediction of mechanical entrainment of hydrophilic solids in the laboratory Mechanobr flotation machine equipped with a.2 dm 3 flotation cell. REFERENCES [1] '5=<\$à\$ - /(.., - Flotometry-another way of characterizing flotation, J. Colloid Interface Sci., 13, 1989, [2] '5=<\$à\$ - Characterization of materials by Hallimond tube flotation, Part 1: maximum size of entrained particles, Int. J. Miner. Process., 42, 1994, [3] KIRJAVAINEN V.M., Review and analysis of factors controlling the mechanical flotation minerals, Int. J. Miner. Process., 46, 1996, [4] SAVASSI O.N., ALEXANDER D.J., FRANZIDIS J.P., MANLAPIG E.V., An empirical model for entrainment in industrial flotation plants, Minerals Engineering, Vol. 11, No. 3, 1998, [5] WARREN L.J., Determination of the contributions of true flotation and entrainment in batch flotation tests, Int. J. Miner. Process., 14, 1985,

9 29 WYNIESIENIE MECHANICZNE ZIAREN HYDROFILNYCH W LABORATORYJNEJ MASZYNCE FLOTACYJNEJ TYPU MECHANOBR Wyniesienie mechaniczne ziaren hydrofilnych w czasie flotacji ziaren hydrofobowych jest zwykle FKDUDNWHU\]RZDQH ]D SRPRF IXQNFML OXE SDUDPHWUX RGQLHVLRQHJR GR LORFL RG]\VNDQHM ] SLDQ ZRG\ W WHM SUDF\ RSLVDQR LQQH SRGHMFLH GR FKDUDNWHU\]RZDQLD Z\QLHVLHQLD PHFKDQLF]QHJR ]LDUHQ K\GURILl- Q\FK=DDGRSWRZDQR SURFHGXU ]ZDQ IORWRPHWUL VWRVRZDQ SU]\ RSLVLH Z\QLHVLHQLD PHFKDQLF]QHJR ziaren w mikroforwrzqlnx +DOOLPRQGD3ROHJDáD RQD QD SU]HSURZDG]HQLX SRPLDUyZ Z\QLHVLHQLD PHFKa- QLF]QHJR ]LDUHQ Z REHFQRFL VSLHQLDF]D GOD Uy*Q\FK NODV ]LDUQRZ\FK Uy*Q\FK VXEVWDQFML WDN GáXJR D* X]\VN ]LDUHQ RVLJD SODWHDX3URFHGXUD WD SR]ZDODáD QD Z\HOLPLQRZDQLH F]DVX Z UyZQDQLDFK QD Z\QLe- VLHQLH PHFKDQLF]QH ]LDUHQ3U]HSURZDG]RQH EDGDQLD Z\QLHVLHQLD PHFKDQLF]QHJR GRVWDUF]\á\ GDQ\FK o Z\QLHVLHQLX PHFKDQLF]Q\P EDGDQ\FK PDWHULDáyZ Z SRVWDFL NU]\ZHM UR]G]LDáX WMX]\VNX MDNR IXQNFML ZLHONRFL ]LDUHQ SRVLDGDMFHM FKDUDNWHU\VW\F]Q\ SXQNW d 5. Parametr d 5 odpowiada rozmiarowi ziarna, GOD NWyUHJR X]\VN SRZRGRZDQ\ Z\QLHVLHQLHP PHFKDQLF]Q\P SR GáXJLP F]DVLH SU]HSXV]F]DQLD SFKe- U]\NyZ SU]H] IORWRZQLN Z\QRVL 3U]HSURZDG]RQH WHVW\ ] VXEVWDQFMDPL R Uy*QHM JVWRFL SR]ZROLá\ na wyprowadzenie równania, które opisuje wyniesienie mechaniczne ziaren hydrofilowych w laborato- U\MQHM PDV]\QFH IORWDF\MQHM W\SX HFKDQREU R SRMHPQRFL NRPRU\ IORWDF\MQHM FP 3 Z REHFQRFL 12,5 mg/dm 3 α-terpineolu jako spieniacza. Uzyskano równanie: d 5 (ρ /ρ ) 1,65 = L, gdzie L MHVW VWDá Zy- QRV]F ±9 µm, d 5 jest charakterystycznym rozmiarem ziaren, ρ MHJR JVWRFL Z ZRG]LH ]D ρ ±JVWRFL ZRG\ Z\QoV]F g/cm 3. 5HFHQ]HQW SURI GU KDE LQ* -DGZLJD :LFNRZVND 3ROLWHFKQLND :URFáDZVND

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