A Preliminary Investigation into Separating Performance and ... - MDPI

minerals Article

A Preliminary Investigation into Separating Performance and Magnetic Field Characteristic Analysis Based on a Novel Matrix Wenbo Li

ID

, Yuexin Han *, Ruiqing Xu and Enpu Gong

School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China; [email protected] (W.L.); [email protected] (R.X.); [email protected] (E.G.) * Correspondence: [email protected]; Tel.: +86-024-8368-0162 Received: 1 January 2018; Accepted: 26 February 2018; Published: 2 March 2018

Abstract: The matrix is the agglomeration carrier of magnetic mineral particles in high-gradient magnetic separation (HGMS). Its structural parameters have a great influence on the distribution of the magnetic field in the separation space, and therefore affect the separation effect. This paper introduces a novel matrix called a screw thread rod matrix, which has the dual advantages of the rod matrix and the grooved magnetic plate, i.e., the advantages of better slurry fluidity through the matrix and higher magnetic field gradient at the sharp corners. This research on the novel matrix was performed from the following three aspects: the description of components of the matrix, the effect of structural parameters of the matrix on separation performance of fine hematite ore tailings in Northeast China, and the numerical analysis of the magnetic induction properties of different kinds of magnetic matrices based on three-dimensional structural characteristics. Compared with the smooth rod matrix, the proposed screw thread rod matrix enhances the inhomogeneity of the axial magnetic induction intensity on the surface of the matrix. Accordingly, the recovery of fine-grained iron minerals is improved through the resulting combined effect of the radial curvature of the rod and the inhomogeneous magnetic field in the axial direction. Furthermore, the best moderate distance between equidistant ring-shaped bulges (ERB) as well as the best column gap between adjacent rod elements were determined, respectively. Keywords: horizontal magnetic field orientation; a novel matrix; high gradient magnetic separation; weakly magnetic particles; hematite

1. Introduction The High-gradient magnetic separation (HGMS) technique is widely used in industrial fields including the sufficient recovery of weakly magnetic iron mineral, kaolin clay beneficiation, water treatment, coal desulfurization, and catalytic processes, etc. [1–5]. It has become a powerful approach, especially in the manipulation of micro-fine weakly magnetic mineral particles. Due to the high gradient around the matrix in the presence of a strong magnetic field, the magnetic attraction imposed on weakly magnetic mineral particles is far greater than the counter-acting force from swift-flowing pulp [6]. When mineral grains that present weak magnetic or antiferromagnetic responses are close to the surface of magnetized rod matrices, the magnetic driving force will increase sufficiently to enable magnetic particles to be captured from a carrier fluid [7]. Therefore, both how to improve the capture efficiency of feebly magnetic mineral granules and how to enhance the magnetic force being imposed on the weakly magnetic mineral particles become the key focuses of high gradient magnetic separation in the processing of iron ore. Equation (1) gives the expression of magnetic force which acts on the magnetizable mineral particle in the swift-flowing pulp [8]. B is the magnitude of magnetic induction intensity at a particle Minerals 2018, 8, 94; doi:10.3390/min8030094

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location, ∇B is the magnitude of the gradient, κ p and κ f are the volume magnetic susceptibilities of particle and fluid (water), separately, Vp is the magnetizable particle volume, and µ0 is the magnetic permeability of vacuum. → 1 Fm = (κ p − κ f )Vp B∇ B (1) µ0 As shown in Equation (1), there are various ways to achieve the desired beneficiation effect in the process of high gradient magnetic separation, such as intensifying magnetic induction intensity, improving magnetic field gradient, and strengthening the induction of hydrophobic flocculation of extremely fine weakly magnetic mineral particles to form flocculation [9–12]. The first two ways are more closely related to magnetic field distribution of separation space and the latter one may be accomplished by changing the surface hydrophilic property of feebly magnetic minerals under the action of surfactants. Some basic research can be found on selective hydrophobic or magnetic flocculation [13–17]. However, complex procedures of forming suitable floccules make it difficult to hold steady running in the production of mineral processing. Moreover, flocculation agents may adversely affect the subsequent reverse flotation effect and the quality of the treated water in the concentrator. Therefore, more attention has been paid to the optimization of the distribution of magnetic field by means of putting matrices into a uniform background magnetic field. Since the saturation magnetization of iron-based material is between 2 T and 2.5 T, the conventional HGMS magnetic circuit using the material as iron yoke can hardly generate a background magnetic field of 2 T or more in the sorting space [6,18,19]. Therefore, a larger magnetic force can hardly be generated by improving background magnetic field intensity without superconducting magnetic circuits [20–22]. However, the world’s iron ore reserves are huge and the prices are far below those of precious metals such as gold. It is unacceptable to use superconducting magnetic separation in the preparation of fine hematite concentrate in iron ore concentrators under the current tech-economic conditions [23–25]. Generally, the separation space is filled with a lot of matrix rod elements as secondary poles in ordered arrangement [26]. To improve the recovery effect of magnetic minerals, the method of adjusting the matrix is not only economically reasonable but also environmentally friendly. Thus, it is a good alternative to add a magnetic field gradient followed by enlargement of the magnetic force by adjusting magnetic field distribution around the matrix. This work focuses on the effect of the matrix parameters on the separation results for micro-fine hematite particles. The magnetic flux density distribution character of a novel matrix was investigated and is discussed in great detail. The major contributions of this paper are as follows: First, the way to enhance the recovery of fine-grained iron ore by changing the structure of the medium was put forward. Second, a new type of matrix was designed and the optimum structural parameters for the separation determined. Finally, the recovery of the iron tailings from Dong’anshan was shown to be improved. 2. Experimental 2.1. The Screw Thread Rod Matrix As Figure 1 shows, the screw thread rod matrix is composed of many screw thread stainless steel rods in an oriented arrangement. Apart from possessing the advantage of the conventional rod matrix, the design of the screw thread generates an axial magnetic gradient along the rod, strengthening the inhomogeneity of the induced magnetic field around the matrix. The screw thread stainless steel rod, as the basic unit of the new type of matrix, consists of a cylinder and lots of equidistant ring-shaped bulges (ERB). The material of the matrix rod is stainless steel (SUS430) with high permeability. The stainless steel (SUS304) is used for the punched-plates fixing rod-group. Rods are welded with double punched-plates into a single system on an interlaced arrangement of adjoining rows. The influence of the rod diameter has drawn much attention from global researchers. Beneficial results can be found in former research works [27–30]. Hence, this paper did not dig deeply into the effect of rod diameter.

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researchers. Beneficial results can be found in former research works [27–30]. Hence, this paper did not dig deeply into the effect of rod diameter. Stainless steel rod with 3 mm diameter has been Stainless steelinrod with 3 mm diameter has been widely in processing of refractory hematite widely used processing of refractory hematite ore [19].used In view of the above-mentioned facts, 3 ore [19]. In view of the above-mentioned facts, 3 mm fixed rod diameter was used in this study. mm fixed rod diameter was used in this study.

Figure 1. The screw thread rod matrix. Figure 1. The screw thread rod matrix.

2.2. A Horizontal Magnetic Field Orientation HGMS Separator and Its Principle 2.2. A Horizontal Magnetic Field Orientation HGMS Separator and Its Principle A pilot pulsating HGMS separator was used to conduct the physical testing on different matrix A pilot pulsating separator used toconfiguration conduct the physical testing on matrix parameters, as shownHGMS in Figure 2. Thewas C-dipole was employed in different the equipment parameters, as shown in Figure 2. The C-dipole configuration was employed in the equipment which consists of a combination of ferrite yoke, magnetic poles, exiting coils, separating which zone, consists of a combination of ferrite yoke, magnetic poles, exiting coils, separating zone, matrix, tailings matrix, tailings jig, and a drive motor. The major difference from the typical mode of a cyclic jig, and a drive HGMS motor. The major from flow the typical modeofofthe a cyclic KolmMarston HGMS KolmMarston system is difference that the pulp direction horizontal magnetic field system is that the pulp flow direction of the horizontal magnetic field orientation HGMS separator is orientation HGMS separator is perpendicular to the magnetic force line in the air gap between the perpendicular the magnetic force in the air gap between the magnetic [18]. In addition, magnetic polesto[18]. In addition, theline magnetic particles aggregation regionspoles on the surface of the the magnetic particles aggregation regions on the surface of the matrix rod in the horizontal magnetic matrix rod in the horizontal magnetic field are located on both sides of the rod along the force lines field are located on both sides of the rod along the force lines of a magnetic field rather than along the of a magnetic field rather than along the direction of the flowing pulp. direction of the flowing pulp. When a direct current to the excitation coil is applied, a strong magnetic field is generated in the When a direct current to theelectromagnet excitation coilwith is applied, a strongconfiguration. magnetic fieldThe is generated in the working gap by the iron-core the C-dipole high magnetic working gap byisthe iron-core withof thethe C-dipole configuration. magnetic field field gradient enhanced inelectromagnet the close vicinity rod matrix. Slurry is The fed high into the separation gradient is enhanced in the close vicinity of the rod matrix. Slurry is fed into the separation chamber chamber evenly through the feed box. The magnetic particles are attracted onto the surface of the evenly through feed The magnetic are attracted onto surface of tailings the magnetic magnetic matrixthe due to box. the high magnetic particles force produced around thethe matrix. The jig is matrix dueadjusted to the high around the matrix. tailings is normally normally formagnetic a higher force pulseproduced frequency and lower stroke.The The fluid jig power reducesadjusted to only for a higher pulseweak frequency and lower stroke. fluid powerparticles reduces to to only allow extremely weak allow extremely magnetic particles andThe non-magnetic be washed away from the magnetic particles and non-magnetic particles to be washed away from the matrix. The washed-away matrix. The washed-away material passes through the matrix into the tailings discharge launder. material passes through particles the matrix into the tailings discharge TheHGMS stronger magneticwhen particles The stronger magnetic are collected by the matrix. launder. A cycle of is finished the are collected by the matrix. A cycle of HGMS is finished when the tailing pulp flowing in the tailings tailing pulp flowing in the tailings collecting barrel is replaced by water. The tailings collecting collecting by water.the Theformer tailingsconcentrate collecting barrel will then beAfter settled replacing the barrel willbarrel then is bereplaced settled replacing collecting barrel. that, the direct former concentrate collecting barrel. After that, the direct current is shut off and the magnetic force is current is shut off and the magnetic force is gradually reduced until sufficiently weak. The flushing gradually reduced until sufficiently weak. The flushing water washes away the magnetic particles water washes away the magnetic particles from the magnetic matrix assembly compartment into the


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from the magnetic matrix assembly compartment into the concentrate collecting barrel. effectively concentrate collecting barrel. This effectively separates the feed into two products withThis different iron separates the feed into two products with different iron contents. contents.

Figure 2. The structure schematic drawing of the cyclic horizontal magnetic field orientation Figure 2. The structure schematic drawing of the cyclic horizontal magnetic field orientation high-gradient magnetic separation (HGMS) separator. high-gradient magnetic separation (HGMS) separator.

2.3. Sample 2.3. Sample The fine hematite ore tailings used in this investigation were taken from Dong Anshan The fine hematite ore tailings used in this investigation were taken from Dong Anshan beneficiation plant in Liaoning province, China. The sample has an iron grade of 14.30%, and beneficiation plant in Liaoning province, China. The sample has an iron grade of 14.30%, and consists consists of iron-bearing minerals, large amounts of quartz, and other silicate minerals. The of iron-bearing minerals, large amounts of quartz, and other silicate minerals. The iron-bearing iron-bearing minerals are mainly composed of hematite and siderite in the ratio of 8:1. The magnetic minerals are mainly composed of hematite and siderite in the ratio of 8:1. The magnetic iron content in iron content in the sample is very low due to former treatment by high intensity magnetic separation the sample is very low due to former treatment by high intensity magnetic separation in the mineral in the mineral processing production. The −43 μm size fraction accounts for 75.26% of the overall processing production. The −43 µm size fraction accounts for 75.26% of the overall particle size particle size fractions. However, the iron content of the −43 μm size fraction accounted for 95.08% of fractions. However, the iron content of the −43 µm size fraction accounted for 95.08% of the total iron the total iron in the material. in the material. 2.4. The Procedures and and Conditions Conditions 2.4. The Physical Physical Testing Testing Procedures The specified specified matrix matrix is is put put into into the the separating separating chamber chamber and then the the separating separating zone filled The and then zone is is filled with flowing water. The material and running water are mixed together with a mass ratio of 4:1 in aa with flowing water. The material and running water are mixed together with a mass ratio of 4:1 in stirred tank for 10 min before each unit experiment. After completion of setting the exciting current stirred tank for 10 min before each unit experiment. After completion of setting the exciting current producing magnetic magnetic field, the feed feed stream stream containing containing weak magnetic minerals slurry producing field, the weak magnetic minerals in in the the form form of of slurry is evenly poured into the separating zone within 15 s. It is worth mentioning that the matrix should is evenly poured into the separating zone within 15 s. It is worth mentioning that the matrix should be entirely entirely submerged submerged in in the the flowing flowing water water during during the the whole whole high high gradient gradient magnetic magnetic separation separation so so be that the pulsating energy coming from the reciprocate motion of the tailings jig can be transmitted to that the pulsating energy coming from the reciprocate motion of the tailings jig can be transmitted to the separating zone [27]. The magnetic particles in this feed stream are captured on the surface of the the separating zone [27]. The magnetic particles in this feed stream are captured on the surface of the magnetized matrix while the the non-magnetic non-magnetic particles particles follow flowing slurry slurry into into the the tailings tailings magnetized matrix rods, rods, while follow the the flowing collecting barrel. Finally, the intensity of the magnetic field is reduced to zero and the magnetic collecting barrel. Finally, the intensity of the magnetic field is reduced to zero and the magnetic particles particles easilyfrom washed from the matrix by the separate flushing water. Based onprocedures, the above are easilyare washed the matrix by the separate flushing water. Based on the above procedures, of the following main structuralofparameters of screw thread rod investigated: matrix were the effects ofthe theeffects following main structural parameters screw thread rod matrix were investigated: (1) the distance parameter between ERB on the surface of the screw thread rod; (2)gap the (1) the distance parameter between ERB on the surface of the screw thread rod; (2) the column column gap parameter between adjacent rod elements on the separation performance of HGMS in parameter between adjacent rod elements on the separation performance of HGMS in retrieving fine retrieving fine hematite. The optimal operating parameters of HGMS were appropriately determined beforehand and are listed in Table 1.


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hematite. The optimal operating parameters of HGMS were appropriately determined beforehand and are listed in Table 1. Table 1. Experimental conditions. Type of Parameters

Numerical Values

Magnetic field intensity (T) Feed solid density (%) Flowing speed of slurry (cm/s) Output size (mm) Pulsating stroke (mm) Pulsating frequency (Hz) Distance between ERB (mm) Column gap in matrix (mm)

0.8 20 4.39 10 11.4 30 p = 0, 0.5, 1.0, 1.5, 2.0 d = 2, 3, 4, 5

2.5. Evaluation Methods of Separation Performance The separation performance was closely related to the iron concentrate grade, the iron recovery, and the separation efficiency. Iron recovery (ε) and separation efficiency (η) were calculated according to Equations (2) and (3), respectively: β·(α − θ) (2) ε= α·(β − θ) η = ε·

βm ·(β − α) β·(βm − α)

(3)

where α is the feed grade, β is the concentrate grade, and βm is the maximum Fe grade of hematite (70% Fe in Fe2 O3 ). 3. Results and Discussion 3.1. Influence of the Distance between ERB on Separation Performance According to the principle of magnetism, the appearance of magnetized metal wire has a great impact on the surrounding magnetic field distribution as well as on the capture of fine-grained weakly magnetic iron minerals [30,31]. The presence of the screw thread plays a positive role in the convergence of the magnetic field lines on the surface of the matrix. Therefore, the influence of distance between ERB (p value) on the separation performance of fine hematite tailings from the Dong Anshan beneficiation plant was analyzed especially under the conditions of different column gaps of 2 mm, 3 mm, 4 mm, and 5 mm, respectively. As illustrated in Figure 3, for a matrix diameter of 3.0 mm at a column gap of 2 mm, the separation efficiencies with p values of 0 mm, 0.5 mm, 1.0 mm, 1.5 mm, 2.0 mm are 38.53%, 41.84%, 39.44%, 39.20%, 38.11%, respectively. The separation efficiency increases first and then decreases at a p value greater than 0.5 mm, indicating the optimum p value is 0.5 mm. With the increase of distance between ERB (p value) from 0 mm to 2.0 mm, the trends of separation performance for different column gaps (d value) are similar. Obviously, regardless of the column gap between adjacent rod elements, the separation efficiency and iron recovery of the screw thread rod (p = 0.5 mm) are better than those of the smooth matrix rod (p = 0 mm) with 3% increase in the recoveries. Notably, the iron grade did not decline with the increase of recovery, but increased by one percent or more. Without exception, this regularity is ubiquitous for the column gap at 2 mm, 3 mm, 4 mm, and 5 mm in Figure 3. It can be found that the distance between ERB (p value) is an important variable when determining the iron recovery and the separation efficiency of the magnetic product. The reason for this phenomenon is that, due to the presence of helical protrusions, the magnetic field distribution on the surface of the rod changes significantly, which further enhances the rod’s ability to capture the magnetic particles [32]. For a better explanation of this effect, a detailed description is now made with subsequent numerical simulations.

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Figure 3. Influence Influence of of distance distance between between equidistant equidistant ring-shaped ring-shaped bulges bulges (ERB) (ERB) (p (p value) value) on on the separation performance. The matrix diameter is 3 mm, background magnetic induction is 0.8 separation performance. The matrix diameter is 3 mm, background magnetic induction is T, 0.8the T, fluid velocity is 0.05 m/s,m/s, the length of stroke is 11.4 mm,mm, and and the frequency of pulsation is 30isHz. (a) the fluid velocity is 0.05 the length of stroke is 11.4 the frequency of pulsation 30 Hz. Column gapgap d =d2=mm; (b)(b) Column gap d =d = 3 3mm; (a) Column 2 mm; Column gap mm;(c)(c)Column Columngap gapdd==44 mm; mm; (d) (d) Column Column gap gap d == 55 mm. mm.

3.2. Performance 3.2. Influence Influence of of Column Column Gap Gap between between Adjacent Adjacent Rod Rod Elements Elements on on the the Separation Separation Performance When thematrix matrixfibers fibers randomly deployed, the capture efficiency (recovery) of the When the areare randomly deployed, the capture efficiency (recovery) of the separator separator is considerably Therefore, ordered arrangement rod units becomes is considerably weakened. weakened. Therefore, the orderedthe arrangement of rod units of becomes common law common law for wet high-intensity magnetic separation [33]. The influences of rod diameter, rod for wet high-intensity magnetic separation [33]. The influences of rod diameter, rod gap and filling gap filling rate on the separating effect have beenby investigated a previouswork meaningful rate and on the separating effect have been investigated a previousby meaningful [28,30].work The [28,30]. The gaps the matrix consist of the row and the column gap.gap Theaffects row gap gaps between thebetween matrix rods consistrods of the row gap and thegap column gap. The row the affects the layers of the matrix bed when the depth of the matrix is fixed, which in turn determines layers of the matrix bed when the depth of the matrix is fixed, which in turn determines the collision the collisionofprobability of magnetic with matrix elements [6]. The column affects probability magnetic particles withparticles matrix elements [6]. The column gap affects the gap intensity of the the intensity theinmagnetic fieldofinthe themagnetic directionfield of the magnetic field lines, the which determines the magnetic of field the direction lines, which determines degree of magnetic degree of in magnetic in the catch area. Whenmatrix the distance between matrix rods in the induction the catchinduction area. When the distance between rods in the direction of the magnetic direction of the magnetic the in filling rate of the matrix in thelarger. sortingAccordingly, space becomes field is smaller, the fillingfield rate is ofsmaller, the matrix the sorting space becomes the larger. Accordingly, the magnetic induction intensity on the surface of the rod will be higher. In the magnetic induction intensity on the surface of the rod will be higher. In the case of the same matrix case of the same rodgap diameter, theadjacent columnrod gapelements between has adjacent rod elements greater rod diameter, thematrix column between a greater effect onhas the amaterial effect on the material separating characteristics in field. the horizontal field. discussed The effects are separating characteristics in the horizontal magnetic The effectsmagnetic are separately under separately discussed under the conditions of different distances between ERB (p = 0, 0.5 mm, 1.0 mm, the conditions of different distances between ERB (p = 0, 0.5 mm, 1.0 mm, 1.5 mm, 2.0 mm). 1.5 mm, mm). to note from Figure 4 that the trends of separation efficiency with the increase of It is2.0 interesting It isgap interesting note from Figure 4 that the trends of separation with theAs increase of column (d value)tounder the condition of different distance betweenefficiency ERB are similar. is shown column gap (d value) under the condition of different distance between ERB are similar. As is shown in Figure 4a, for the smooth matrix rod (p = 0 mm), the iron recovery and the grade decrease with the in Figureof 4a,the ford the smooth matrix (p is = 02 mm), the iron recovery and the grade decrease with the increase value. When the d rod value mm, iron recovery is 49.21% and the grade is 38.11% of increase of the d value. When the d value is 2 mm, iron recovery is 49.21% and the grade is 38.11% of magnetic product. For the screw thread rod (p = 0.5 mm), the best separation effect corresponds to a d magnetic rod (p = 0.5 mm), theofbest separation to a d value of 2product. mm withFor an the ironscrew gradethread of 39.24% and a recovery 52.94%. At theeffect same corresponds time, the recovery value ofgrade 2 mmofwith an iron grade ofas39.24% and agap recovery of in 52.94%. time,three the and the iron decrease notably the column increases FigureAt 4b.the Forsame the other recovery and the grade of iron decrease notably as the column gap increases in Figure 4b. For the screw thread rods (p = 1.0 mm, p = 1.5 mm and p = 2.0 mm) in Figure 4c–e, the results at d = 2 mm and other three screw rods similar. (p = 1.0 However, mm, p = 1.5 mmthe and p = 2.0increases mm) in Figure 4c–e, at d = 3 mm are foundthread to be very when d value to 4 mm or 5 the mm,results the iron drecovery = 2 mm is and d = smaller 3 mm are found to be very However, when theall, d value increases to 4 mm or even than the index of d =similar. 2 mm or d = 3 mm. Above no matter whether for the 5screw mm, thread the iron recovery is even smaller than the index of d = 2 mm or d = 3 mm. Above all, no matter rods or for the smooth matrix rods, the smaller column gap gives a better recovery effect whether forofthe screw thread rods orThe for interaction the smoothbetween matrix the rods, the smaller columnthe gapmagnetic gives a in the case no clogging of matrices. matrix units enhances better recovery effect in the case of no clogging of matrices. The interaction between the matrix field distribution in the separating zone, which explains why the selection effect is improved. units enhances the magnetic field distribution in the separating zone, which explains why the selection effect is improved.


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Figure Influence of ofcolumn columngap gapbetween betweenadjacent adjacent rod elements separation performance. Figure 4. Influence rod elements on on the the separation performance. The The matrix radius is 3 mm, background magnetic induction is the 0.8 T, thevelocity fluid velocity is 0.05the m/s, the matrix radius is 3 mm, background magnetic induction is 0.8 T, fluid is 0.05 m/s, length length of stroke is 11.4 mm, and the frequency of pulsation is 30 Hz. (a) Distance between ERB of stroke is 11.4 mm, and the frequency of pulsation is 30 Hz. (a) Distance between ERB p = 0 mm. p(b) = 0Distance mm. (b)between DistanceERB between ERB p =(c) 0.5Distance mm. (c) between Distance ERB between ERB p = (d) 1.0 Distance mm. (d) Distance p = 0.5 mm. p = 1.0 mm. between between ERBmm. p = 1.5 mm. (e) Distance ERBmm. p = 2.0 mm. ERB p = 1.5 (e) Distance between between ERB p = 2.0

4. 4. Numerical Numerical Analysis Analysis of of Magnetic Magnetic Field Field Distribution Distribution Based Based on on Matrix Matrix Parameters Parameters Apparently, is significant significantto toexamine examinethe theeffect effectofofparameters parametersofof the screw thread matrix Apparently, itit is the screw thread rodrod matrix on on the static spatial magnetic field for the investigation and analysis of the improvement of the static spatial magnetic field for the investigation and analysis of the improvement of separation separation performance. However, there are someindifficulties in measurement the accurate measurement offield the performance. However, there are some difficulties the accurate of the magnetic magnetic field distribution by adopting numerical type Gauss account (i.e., Hall effect) due to the distribution by adopting numerical type Gauss account (i.e., Hall effect) due to the narrow spaces narrow inside a matrix. So far, the finite element hasextensively been used extensively solve inside aspaces matrix. So far, the finite element method has method been used to solve all to sorts of all sorts of problems of electromagnetic field governed by partial differential equations [34,35]. In problems of electromagnetic field governed by partial differential equations [34,35]. In this work, the this work, the available commercially available tool ofmethod finite element (FEM), Ansoft Maxwell commercially analysis tool ofanalysis finite element (FEM),method Ansoft Maxwell 3D was used to 3D was usedthe to understand the effects of different matrices field on the magnetic field distribution. In this understand effects of different matrices on the magnetic distribution. In this way, the physical way, the physical testing workloads and material costs will be reduced significantly. testing workloads and material costs will be reduced significantly.

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4.1. Establishment and Optimization of the Simulation Model 4.1. Establishment and Optimization of the Simulation Model It is worth noting that three-dimensional magnetic field distribution of the actual matrix is so It is worth thatcan three-dimensional magnetic field distribution actualbut matrix so of thework complex that it noting not only bring about a significant amount of calculation it is isalso complex that it not only can bring about a significant amount of calculation work but it is also difficult complex that it not only can bring about a significant amount of calculation work but it is also difficult for post-processing due to the cylindrical spiral. Therefore, the actual model was simplified for post-processing to thedue cylindrical spiral. Therefore, the actual model wasmodel simplified in that difficult for post-processing tobulges the cylindrical spiral. Therefore, the actual was simplified in that the helical due saw-toothed on the surface of the matrix rod were adjusted to the be helical saw-toothed bulges on the surface of the matrix rod were adjusted to be perpendicular to the in that the helical saw-toothed bulges on the surface of the matrix rod were adjusted be perpendicular to the rod axis according to the theory of geometric similarity. A sample model of the rod axis according to the theory of geometric similarity. A sample model of the novel matrix rod is perpendicular to the rod axis according to the theory of geometric similarity. A sample model of the novel matrix rod is shown in Figure 5. The C-dipole configuration model was built and each shown in Figure The C-dipole configuration wasconfiguration built and each component of the magnet novel matrix is shown in Figure 5. The model C-dipole model was source built and each component of rod the5.magnet assembly is indicated, as shown in Figure 6. The current acts as a assembly is indicated, as shown in Figure 6. The current source acts as a source of excitation for thea component of the magnet assembly is indicated, as shown in Figure 6. The current source acts as source of excitation for the three-dimensional magnetic field. The materials of the model three-dimensional magnetic field. The materials of the model components are listed in Table 2. source of excitation forTable the 2.three-dimensional magnetic field. The materials of the model components are listed in components are listed in Table 2.

Figure 5. Schematic of the thread matrix rod. Figure 5. Schematic of the thread matrix rod. Figure 5. Schematic of the thread matrix rod.

Figure 6. Simulation model of the magnetic system. Figure 6. Simulation model of the magnetic system. Figure 6. Simulation model of the magnetic system. Table 2. Material of the physical model. Table 2. Material of the physical model. Table 2. Material of the physical model. Type of Parameters Description

Type ofofParameters Material ferrite yoke Material of ferrite yoke Material of exiting coils Material of ferrite yoke Material of exiting coils Material magnetic Material of of exiting coils pole Material of magnetic Material of magnetic pole pole Material of matrix Material of matrix Material of matrix Separating zone Separating zone Separating zone Gap between magnetic Gap between magnetic polespoles (mm)(mm) Gap between magnetic poles (mm) Number of turns in the excitation coil Number of turns in the excitation coil Magnetizing current (A) Number of turns in the excitation Magnetizing current (A) coil Background magnetic induction (Tesla) Magnetizing current (A) (Tesla) Background magnetic induction Background magnetic induction (Tesla) Type of Parameters

Description Low carbon steel (Q235) Description Low carbon steel (Q235) Copper Low carbon steel (Q235) Copper Low carbon steel (Q235) Copper Low carbon steel (Q235) Low carbon steel (Q235) Stainless steel (SUS430) Stainless steel (SUS430) Stainless steel (SUS430) Vacuum Vacuum Vacuum 80 80 80300 300 87 300 870.8 87 0.8 0.8


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4.2. Governing Equations Since the high gradient magnetic field around the matrix is a static magnetic field generated from a direct current electromagnet, a DC current solver in Maxwell 3D was employed to compute the magnetic field strength (H) and magnetic flux density (B). The three-dimensional static magnetic field was calculated by the edge method. According to Ampere’s law and the Gaussian flux law, Maxwell’s equations can be simplified into the following equations.

∇ × H ( x, y, z) = J ( x, y, z)

(4)

∇ × B( x, y, z) = 0

(5)

where B (x, y, z) is the magnetic flux density, H (x, y, z) is the magnetic field intensity, and J (x, y, z) is the current density. These three vectors are the functions of the vector of each direction, out of which B (x, y, z) can be expressed as → → → B( x, y, z) = Bx · x + By · y + Bz · z (6) where Bx, By, and Bz are the scalar magnetic induction intensities in the three directions, respectively. 4.3. Mesh Generation and Defined Parameters for the Solution Process The mesh size varies in each of the simulations depending on the model structure. In most of our simulations, the grid meshing was carried out by using the adaptive meshing function, and the meshing unit was tetrahedron. Considering the high precision of the thread structure of the magnetic adsorption, manual mesh was used to increase the mesh density for the local range of the thread structure by Loop encryption grid operation. About 100,000 tetrahedrons were used when employing an outer solution in each model mesh. The average time consumed to obtain a solution of 100,000 tetrahedrons was about 6–8 h on a Pentium 4 CPU personal computer. The maximum convergence step required for solving the calculation was set to 20, and the convergence error was set as 0.15%. Default natural boundary conditions were adopted in Maxwell 3D. 4.4. Numerical Test Results Considering the structural similarity and variability of the screw thread rod matrix and the smooth rod matrix, the simulation results were further processed along the axial and radial directions of the geometry structure to obtain the analysis results. The results in Figure 7 show that the change of the matrix unit structure has a great influence on the magnetic field distribution on the matrix surface, which then affects the recovery effect of the fine-grained iron minerals. Due to the near-equal matrix overall size, the distribution of different color clouds has a similar range of action. However, the convexity of the matrix surface arrangement causes a sharp increase of the magnetic flux density at the sharp corners. As a result, the difference between the magnetic flux density inside the iron-based material and the periphery of the matrix is widened, which in turn strengthens the magnetic field gradient at the matrix rod surface. To view the data of magnetic parameters, the specified paths are set in Figure 8. This regularity is known from the data of magnetic flux density and magnetic field gradient along the specified path in Figure 9. It can be observed that both the magnetic field induction and the magnetic field gradient along path 1, path 2, path 3, and path 4 tend to decrease as it moves away from the rod. However, the decline rates are different for the four curves in Figure 9a,b. The product of the magnetic field strength and the magnetic field gradient (B·gradB) is the key factor of the magnetic attraction on the mineral particle [8]. Figure 9c shows the variation of the product (B·gradB) with increasing distance away from the matrix rod surface. The curves of the magnetic field gradient (gradB) and that of the product (B·gradB) are similar, which indicates that the effect of the magnetic field gradient is much larger than that of the magnetic field strength. In addition, within a distance of 0.8 mm from the matrix rod, the product of the magnetic field strength and the magnetic field gradient, both along path 1 and path 2, is greater than the corresponding value of the smooth rod matrix. Thus,


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it follows the fact that magnetic force exerted by the screw thread rod matrix on the surrounding corresponding value of the smooth rod matrix. Thus, it follows the fact that magnetic force exerted magnetic particles is more prominent. by the screw thread rod matrix on the surrounding magnetic particles is more prominent.

Figure 7. The cloud chart of magnetic induction intensity distribution in the axial and radial

Figure 7. The cloud chart of magnetic induction intensity distribution in the axial and radial directions. directions. (a) The smooth rod matrix with a diameter of 3 mm. (b) The screw thread rod matrix. (c) (a) The matrixwith witha adiameter diameter of 3mm. mm. (b) The screw thread rod matrix. (c) The smooth Thesmooth smooth rod rod matrix of 3.5 rod matrix with a diameter of 3.5 mm. The role of screw threads on the surface of the matrix rod has been described in previous sorting and magnetic field the rod effect ofbeen distance between ERB on the The roletests of screw threads on theanalysis. surface However, of the matrix has described in previous sorting magnetic induction distribution of the surface of screw thread rod plays an important role in tests and magnetic field analysis. However, the effect of distance between ERB on the magnetic explaining the beneficiation results. As can be seen from Figure 10, when the distance between ERB induction distribution of the surface of screw thread rod plays an important role in explaining the increases, the red area of cloud picture at the sharp corners expands. At the same time, the blue area beneficiation results. be seen from Figure replaced 10, whenby thethe distance between increases, the red of the groove on As the can rod-surface is gradually green area. This ERB indicates that the area of cloud picture at the sharp corners expands. At the same time, the blue area of the groove magnetic induction intensity in the groove becomes larger and the magnetic induction interactionon the rod-surface is gradually by the green indicates that the magnetic induction intensity with adjacent bumpsreplaced diminishes. Under thearea. actionThis of the radial curvature of the matrix rod, both of the rod along theand direction of the magnetic become with the aggregation area diminishes. of the in thesides groove becomes larger the magnetic inductionfield interaction adjacent bumps magnetic forceoflines. In addition, the screw the both matrix rod of surface make the the periodic Under the action the radial curvature of thethreads matrixonrod, sides the rod along direction change of the magnetic induction intensity in the axial direction of the rod. This leads to thescrew of the magnetic field become the aggregation area of the magnetic force lines. In addition, the magnetic field inhomogeneity along the axial direction, i.e., the axial magnetic field gradient. When threads on the matrix rod surface make the periodic change of the magnetic induction intensity in the

axial direction of the rod. This leads to the magnetic field inhomogeneity along the axial direction, i.e., the axial magnetic field gradient. When the distance between ERB is equal to zero or is infinite, the


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Minerals2018, 2018,8, 8,xxFOR FORPEER PEERREVIEW REVIEW Minerals

13of of16 16 13

the distance between ERB is is equal equal to zero zerobar. or is isTherefore, infinite, the the screw thread rod is equivalent equivalent tomatrix the is screwthe thread rod between is equivalent to the smooth thescrew pitchthread of therod screw thread rodto distance ERB to or infinite, is the smooth bar. Therefore, the pitch of the screw thread rod matrix is either too large or too small, which bar.or Therefore, thewhich pitch of thread to rodstrengthening matrix is eitherthe toocapturing large or tooeffect small,ofwhich eithersmooth too large too small, is the notscrew conducive magnetic is not not conducive conducive to to strengthening strengthening the the capturing capturing effect effect of of magnetic magnetic minerals. minerals. This This also also reasonably reasonably is minerals. This also reasonably explains why magnetic separation is best when the pitch is 0.5 mm for explains why whymagnetic magneticseparation separation is is best bestwhen when the pitch pitch is is0.5 0.5 mm mm for for fine hematite ore tailings from explains fine hematite ore tailings from the Dong Anshanthe beneficiation plant. fine hematite ore tailings from the Dong Dong Anshan Anshan beneficiation beneficiation plant. plant. the

.. Figure 8. Path locations of different matrix rods.

Figure Pathlocations locations of of different Figure 8. 8.Path differentmatrix matrixrods. rods.

1.3 1.3

(a) (a)

Path11 Path Path22 Path Path33 Path Path44 Path

1.2 1.2

BB(T) (T)

1.1 1.1 1.0 1.0 0.9 0.9 0.8 0.8 0.0 0.0

0.5 0.5

0.5 0.5

1.0 1.5 2.0 1.0 1.5 2.0 Distance(mm) (mm) Distance

3.0 3.0

Path11 Path Path22 Path Path33 Path Path44 Path

(b) (b)

0.4 0.4

gradB gradB(T/mm) (T/mm)

2.5 2.5

0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0.0 0.0

0.5 0.5

1.0 1.5 2.0 1.0 1.5 2.0 Distance(mm) (mm) Distance

Figure 9. Cont.

2.5 2.5

3.0 3.0


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2

2

BgradB (T /mm) BgradB (T /mm)


0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0

(c) (c)

0.0 0.0

0.5 0.5

Path 1 Path Path 21 Path Path 32 Path Path 43 Path 4

1.0 1.5 2.0 1.0Distance 1.5 (mm)2.0

2.5 2.5

3.0 3.0

Distance (mm)

Figure 9. The of magnetic parametersalong along the the specified The relationship between the the Figure 9. The datadata of magnetic parameters specifiedpath. path.(a)(a) The relationship between Figure 9. The data ofand magnetic parameters along away the specified path. (a) The relationship between the magnetic field strength and distancemoving moving away from matrix surface. (b) (b) TheThe relationship magnetic field strength thethe distance fromthe the matrix surface. relationship magnetic field strength and the distance moving awaymoving from the matrix surface. (b) The relationship between the magnetic field gradient andthe thedistance distance away from thethe matrix surface. (c) The between the magnetic field gradient and moving away from matrix surface. (c) The between the magnetic field gradient and the distance moving away from the matrix surface. (c) The relationship between the product of the magnetic field strength and the magnetic field gradient and relationship between the product of the magnetic field strength and the magnetic field gradient and relationship betweenaway the product ofmatrix the magnetic the distance moving from the surface.field strength and the magnetic field gradient and the distance moving away from the matrix surface. the distance moving away from the matrix surface.

Figure 10. The cloud chart of magnetic induction intensity distribution based on different distances Figure 10.ERB. The (a) cloud chart ofbetween magnetic induction based on different between Distance ERB p = 0.3 intensity mm. (b) distribution Distance between ERB p = 0.5distances mm. (c) Figure 10. The cloud chart of magnetic induction intensity distribution based on different distances between ERB. (a) Distance between ERB p = 0.3 mm. (b) Distance between ERB p =between 0.5 mm.ERB (c) Distance between ERB p = 1.0 mm. (d) Distance between ERB p = 1.5 mm. (e) Distance between ERB. between (a) Distance ERB = 0.3 mm. (b) Distance ERB p = 0.5 between mm. (c) ERB Distance ERB between p = 1.0 mm. (d)pDistance between ERB p =between 1.5 mm. (e) Distance pDistance = 2.0 mm. between ERB p = 1.0 mm. (d) Distance between ERB p = 1.5 mm. (e) Distance between ERB p = 2.0 mm. p = 2.0 mm.

5. Conclusions 5. Conclusions 5. Conclusions Based on the work in this paper, it is confirmed that the structural change of the matrix has an Based on the work in this paper,it itisfield isconfirmed confirmed that the change of weakly the matrix has an important influence on this the magnetic distribution and on the capture of magnetic Based on the work in paper, that thestructural structural change of the matrix has an important influence on the magnetic field distribution and on the capture of weakly magnetic mineral particles. The screw thread rod matrix has the dual advantages of the smooth rod matrix important influence on the magnetic field distribution and on the capture of weakly magnetic mineral mineral particles.magnetic The screw thread has of thebetter dual slurry advantages of through the smooth rod matrix and the grooved plate, i.e., rod the matrix advantage fluidity the matrix and particles. The screw thread rod matrix has the dual advantages of the smooth rod matrix and the and the grooved magnetic plate, i.e., the advantage of better slurry fluidity through the matrix higher magnetic field gradient at the sharp corners. Compared with the smooth rod matrix, and the grooved magnetic plate, i.e., the advantage ofcorners. better slurry fluidity through the rod matrix andthe higher higher magnetic gradient at the Compared the smooth matrix, screw thread rod field matrix enhances the sharp inhomogeneity of the axialwith magnetic induction intensity on magnetic gradient at theenhances sharp corners. Compared of with smooth rodinduction matrix, the screwon thread screwfield thread rod matrix the inhomogeneity the the axial magnetic intensity rod matrix enhances the inhomogeneity of the axial magnetic induction intensity on the surface of the matrix. Furthermore, the combined effects of the radial curvature of the rod and the inhomogeneous magnetic field in the axial direction improve the recovery of fine-grained iron minerals. For the fine


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hematite ore tailings from the Dong Anshan beneficiation plant, the suitable distance between ERB on the surface of 3 mm rod matrix is 0.5 mm, offering a recovery increase of 3% over the smooth rod matrix. Besides, whether it is for the screw thread rods or for the smooth matrix rods, the smaller column gap provides a better recovery in the case of no clogging of matrices. Numerical test results of magnetic field distribution based on matrix parameters show that the product of the magnetic field strength and the magnetic field gradient for the screw thread rod matrix is greater than the corresponding value of the smooth rod matrix within 1 mm along the radial direction on the matrix rod. Therefore, the magnetic force exerted by the screw thread rod matrix on the surrounding magnetic particles is more prominent. The influences of structural parameters of magnetic matrix on the iron minerals processing are worthy of attention in the field of high gradient magnetic separation. By adjusting the structural parameters of the matrix, not only the recovery rate of the weak magnetic minerals can be improved, but also the background magnetic field strength can be reduced under the same sorting effect so as to improve the power consumption of the equipment. Acknowledgments: This creative research work was supported by the National Natural Science Foundation of China (Grant No. 51604064), the Fundamental Research Funds for the Central Universities (Grant No. 150103003) and the Doctoral Scientific Research Foundation of Liaoning Province (201601027), for which the authors express their appreciation. Author Contributions: W.L., Y.H., and E.P. conceived and designed the experiments; W.L. performed the physical experiments; W.L. and R.X. performed the numerical experiments; W.L. and Y.H. analyzed the data; E.P. contributed materials/analysis tools; W.L. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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