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Separation performance of sub-micron silica particles by electrical hydrocyclone
Powder Technology 196 (2009) 147–155
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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c
Separation performance of sub-micron silica particles by electrical hydrocyclone Romanus Krisantus Tue Nenu ⁎, Hideto Yoshida, Kunihiro Fukui, Tetsuya Yamamoto Department of Chemical Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8527, Japan
a r t i c l e
i n f o
Article history: Received 2 November 2008 Received in revised form 18 May 2009 Accepted 13 July 2009 Available online 23 July 2009 Keywords: Hydrocyclone Electrical enhancement Sub-micron silica Particle classification
a b s t r a c t Separation performance of sub-micron particles by use of a special electrical hydrocyclone was studied. The effects of feed suspension waiting time, applied electrostatic potentials, and the feed suspension concentration, on the separation performance of the electrical hydrocyclone were investigated. An aqueous suspension of sub-micron silica particles with median diameter of about 0.2 µm was used as the test powder. A 20 mm diameter of electrical hydrocyclone operated at 20% of the underflow ratio was used. A negative center wire electrode was inserted vertically inside the conical section, and electrostatic potentials up to 100 V were applied in this electrical hydrocyclone. It was found that the 50% cut size of the electrical hydrocyclone increased with the increase of the feed suspension waiting time after a particle dispersion process by the beads mill. The classification of the submicron particles occurred under applied electrostatic potentials greater than about 40 V, while better classification performance was obtained with the increase of the applied electrostatic potentials. The 50% cut size decreased with the increase of the feed suspension concentration up to 1.5 wt.%, and further increasing of the concentration led to the increase of 50% cut size. A simple model based on the time of flight model, was developed in order to predict the 50% cut size of the electrical hydrocyclone. The model results qualitatively agreed with the experimental results. It was found that classification the sub-micron particles is possible by use of the special electrical hydrocyclone proposed in this study. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Hydrocyclones have been widely used as size classification apparatus on solid–liquid flow because of their simple structures, lack of moving parts, and low cost. In order to increase the separation efficiency of particles in gas cyclones, without the increase of pressure drop, the use of electrostatic force has been studied, and the factors affecting the separation performance of electrically enhanced gas cyclones have been observed and explained [1]. The particle charging mechanism in the electrical cyclone is similar to that of the electrostatic precipitator (ESP). When a high electrostatic potential is applied to a wire inserted inside the cyclone, a multitude of ions are generated, and an electrical field is created due to the gradient of potential between the center wire and the collecting wall. The ions transfer their energy, and support the movement of particles toward to the collection wall which has an electric polarity opposite to the charged particles. The phenomenon of particles moving in such a way is called electrophoresis. In the case of the ESP and the electrical cyclone separators, the determination of electric polarities of the wire and wall depend on which ions charge the particles, and it is found that most particles are charged by the negative ions. By centrifugal force, as the main force of the cyclone, the particles
⁎ Corresponding author. Tel./fax: +81 082 424 7853. E-mail address: [email protected] (R.K. Tue Nenu). 0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.07.011
are collected and deposited on the wall. And combined with the electrostatic force, a greater amount of particles are collected compared to the standard hydrocyclone. Several investigations regarding the electrical enhancement of the separation performance of gas cyclones have been reported [2,3], and some models to predict the separation performance of electrical cyclones have been conducted [4,5], but very few studies have been carried out regarding the effect of electrical enhancement on the classification performance of the hydrocyclone. Since the dimensions of most hydrocyclones are small compared to the gas cyclones, and the dielectric constant of liquids is greater than that of gases, smaller applied electrostatic potentials can be used in the electrical hydrocyclone. Yoshida et al. studied the performance of electrically enhanced hydrocyclone without the underflow. They found that particle classification performance increased with the increase of applied electrostatic potentials, the diameter of the center negative electrode, and the pH of the feed suspension [6]. But the applied electrostatic potentials were limited to nothing greater than 50 V. Pratarn et al. examined the performance of the same electrical hydrocyclone, and found that the 50% cut size became smallest under the longest dust box and the presence of underflow conditions. The semi empirical correlations to predict the 50% cut size, based on the experimental data were developed and proposed in their report [7]. This study examines the effect of the feed suspension waiting time after particle dispersion by the beads mill apparatus, the feed suspension concentration, and the applied electrostatic potentials
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up to 100 V on the classification performance of sub-micron particles by use of the special electrical hydrocyclone. A simple model, based on the time of flight model was used to predict the 50% cut size of the electrical hydrocyclone. 2. Experimental method Sub-micron silica particles with a median diameter of about 0.2 µm, specific surface area of 22.7 m2/g, and density of 2200 kg/m3 were used as the experimental test powder. The particle size distribution of the powder is shown in Fig. 1. Before the classification experiment was carried out, the powder was treated in the beads mill apparatus (UAM015 by Kotobuki Industries Co. Ltd.), in order to break up the agglomerated silica particles into well dispersed particles. Fig. 2 shows the simplified flow chart of the beads mill. The sub-micron silica powder was supplied into the vessel from a container tank. The vessel contained 150 µm of spherical silica beads and a centrifugation rotor. Beads were agitated in the lower part of the vessel, and drove the break up of the agglomerated particles. The sub-micron silica powder was pumped to the upper part of the vessel, while the beads were removed from suspension with the use of centrifugal force. Large agglomerated particles were also removed by centrifugal force until they were broken into well dispersed particles. The well dispersed sub-micron silica particles were then recycled back to the container tank. The whole re-circulated process was carried out within 30 min. The experimental outline and the dimension of the electrical hydrocyclone system are shown in Fig. 3. The system consists of the electrical hydrocyclone with 20% underflow ratio, and the slurry tank which is equipped with a 250 rpm rotating impeller. De-ionized water with electrical conductivity below 5 × 10− 5 S/m was used in all experimental works. The experiments were carried out under the feed suspension flow rate conditions of 1.67 × 10− 5 m3/s (1 l/min). Under this low flow rate condition, the centrifugal force of particles in the hydrocyclone was considered to be very low and has negligible effect on the separation of the small sized of particles used in this study. Hence the electrostatic force was considered to be only driving force for the particle separation. The temperature of the feed suspension was kept constant at 30 °C by use of a temperature controller. The discharged flows of both the overflow and underflow sections were returned to the slurry tank. The experiments were carried out within 20 min to assure that the system maintained steady conditions. After the experiments were carried out, samples from both the underflow and overflow sides were collected, evaporated and weighed. The particle size distribution of both underflow and overflow sides was analyzed using the Dynamic Light Scattering method, (HORIBA Co. Ltd., LB-550), while the zeta potential of suspensions was measured
Fig. 1. Particle size distributions of the test powder.
Fig. 2. Schematic diagram of the beads mill.
by a zeta size measuring device (Zetasizer 2000 by Malvern Instrument Co. Ltd.). In order to confirm the reliability of the measured data, the measurements of particle size distributions were carried out 10 times for each sample with below 10% in the difference of median diameter, while the measurement of zeta potential was conducted 18 times with the difference below 7% for each sample. The partial separation efficiency, Δη, and the 50% cut size diameter, Dp50, were calculated based on the weight and the particle size distributions of the overflow and underflow samples, respectively. The partial separation efficiency, Δη, is calculated by: Δη =
mc fc ΔDp mc fc ΔDp + mf ff ΔDp
ð1Þ
where mc and mf are the mass of the dried collected particles of the coarse and fine sides, while fcΔDp and ffΔDp are the particle size distributions of the coarse and fine sides, respectively. A hydrocyclone with the interior diameter of 20 mm was used in this study. The metal center electrode wire was inserted vertically inside the conical section of the hydrocyclone, and a strong electrostatic field was created in the space between the electrodes, when the electrostatic potentials were applied. Therefore, it is thought that the electrostatic force is the main factor of the electrical hydrocyclone's classification performance with the center wire placed at this location. The conical section was electrically insulated from the upper cylindrical and the lower underflow parts. The center wire and the wall of the conical part were connected to a DC power generator. Due to having a similar mechanism to the electrostatic precipitator, the wall of the hydrocyclone should act as the collecting wall, and the center wire as the negative electrode. Hence the positive polarity was applied to the wall and the negative one was to the wire, since the particles with negative charges move to the wall of the conical section. Fig. 4 describes the particle collection phenomenon taking place in the electrical hydrocyclone. The electrical fields resulting from the gradient of voltages between the center wire and the wall of the conical part affect the movement of the negatively charged particles, so that they were collected at the conical part. The small particles which cannot be collected by use of the standard hydrocyclone, move to the overflow section. Hence it is expected that a higher amount of particles collect at the conical wall of the electrical hydrocyclone compared to that of the standard hydrocyclone. In this study, several different operational conditions were investigated as follows: 1. The feed suspension waiting time after particle dispersion by the beads mill apparatus ranged from 1.5 to 24 h. 2. The applied electrostatic potentials ranged from 0 to 100 V. 3. The feed suspension concentrations ranged from 0.1 to 2 wt.%.
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Fig. 3. Schematic diagram of the electrical hydrocyclone.
3. Results and discussions 3.1. Effect of the feed suspension waiting time on the particle classification of electrical hydrocyclone Since the particle distribution of powder in the suspension after particle dispersion by the beads mill changes over time, then the performance of the electrical hydrocyclone was evaluated under various feed suspension waiting time conditions from just after pretreatment by the beads mill to the startup of the classification experiment. Fig. 5 shows the particle size distribution of the powder in the suspension for the waiting time, t, from 0 to 20 h. Particles tended to have larger diameters with the increase of waiting time. The reason of
this phenomenon might be due to the particle re-agglomeration process until the particle charge changes to an equilibrium state. The concentration of feed suspension was 0.5 wt.%. Fig. 6 summarizes the relationship between zeta potential, ζ, of the feed suspension and the waiting time. The zeta potential decreased from about −49 to an equilibrium value of − 40 mV with the increase of the waiting time. The zeta potential represents the potential on the Stern layer of the particles. The absolute value of ζ decreased with the increase of t from 0 to 8 h and remained relatively constant after 8 h. Fig. 7 shows the partial separation efficiency of the electrical hydrocyclone under the various feed suspension waiting times, t. The particle cut size of the electrical hydrocyclone increased with the increase of t until t = 12 h, and remained relatively constant at t greater than 12 h. These results corresponded directly to the ζ value of the suspension under various
Fig. 4. Particle collection mechanism in the electrical hydrocyclone.
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Fig. 5. Effect of feed waiting time on its particle size distribution.
Fig. 8. Effect of feed waiting time on 50% cut size.
between the 50% cut size and the waiting time. It was found that the value of Dp50 increased with the increase of the waiting time. For t = 24 h, the Dp50 increased by 28.9% at 80 V (Dp50 = 0.519 µm) and 27.4% at 100 V (Dp50 = 0.461 µm), compared to the data of t = 1.5 h (Dp50 = 0.409 and 0.362 µm at the ΔV = 80 and 100 V, respectively). The absolute ζ values play an important role of in the particle charging mechanism because they correspond to the magnitude of the particle charging. When the same electrostatic potential is applied, the low absolute value of ζ reflects a low particle charging, and causes the migration radial velocity of the particles inside the electrical hydrocyclone is low. Lower radial migration velocity of the particles indicates lower partial separation efficiency. By comparing Figs. 6 and 8, it is found that 50% cut size indicated nearly constant values when the waiting time was greater than about 12 h. These results corresponded directly to the zeta potential of the feed suspension, which showed a relatively constant value after 8 h. Fig. 6. Effect of feed waiting time on its zeta potential.
3.2. Effect of the applied electrostatic potentials on the particle classification performance of the electrical hydrocyclone
waiting times as shown in Fig. 6. The 50% cut size increased with the increase of zeta potential, and were relatively constant at the time when the zeta potential had the equilibrium value. The fluctuation of partial separation efficiency curves appeared under the particle size of 0.1 to 0.2 µm. The fluctuation was known as the “fish-hook” phenomenon, and caused by the particle deposition due to diffusion. The particle deposition due to diffusion took place for the very small particles when the effect of both inertial (centrifugal) and electrostatic force were considered negligible. Fig. 8 shows the relationship
In order to examine the effect of applied electrostatic potential on the classification performance of sub-micron silica powder, experiments with various applied electrostatic potentials, ranging from 0 to 100 V were carried out. The experiments were conducted under the Co = 0.5 wt.% and t = 1.5 h conditions. Fig. 9 shows the effect of applied electrostatic potentials on the partial separation efficiency of the electrical hydrocyclone. The separation of sub-micron silica particles in the electrical hydrocyclone took place under the ΔV
Fig. 7. Effect of feed waiting time on partial separation efficiency.
Fig. 9. Effect of applied electrostatic potential on partial separation efficiency.
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equal to or greater than 40 V, and better partial separation efficiency was obtained with higher applied electrostatic potentials. The Dp50 of the hydrocyclone at ΔV = 100 V decreased up to 18.2% (Dp50 = 0.364 µm) compared to the result of 40 V conditions (Dp50 = 0.446 µm). Higher electrostatic potentials increased the strength of electrostatic fields inside the conical section of the hydrocyclone. As the results show, for the same inlet flow rate, the radial migration velocity of the particles became higher. Then, the smaller particles could reach the conical collecting wall and the number of collected particles increased. Subsequently, higher particle collection efficiency was obtained by increasing the applied electric potentials. For the applied potentials below 40 V, the combination of centrifugal and electrostatic force of the particles which acted radially outward was too low to overcome the effect of the drag force acted inside, and there was no separation taking place. The coarse and fine particle size distributions obtained from the electrical hydrocyclone under ΔV of 0 V and 100 V conditions, respectively, are shown in Fig. 10a and b. The particle size distributions of the coarse and fine sides are nearly equal under the electrostatic potential of the 0 V condition, as shown in Fig. 10a. Hence the separation of sub-micron silica particles was very difficult in this case. The difference of particle size distributions between fine and coarse particles increases under the electrostatic potential of the 100 V case, as shown in Fig. 10b. The sample suspensions of both fine and coarse sides after 6 days of sedimentation time are shown in Fig. 11. Denser suspensions of the coarse side under 100 V electrical potential were obtained compared to the fine side, while there was no clear color difference between fine and coarse side suspensions of the 0 V case. From Figs. 10 and 11, it is
151
Fig. 11. Photographs of the classified slurry samples of the electrical hydrocyclone.
clear that the classification of sub-micron silica powder could be obtained by applying the electrostatic force to the hydrocyclone. Furthermore, lower applied electrostatic potentials are needed by the electrical hydrocyclone to achieve the classification of sub-micron particles, compared to that of the electrical gas cyclone, since the latter needs the applied potential above of 1000 V, in order to separate the submicron particles. Fig. 12 shows the relationship between the applied electrostatic force and the electrostatic current, when the classification experiment was carried out in the electrical hydrocyclone. The figure shows a linear relationship between electrostatic potentials and current under the slurry conditions of Co = 0.5 wt.% and t = 1.5 hr. This means that particles in the slurry have a constant resistance under various applied electrostatic potentials. This leads to the conclusion that a uniform particle charging occurred when the electrostatic potential was applied to the hydrocyclone under the slurry conditions indicated above. 3.3. Effect of the feed suspension's concentration on the particle classification performance of the electro hydrocyclone Fig. 13 shows the effect of the concentration of feed suspension, Co, on the partial separation efficiency of the electrical hydrocyclone. Fig. 14 shows the relationship between feed suspension concentration, Co, and 50% cut size, Dp50. The experiments were carried out at t = 1.5 h, and the ΔV were equal to 80 and 100 V. As can be seen, the
Fig. 10. Effect of applied electrostatic potentials on particle size distributions (a: 0 V, b: 100 V).
Fig. 12. Relationship between electrostatic potential and current.
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Fig. 13. Effect of feed suspension concentration on partial separation efficiency.
Dp50 decreased slightly, as the Co increased, when the values of Co were below 1.5 wt.%. As an example, in the case of 100 V, from 0.375 to 0.294 µm, until the value of Co was equal to 1.5 wt.%. But when the Co was higher than 1.5 wt.%, the Dp50 increased with the increase of feed suspension concentration (Fig. 15). In the case of 100 V, the Dp50 was 0.413 µm for Co equal to 2 wt.%. The Dp50 of the 100 V electrical hydrocyclone was lower than that of 80 V case. The increase of the hindered sedimentation's effect with the increase of the suspension concentration on the particle radial migration velocity might be the main factor of this phenomenon. The motion of the particles could be considered equal to that of the motion of single particle when the suspension concentration was below 1.5 wt.%, since the motion of particles was independent each other. When the concentration became higher, the effect of hindered sedimentation took place, the motion of the particles was interfered by the other's motion, and the radial migration velocity of the particles was decreased. These phenomenon caused the amount of the collected particles on the collecting wall was decreased, and resulted in the decreased separation performance of the electrical hydrocyclone, with the increase of the suspension concentration. On the other hand, Fig. 16 shows the relationship between the applied electrostatic current and potential under various suspension concentrations. The non-linear relationship between electrostatic current and potential took place under the condition of 2 wt.% of suspension concentration. The non-linear relationship between electrostatic current and potential means the difference resistance, compared to that of in the linear relationship. The change of the
Fig. 14. Effect of feed suspension concentration on 50% cut size.
Fig. 15. Relationship between electrostatic potential and current under various feed suspension concentrations.
resistance possibly means the change of the morphology of the attached ions at the surface of the particles changes. Higher electrical conductance of the particles was occurred for the higher suspension concentration in the case of applied potentials greater than 40 V. These conditions mean that the electrostatic conductance of the particles in that suspension was increased with the increase of the suspension concentration, and increased the particles' migration velocity. As mentioned above, under the dilute feed suspension condition (Co = 0.1 wt.%), the effect of hindered sedimentation on the radial migration velocity of the particles was still negligible. When the feed suspension's concentration increased slightly (Co ≤ 1.5 wt.%), the effect of hindered sedimentation on the radial migration velocity of the particles was still negligible, but the particles' electrostatic conductance was increased, and the amount of collected particles at the wall increased, and resulting in the decrease of Dp50 until a suspension concentration limit (Co = 1.5 wt.%). The effect of hindered sedimentation was increased with the further increase of the slurry concentration (Co N 1.5 wt.%). Even the particles' electrostatic conductance was increased with the increase of the suspension concentration, the hindered sedimentation phenomenon was considered has superior effect on the particles' radial migration velocity, and overcame the effect of electrical conductance. As the result, the radial migration velocity of the particles was decreased, and led to the
Fig. 16. Comparison between experimental and calculated results of 50% cut size diameter.
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decrease of collected particles in the wall, under the suspension concentration higher than 1.5 wt.%. Hence, the separation performance of the electrical hydrocyclone decreased with the increase of suspension concentration higher than 1.5 wt.%. This phenomenon is different with the standard hydrocyclone, since in the standard hydrocyclone, the 50% cut size diameter increases with the increase of suspension viscosity [8], but in the case of the electrical hydrocyclone, the separation performance shows the optimum value under a certain suspension concentration. From practical application, the special electrical hydrocyclone proposed in this study is able to separate the sub-micron particles.
in Eq. (7), the simple formulation of Richardson and Zaki [10] was used as the correction factor: f ðCo Þ = ðeÞ
− 4:65
ð8Þ
where ε denotes the fraction of liquid in the suspension. ε is defined as: ρs
ρf e= 1+
ð1 − Co Þ ρs ρf
ð1 − Co Þ
ð9Þ
Subtituting Eq. (9) to Eq. (7) results:
4. Proposed models To explain the experimental results of our special electrical hydrocyclone, the time of flight model, as derived by Rosin et al., [9] is used as the base of modeling. The model is modified with the addition of electrostatic mobility in the radial velocity term, and was applied in the conical section only. This model was based on the fact that the particles would reach the wall of the hydrocyclone's conical section, with equal traveling time in tangential and radial directions. The assumptions made in this model development are: (1) The particle is spherical in shape. (2) The drag force on the particle follows Stokes' law. (3) The charge on the central rod is relatively low, hence the ionic space charge density is assumed to be negligible. (4) The particle surface charge density shows a constant value. The time required to reach the wall of the conical section of hydrocyclone for single particle in a fluid medium is defined as: tθ =
153
2πRN uo
ð2Þ
vre
0 14:65 ρs 7 ð1−Co Þ Dp σ10 Er ρ f @ A = 3μ o 1 + ρρs ð1− Co Þ
ð10Þ
f
Eq. (10) indicates that the radial migration velocity of the particle is proportional to the particle diameter, the strength of the electrostatic field, and the inverse of the suspension concentration. The distance between the inlet section and the wall of the conical part is denoted as x, then, the time it took particles to reach this distance in radial direction is: tx =
x = vre
3μ o x
0
σ 10 Dp Er @ 7
ρs ρf ð1 − Co Þ
1 +
ð11Þ
14:65 A
ρs ρf ð1 − Co Þ
Equating Eqs. (11) and (2), and taking uo = Q/al will result in x: 0 14:65 ρs 7 2πRNσ 10 Dp Er al ρf ð1− Co Þ @ A x= 3Q μ o 1 + ρρs ð1− Co Þ
ð12Þ
f
where R is the mean radius of the hydrocyclone's conical part, and N is the number of the particle rotations inside the conical part of the hydrocyclone. The radial terminal velocity is defined as follows: ð3Þ
vr = vrc + vre
vrc and vre are the radial velocity of particles which is contributed to by the centrifugal and electrostatic force, respectively. In this study, the contribution of the centrifugal force on the radial velocity is considered to be negligible, because of the low inlet velocity and very small particle diameter. Hence, the particles' radial velocity was the product only of electrostatic force. The radial migration velocity is defined as:
Partial separation efficiency is defined as the fraction of particles which reach the wall: 0 14:65 ρs 2πRNσ 107 Dp Er l Co xluo x ρf ð1−Co Þ @ A Δη = = = a 3Q μ o Co aluo 1 + ρρs ð1− Co Þ
Dp50 is the particle diameter which corresponds to Δη = 0.5, then: 3Q μ 0 o
Dp50 =
4πRNσ 10 Er l@ 7
ρs ρf ð1 − Co Þ
1 +
7
vr = vre = μ e Er = 2
q = πDp σ
qEr 10 3πμ o Dp
ð4Þ ð5Þ
ρs ρf ð1 − Co Þ
14:65
ð14Þ
A
In order to determine the electrical field strength, assumption (3) is employed, then in cylindrical coordinates, with the axis of the two coaxial cylinders, the Laplace's equation can be written as [11]: dEr E + r =0 dr r
Then,
ð13Þ
f
ð15Þ
7
vre =
Dp σ10 Er 3μ o
ð6Þ
where σ is the surface charge density of the particles, while µo and Er are the suspension viscosity and the electrostatic field strength, respectively. For large amount of the particles suspended in the liquid medium, the correction factor of hindered sedimentation was added to Eq. (6) 7
vre =
Dp σ10 Er 3μ o f ðCo Þ
ð7Þ
Integration gives: Er =
1 ΔV ðR = Ri Þ r ln
ð16Þ
Ri is the radius of the center electrode. The particle is located somewhere between the center electrode and the wall of the conical section, and in this study, the location is assumed to be the center position between electrodes: r = 0:5ðR + Ri Þ
ð17Þ
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N is the number of particle rotations inside the conical section, and from Eq. (2) is given by: tθ =
2πRN V = uo Q
ð18Þ
N=
V 2πRal
ð19Þ
where V is the volume of the conical section in the hydrocyclone. Substituting Eqs. (16), (17) and (19) into Eq. (14) gives the final form of the equation to determine Dp50. Dp50 =
3Qμ o aðR = Ri Þ lnðR = Ri Þ 0 14:65 4Vσ 10 ΔV @ 7
ρs ρf ð1 − Co Þ
1 +
ρs ρf ð1 − Co Þ
ð20Þ
A
Eq. (20) indicates that the 50% cut size decreases as the electrostatic potential (ΔV) increases, and increases with the increase of the suspension concentration (Co), as long as the particle charge density (σ) has the constant value. The only unknown parameter is σ, and by fitting the calculated Dp50 data into the experimental results, with the use of the least square method, the constant value of σ can be found. The comparison between experimental and calculated results of Dp50 is shown in Fig. 17. The surface charge densities of silica particles which are found by fitting them into experimental results, have the values of about 2.3 µC/ cm2. These values have the same order as the values that have been reported previously [12,13]. Therefore it can be concluded that the σ values obtained are acceptable. By fitting the Eq. (20) to the Dp50 of experimental data, it is found that the surface charge density of the particles increases with the increase of the suspension concentration, within the range of suspension concentration up to 1.5 wt.%. The difference between the experiment and calculated results of Dp50 occurred, mainly because the time of flight model assumes that the tangential velocity of the particles in the conical section is equal to that of in the circular inlet section, as described in Eq. (2). In reality, the particles' tangential velocity in the conical section was smaller, because it is affected by the upward motion of liquid in the inner region of the hydrocyclone. The exact value of the tangential velocity in the conical section cannot be determined theoretically or empirically, but can be estimated by use of a more comprehensive method, such as Laser Doppler Velocimetry (LDV), or by CFD based numerical calculation. Assuming the tangential velocity of the particle in the conical section equal to that of in the inlet circular section, would result in the excessive slope of the calculated model. The other factors that might cause the calculated results is different with the experimental data are the assumption of negligibility tangential force and ionic space charge in the center rod. The tangential force still contributed in the particle deposition even under very low of inlet flow rate of the electrical hydrocyclone. Under the high applied electrostatic potential, the center rod possibly was subjected to a sufficient amount of charging, hence the values of the right hand term in Eq. (15) was not equal to zero. However, the simple developed model is in qualitative agreement with the experimental data. 5. Conclusions 1. The 50% cut size in the electrical hydrocyclone increased with the increase of feed suspension's waiting time after particle dispersion by the beads mill. 2. The classification of the sub-micron silica powder occurred at the applied electrostatic potentials equal to and greater than 40 V. The
classification performance of the electrical hydrocyclone increased with the increase of applied electrostatic potentials. 3. The 50% cut size decreased with the increase of feed suspension concentration until the concentration limit of 1.5 wt.%. The 50% cut size increased with further increasing of the feed suspension concentration. 4. The simple model, based on the time of flight model is qualitatively agreed with the experimental results. Nomenclatures a Inlet length (cm) Co Feed suspension concentration (wt.%) Dp50 50% cut size (µm) Dp̅ Mass median diameter (µm) E Total collection efficiency (–) Er Radial electrostatic field strength (V/cm) fcΔDp, ffΔDp Particle size distributions of coarse and fine sides, respectively (–) I Electrostatic current (mA) l Inlet height (cm) M, mc, mf Mass of particles on the feed suspension, collected particles in coarse and fine sides, respectively (g) N Number of particle rotations (–) q Charge of particles (C) Q Inlet flow rate (cm3/s) R Mean radius of the conical section in hydrocyclone (cm) Ri Radius of center electrode (cm) t Feed suspension waiting time (h) tx, tθ Time of the particles to reach the collecting wall in radial and tangential direction, respectively (m/s) T Feed suspension temperature (°C) uo Velocity of fluid medium (m/s) V Volume of hydrocyclone's conical section vr,vre,vrc Particle total radial velocity, particle radial velocity contributed by centrifugal force and electrostatic force, respectively (cm/s)
Greek letters Δη Partial separation efficiency (–) ΔV Applied electrostatic potentials (V) μo Fluid viscosity (g/cm s) ρp, ρf Particle and fluid density, respectively (g/cm3) μe Particle electrostatic mobility (cm2/V.s) σ Surface charge density (C/cm2) ζ Zeta potential (mV)
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[12] R.P. Abendroth, Behavior of pyrogenic silica in simple electrolytes, J. Colloid Interface Sci. 34 (4) (1970) 591–596. [13] P.M. Dove, C.M. Craven, Surface charge density on silica in alkali and alkaline earth chlorine electrolyte solutions, Geochim. Cosmochim. Acta 49 (21) (2005) 4963–4970.
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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c
Separation performance of sub-micron silica particles by electrical hydrocyclone Romanus Krisantus Tue Nenu ⁎, Hideto Yoshida, Kunihiro Fukui, Tetsuya Yamamoto Department of Chemical Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8527, Japan
a r t i c l e
i n f o
Article history: Received 2 November 2008 Received in revised form 18 May 2009 Accepted 13 July 2009 Available online 23 July 2009 Keywords: Hydrocyclone Electrical enhancement Sub-micron silica Particle classification
a b s t r a c t Separation performance of sub-micron particles by use of a special electrical hydrocyclone was studied. The effects of feed suspension waiting time, applied electrostatic potentials, and the feed suspension concentration, on the separation performance of the electrical hydrocyclone were investigated. An aqueous suspension of sub-micron silica particles with median diameter of about 0.2 µm was used as the test powder. A 20 mm diameter of electrical hydrocyclone operated at 20% of the underflow ratio was used. A negative center wire electrode was inserted vertically inside the conical section, and electrostatic potentials up to 100 V were applied in this electrical hydrocyclone. It was found that the 50% cut size of the electrical hydrocyclone increased with the increase of the feed suspension waiting time after a particle dispersion process by the beads mill. The classification of the submicron particles occurred under applied electrostatic potentials greater than about 40 V, while better classification performance was obtained with the increase of the applied electrostatic potentials. The 50% cut size decreased with the increase of the feed suspension concentration up to 1.5 wt.%, and further increasing of the concentration led to the increase of 50% cut size. A simple model based on the time of flight model, was developed in order to predict the 50% cut size of the electrical hydrocyclone. The model results qualitatively agreed with the experimental results. It was found that classification the sub-micron particles is possible by use of the special electrical hydrocyclone proposed in this study. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Hydrocyclones have been widely used as size classification apparatus on solid–liquid flow because of their simple structures, lack of moving parts, and low cost. In order to increase the separation efficiency of particles in gas cyclones, without the increase of pressure drop, the use of electrostatic force has been studied, and the factors affecting the separation performance of electrically enhanced gas cyclones have been observed and explained [1]. The particle charging mechanism in the electrical cyclone is similar to that of the electrostatic precipitator (ESP). When a high electrostatic potential is applied to a wire inserted inside the cyclone, a multitude of ions are generated, and an electrical field is created due to the gradient of potential between the center wire and the collecting wall. The ions transfer their energy, and support the movement of particles toward to the collection wall which has an electric polarity opposite to the charged particles. The phenomenon of particles moving in such a way is called electrophoresis. In the case of the ESP and the electrical cyclone separators, the determination of electric polarities of the wire and wall depend on which ions charge the particles, and it is found that most particles are charged by the negative ions. By centrifugal force, as the main force of the cyclone, the particles
⁎ Corresponding author. Tel./fax: +81 082 424 7853. E-mail address: [email protected] (R.K. Tue Nenu). 0032-5910/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2009.07.011
are collected and deposited on the wall. And combined with the electrostatic force, a greater amount of particles are collected compared to the standard hydrocyclone. Several investigations regarding the electrical enhancement of the separation performance of gas cyclones have been reported [2,3], and some models to predict the separation performance of electrical cyclones have been conducted [4,5], but very few studies have been carried out regarding the effect of electrical enhancement on the classification performance of the hydrocyclone. Since the dimensions of most hydrocyclones are small compared to the gas cyclones, and the dielectric constant of liquids is greater than that of gases, smaller applied electrostatic potentials can be used in the electrical hydrocyclone. Yoshida et al. studied the performance of electrically enhanced hydrocyclone without the underflow. They found that particle classification performance increased with the increase of applied electrostatic potentials, the diameter of the center negative electrode, and the pH of the feed suspension [6]. But the applied electrostatic potentials were limited to nothing greater than 50 V. Pratarn et al. examined the performance of the same electrical hydrocyclone, and found that the 50% cut size became smallest under the longest dust box and the presence of underflow conditions. The semi empirical correlations to predict the 50% cut size, based on the experimental data were developed and proposed in their report [7]. This study examines the effect of the feed suspension waiting time after particle dispersion by the beads mill apparatus, the feed suspension concentration, and the applied electrostatic potentials
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up to 100 V on the classification performance of sub-micron particles by use of the special electrical hydrocyclone. A simple model, based on the time of flight model was used to predict the 50% cut size of the electrical hydrocyclone. 2. Experimental method Sub-micron silica particles with a median diameter of about 0.2 µm, specific surface area of 22.7 m2/g, and density of 2200 kg/m3 were used as the experimental test powder. The particle size distribution of the powder is shown in Fig. 1. Before the classification experiment was carried out, the powder was treated in the beads mill apparatus (UAM015 by Kotobuki Industries Co. Ltd.), in order to break up the agglomerated silica particles into well dispersed particles. Fig. 2 shows the simplified flow chart of the beads mill. The sub-micron silica powder was supplied into the vessel from a container tank. The vessel contained 150 µm of spherical silica beads and a centrifugation rotor. Beads were agitated in the lower part of the vessel, and drove the break up of the agglomerated particles. The sub-micron silica powder was pumped to the upper part of the vessel, while the beads were removed from suspension with the use of centrifugal force. Large agglomerated particles were also removed by centrifugal force until they were broken into well dispersed particles. The well dispersed sub-micron silica particles were then recycled back to the container tank. The whole re-circulated process was carried out within 30 min. The experimental outline and the dimension of the electrical hydrocyclone system are shown in Fig. 3. The system consists of the electrical hydrocyclone with 20% underflow ratio, and the slurry tank which is equipped with a 250 rpm rotating impeller. De-ionized water with electrical conductivity below 5 × 10− 5 S/m was used in all experimental works. The experiments were carried out under the feed suspension flow rate conditions of 1.67 × 10− 5 m3/s (1 l/min). Under this low flow rate condition, the centrifugal force of particles in the hydrocyclone was considered to be very low and has negligible effect on the separation of the small sized of particles used in this study. Hence the electrostatic force was considered to be only driving force for the particle separation. The temperature of the feed suspension was kept constant at 30 °C by use of a temperature controller. The discharged flows of both the overflow and underflow sections were returned to the slurry tank. The experiments were carried out within 20 min to assure that the system maintained steady conditions. After the experiments were carried out, samples from both the underflow and overflow sides were collected, evaporated and weighed. The particle size distribution of both underflow and overflow sides was analyzed using the Dynamic Light Scattering method, (HORIBA Co. Ltd., LB-550), while the zeta potential of suspensions was measured
Fig. 1. Particle size distributions of the test powder.
Fig. 2. Schematic diagram of the beads mill.
by a zeta size measuring device (Zetasizer 2000 by Malvern Instrument Co. Ltd.). In order to confirm the reliability of the measured data, the measurements of particle size distributions were carried out 10 times for each sample with below 10% in the difference of median diameter, while the measurement of zeta potential was conducted 18 times with the difference below 7% for each sample. The partial separation efficiency, Δη, and the 50% cut size diameter, Dp50, were calculated based on the weight and the particle size distributions of the overflow and underflow samples, respectively. The partial separation efficiency, Δη, is calculated by: Δη =
mc fc ΔDp mc fc ΔDp + mf ff ΔDp
ð1Þ
where mc and mf are the mass of the dried collected particles of the coarse and fine sides, while fcΔDp and ffΔDp are the particle size distributions of the coarse and fine sides, respectively. A hydrocyclone with the interior diameter of 20 mm was used in this study. The metal center electrode wire was inserted vertically inside the conical section of the hydrocyclone, and a strong electrostatic field was created in the space between the electrodes, when the electrostatic potentials were applied. Therefore, it is thought that the electrostatic force is the main factor of the electrical hydrocyclone's classification performance with the center wire placed at this location. The conical section was electrically insulated from the upper cylindrical and the lower underflow parts. The center wire and the wall of the conical part were connected to a DC power generator. Due to having a similar mechanism to the electrostatic precipitator, the wall of the hydrocyclone should act as the collecting wall, and the center wire as the negative electrode. Hence the positive polarity was applied to the wall and the negative one was to the wire, since the particles with negative charges move to the wall of the conical section. Fig. 4 describes the particle collection phenomenon taking place in the electrical hydrocyclone. The electrical fields resulting from the gradient of voltages between the center wire and the wall of the conical part affect the movement of the negatively charged particles, so that they were collected at the conical part. The small particles which cannot be collected by use of the standard hydrocyclone, move to the overflow section. Hence it is expected that a higher amount of particles collect at the conical wall of the electrical hydrocyclone compared to that of the standard hydrocyclone. In this study, several different operational conditions were investigated as follows: 1. The feed suspension waiting time after particle dispersion by the beads mill apparatus ranged from 1.5 to 24 h. 2. The applied electrostatic potentials ranged from 0 to 100 V. 3. The feed suspension concentrations ranged from 0.1 to 2 wt.%.
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149
Fig. 3. Schematic diagram of the electrical hydrocyclone.
3. Results and discussions 3.1. Effect of the feed suspension waiting time on the particle classification of electrical hydrocyclone Since the particle distribution of powder in the suspension after particle dispersion by the beads mill changes over time, then the performance of the electrical hydrocyclone was evaluated under various feed suspension waiting time conditions from just after pretreatment by the beads mill to the startup of the classification experiment. Fig. 5 shows the particle size distribution of the powder in the suspension for the waiting time, t, from 0 to 20 h. Particles tended to have larger diameters with the increase of waiting time. The reason of
this phenomenon might be due to the particle re-agglomeration process until the particle charge changes to an equilibrium state. The concentration of feed suspension was 0.5 wt.%. Fig. 6 summarizes the relationship between zeta potential, ζ, of the feed suspension and the waiting time. The zeta potential decreased from about −49 to an equilibrium value of − 40 mV with the increase of the waiting time. The zeta potential represents the potential on the Stern layer of the particles. The absolute value of ζ decreased with the increase of t from 0 to 8 h and remained relatively constant after 8 h. Fig. 7 shows the partial separation efficiency of the electrical hydrocyclone under the various feed suspension waiting times, t. The particle cut size of the electrical hydrocyclone increased with the increase of t until t = 12 h, and remained relatively constant at t greater than 12 h. These results corresponded directly to the ζ value of the suspension under various
Fig. 4. Particle collection mechanism in the electrical hydrocyclone.
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Fig. 5. Effect of feed waiting time on its particle size distribution.
Fig. 8. Effect of feed waiting time on 50% cut size.
between the 50% cut size and the waiting time. It was found that the value of Dp50 increased with the increase of the waiting time. For t = 24 h, the Dp50 increased by 28.9% at 80 V (Dp50 = 0.519 µm) and 27.4% at 100 V (Dp50 = 0.461 µm), compared to the data of t = 1.5 h (Dp50 = 0.409 and 0.362 µm at the ΔV = 80 and 100 V, respectively). The absolute ζ values play an important role of in the particle charging mechanism because they correspond to the magnitude of the particle charging. When the same electrostatic potential is applied, the low absolute value of ζ reflects a low particle charging, and causes the migration radial velocity of the particles inside the electrical hydrocyclone is low. Lower radial migration velocity of the particles indicates lower partial separation efficiency. By comparing Figs. 6 and 8, it is found that 50% cut size indicated nearly constant values when the waiting time was greater than about 12 h. These results corresponded directly to the zeta potential of the feed suspension, which showed a relatively constant value after 8 h. Fig. 6. Effect of feed waiting time on its zeta potential.
3.2. Effect of the applied electrostatic potentials on the particle classification performance of the electrical hydrocyclone
waiting times as shown in Fig. 6. The 50% cut size increased with the increase of zeta potential, and were relatively constant at the time when the zeta potential had the equilibrium value. The fluctuation of partial separation efficiency curves appeared under the particle size of 0.1 to 0.2 µm. The fluctuation was known as the “fish-hook” phenomenon, and caused by the particle deposition due to diffusion. The particle deposition due to diffusion took place for the very small particles when the effect of both inertial (centrifugal) and electrostatic force were considered negligible. Fig. 8 shows the relationship
In order to examine the effect of applied electrostatic potential on the classification performance of sub-micron silica powder, experiments with various applied electrostatic potentials, ranging from 0 to 100 V were carried out. The experiments were conducted under the Co = 0.5 wt.% and t = 1.5 h conditions. Fig. 9 shows the effect of applied electrostatic potentials on the partial separation efficiency of the electrical hydrocyclone. The separation of sub-micron silica particles in the electrical hydrocyclone took place under the ΔV
Fig. 7. Effect of feed waiting time on partial separation efficiency.
Fig. 9. Effect of applied electrostatic potential on partial separation efficiency.
R.K. Tue Nenu et al. / Powder Technology 196 (2009) 147–155
equal to or greater than 40 V, and better partial separation efficiency was obtained with higher applied electrostatic potentials. The Dp50 of the hydrocyclone at ΔV = 100 V decreased up to 18.2% (Dp50 = 0.364 µm) compared to the result of 40 V conditions (Dp50 = 0.446 µm). Higher electrostatic potentials increased the strength of electrostatic fields inside the conical section of the hydrocyclone. As the results show, for the same inlet flow rate, the radial migration velocity of the particles became higher. Then, the smaller particles could reach the conical collecting wall and the number of collected particles increased. Subsequently, higher particle collection efficiency was obtained by increasing the applied electric potentials. For the applied potentials below 40 V, the combination of centrifugal and electrostatic force of the particles which acted radially outward was too low to overcome the effect of the drag force acted inside, and there was no separation taking place. The coarse and fine particle size distributions obtained from the electrical hydrocyclone under ΔV of 0 V and 100 V conditions, respectively, are shown in Fig. 10a and b. The particle size distributions of the coarse and fine sides are nearly equal under the electrostatic potential of the 0 V condition, as shown in Fig. 10a. Hence the separation of sub-micron silica particles was very difficult in this case. The difference of particle size distributions between fine and coarse particles increases under the electrostatic potential of the 100 V case, as shown in Fig. 10b. The sample suspensions of both fine and coarse sides after 6 days of sedimentation time are shown in Fig. 11. Denser suspensions of the coarse side under 100 V electrical potential were obtained compared to the fine side, while there was no clear color difference between fine and coarse side suspensions of the 0 V case. From Figs. 10 and 11, it is
151
Fig. 11. Photographs of the classified slurry samples of the electrical hydrocyclone.
clear that the classification of sub-micron silica powder could be obtained by applying the electrostatic force to the hydrocyclone. Furthermore, lower applied electrostatic potentials are needed by the electrical hydrocyclone to achieve the classification of sub-micron particles, compared to that of the electrical gas cyclone, since the latter needs the applied potential above of 1000 V, in order to separate the submicron particles. Fig. 12 shows the relationship between the applied electrostatic force and the electrostatic current, when the classification experiment was carried out in the electrical hydrocyclone. The figure shows a linear relationship between electrostatic potentials and current under the slurry conditions of Co = 0.5 wt.% and t = 1.5 hr. This means that particles in the slurry have a constant resistance under various applied electrostatic potentials. This leads to the conclusion that a uniform particle charging occurred when the electrostatic potential was applied to the hydrocyclone under the slurry conditions indicated above. 3.3. Effect of the feed suspension's concentration on the particle classification performance of the electro hydrocyclone Fig. 13 shows the effect of the concentration of feed suspension, Co, on the partial separation efficiency of the electrical hydrocyclone. Fig. 14 shows the relationship between feed suspension concentration, Co, and 50% cut size, Dp50. The experiments were carried out at t = 1.5 h, and the ΔV were equal to 80 and 100 V. As can be seen, the
Fig. 10. Effect of applied electrostatic potentials on particle size distributions (a: 0 V, b: 100 V).
Fig. 12. Relationship between electrostatic potential and current.
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Fig. 13. Effect of feed suspension concentration on partial separation efficiency.
Dp50 decreased slightly, as the Co increased, when the values of Co were below 1.5 wt.%. As an example, in the case of 100 V, from 0.375 to 0.294 µm, until the value of Co was equal to 1.5 wt.%. But when the Co was higher than 1.5 wt.%, the Dp50 increased with the increase of feed suspension concentration (Fig. 15). In the case of 100 V, the Dp50 was 0.413 µm for Co equal to 2 wt.%. The Dp50 of the 100 V electrical hydrocyclone was lower than that of 80 V case. The increase of the hindered sedimentation's effect with the increase of the suspension concentration on the particle radial migration velocity might be the main factor of this phenomenon. The motion of the particles could be considered equal to that of the motion of single particle when the suspension concentration was below 1.5 wt.%, since the motion of particles was independent each other. When the concentration became higher, the effect of hindered sedimentation took place, the motion of the particles was interfered by the other's motion, and the radial migration velocity of the particles was decreased. These phenomenon caused the amount of the collected particles on the collecting wall was decreased, and resulted in the decreased separation performance of the electrical hydrocyclone, with the increase of the suspension concentration. On the other hand, Fig. 16 shows the relationship between the applied electrostatic current and potential under various suspension concentrations. The non-linear relationship between electrostatic current and potential took place under the condition of 2 wt.% of suspension concentration. The non-linear relationship between electrostatic current and potential means the difference resistance, compared to that of in the linear relationship. The change of the
Fig. 14. Effect of feed suspension concentration on 50% cut size.
Fig. 15. Relationship between electrostatic potential and current under various feed suspension concentrations.
resistance possibly means the change of the morphology of the attached ions at the surface of the particles changes. Higher electrical conductance of the particles was occurred for the higher suspension concentration in the case of applied potentials greater than 40 V. These conditions mean that the electrostatic conductance of the particles in that suspension was increased with the increase of the suspension concentration, and increased the particles' migration velocity. As mentioned above, under the dilute feed suspension condition (Co = 0.1 wt.%), the effect of hindered sedimentation on the radial migration velocity of the particles was still negligible. When the feed suspension's concentration increased slightly (Co ≤ 1.5 wt.%), the effect of hindered sedimentation on the radial migration velocity of the particles was still negligible, but the particles' electrostatic conductance was increased, and the amount of collected particles at the wall increased, and resulting in the decrease of Dp50 until a suspension concentration limit (Co = 1.5 wt.%). The effect of hindered sedimentation was increased with the further increase of the slurry concentration (Co N 1.5 wt.%). Even the particles' electrostatic conductance was increased with the increase of the suspension concentration, the hindered sedimentation phenomenon was considered has superior effect on the particles' radial migration velocity, and overcame the effect of electrical conductance. As the result, the radial migration velocity of the particles was decreased, and led to the
Fig. 16. Comparison between experimental and calculated results of 50% cut size diameter.
R.K. Tue Nenu et al. / Powder Technology 196 (2009) 147–155
decrease of collected particles in the wall, under the suspension concentration higher than 1.5 wt.%. Hence, the separation performance of the electrical hydrocyclone decreased with the increase of suspension concentration higher than 1.5 wt.%. This phenomenon is different with the standard hydrocyclone, since in the standard hydrocyclone, the 50% cut size diameter increases with the increase of suspension viscosity [8], but in the case of the electrical hydrocyclone, the separation performance shows the optimum value under a certain suspension concentration. From practical application, the special electrical hydrocyclone proposed in this study is able to separate the sub-micron particles.
in Eq. (7), the simple formulation of Richardson and Zaki [10] was used as the correction factor: f ðCo Þ = ðeÞ
− 4:65
ð8Þ
where ε denotes the fraction of liquid in the suspension. ε is defined as: ρs
ρf e= 1+
ð1 − Co Þ ρs ρf
ð1 − Co Þ
ð9Þ
Subtituting Eq. (9) to Eq. (7) results:
4. Proposed models To explain the experimental results of our special electrical hydrocyclone, the time of flight model, as derived by Rosin et al., [9] is used as the base of modeling. The model is modified with the addition of electrostatic mobility in the radial velocity term, and was applied in the conical section only. This model was based on the fact that the particles would reach the wall of the hydrocyclone's conical section, with equal traveling time in tangential and radial directions. The assumptions made in this model development are: (1) The particle is spherical in shape. (2) The drag force on the particle follows Stokes' law. (3) The charge on the central rod is relatively low, hence the ionic space charge density is assumed to be negligible. (4) The particle surface charge density shows a constant value. The time required to reach the wall of the conical section of hydrocyclone for single particle in a fluid medium is defined as: tθ =
153
2πRN uo
ð2Þ
vre
0 14:65 ρs 7 ð1−Co Þ Dp σ10 Er ρ f @ A = 3μ o 1 + ρρs ð1− Co Þ
ð10Þ
f
Eq. (10) indicates that the radial migration velocity of the particle is proportional to the particle diameter, the strength of the electrostatic field, and the inverse of the suspension concentration. The distance between the inlet section and the wall of the conical part is denoted as x, then, the time it took particles to reach this distance in radial direction is: tx =
x = vre
3μ o x
0
σ 10 Dp Er @ 7
ρs ρf ð1 − Co Þ
1 +
ð11Þ
14:65 A
ρs ρf ð1 − Co Þ
Equating Eqs. (11) and (2), and taking uo = Q/al will result in x: 0 14:65 ρs 7 2πRNσ 10 Dp Er al ρf ð1− Co Þ @ A x= 3Q μ o 1 + ρρs ð1− Co Þ
ð12Þ
f
where R is the mean radius of the hydrocyclone's conical part, and N is the number of the particle rotations inside the conical part of the hydrocyclone. The radial terminal velocity is defined as follows: ð3Þ
vr = vrc + vre
vrc and vre are the radial velocity of particles which is contributed to by the centrifugal and electrostatic force, respectively. In this study, the contribution of the centrifugal force on the radial velocity is considered to be negligible, because of the low inlet velocity and very small particle diameter. Hence, the particles' radial velocity was the product only of electrostatic force. The radial migration velocity is defined as:
Partial separation efficiency is defined as the fraction of particles which reach the wall: 0 14:65 ρs 2πRNσ 107 Dp Er l Co xluo x ρf ð1−Co Þ @ A Δη = = = a 3Q μ o Co aluo 1 + ρρs ð1− Co Þ
Dp50 is the particle diameter which corresponds to Δη = 0.5, then: 3Q μ 0 o
Dp50 =
4πRNσ 10 Er l@ 7
ρs ρf ð1 − Co Þ
1 +
7
vr = vre = μ e Er = 2
q = πDp σ
qEr 10 3πμ o Dp
ð4Þ ð5Þ
ρs ρf ð1 − Co Þ
14:65
ð14Þ
A
In order to determine the electrical field strength, assumption (3) is employed, then in cylindrical coordinates, with the axis of the two coaxial cylinders, the Laplace's equation can be written as [11]: dEr E + r =0 dr r
Then,
ð13Þ
f
ð15Þ
7
vre =
Dp σ10 Er 3μ o
ð6Þ
where σ is the surface charge density of the particles, while µo and Er are the suspension viscosity and the electrostatic field strength, respectively. For large amount of the particles suspended in the liquid medium, the correction factor of hindered sedimentation was added to Eq. (6) 7
vre =
Dp σ10 Er 3μ o f ðCo Þ
ð7Þ
Integration gives: Er =
1 ΔV ðR = Ri Þ r ln
ð16Þ
Ri is the radius of the center electrode. The particle is located somewhere between the center electrode and the wall of the conical section, and in this study, the location is assumed to be the center position between electrodes: r = 0:5ðR + Ri Þ
ð17Þ
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N is the number of particle rotations inside the conical section, and from Eq. (2) is given by: tθ =
2πRN V = uo Q
ð18Þ
N=
V 2πRal
ð19Þ
where V is the volume of the conical section in the hydrocyclone. Substituting Eqs. (16), (17) and (19) into Eq. (14) gives the final form of the equation to determine Dp50. Dp50 =
3Qμ o aðR = Ri Þ lnðR = Ri Þ 0 14:65 4Vσ 10 ΔV @ 7
ρs ρf ð1 − Co Þ
1 +
ρs ρf ð1 − Co Þ
ð20Þ
A
Eq. (20) indicates that the 50% cut size decreases as the electrostatic potential (ΔV) increases, and increases with the increase of the suspension concentration (Co), as long as the particle charge density (σ) has the constant value. The only unknown parameter is σ, and by fitting the calculated Dp50 data into the experimental results, with the use of the least square method, the constant value of σ can be found. The comparison between experimental and calculated results of Dp50 is shown in Fig. 17. The surface charge densities of silica particles which are found by fitting them into experimental results, have the values of about 2.3 µC/ cm2. These values have the same order as the values that have been reported previously [12,13]. Therefore it can be concluded that the σ values obtained are acceptable. By fitting the Eq. (20) to the Dp50 of experimental data, it is found that the surface charge density of the particles increases with the increase of the suspension concentration, within the range of suspension concentration up to 1.5 wt.%. The difference between the experiment and calculated results of Dp50 occurred, mainly because the time of flight model assumes that the tangential velocity of the particles in the conical section is equal to that of in the circular inlet section, as described in Eq. (2). In reality, the particles' tangential velocity in the conical section was smaller, because it is affected by the upward motion of liquid in the inner region of the hydrocyclone. The exact value of the tangential velocity in the conical section cannot be determined theoretically or empirically, but can be estimated by use of a more comprehensive method, such as Laser Doppler Velocimetry (LDV), or by CFD based numerical calculation. Assuming the tangential velocity of the particle in the conical section equal to that of in the inlet circular section, would result in the excessive slope of the calculated model. The other factors that might cause the calculated results is different with the experimental data are the assumption of negligibility tangential force and ionic space charge in the center rod. The tangential force still contributed in the particle deposition even under very low of inlet flow rate of the electrical hydrocyclone. Under the high applied electrostatic potential, the center rod possibly was subjected to a sufficient amount of charging, hence the values of the right hand term in Eq. (15) was not equal to zero. However, the simple developed model is in qualitative agreement with the experimental data. 5. Conclusions 1. The 50% cut size in the electrical hydrocyclone increased with the increase of feed suspension's waiting time after particle dispersion by the beads mill. 2. The classification of the sub-micron silica powder occurred at the applied electrostatic potentials equal to and greater than 40 V. The
classification performance of the electrical hydrocyclone increased with the increase of applied electrostatic potentials. 3. The 50% cut size decreased with the increase of feed suspension concentration until the concentration limit of 1.5 wt.%. The 50% cut size increased with further increasing of the feed suspension concentration. 4. The simple model, based on the time of flight model is qualitatively agreed with the experimental results. Nomenclatures a Inlet length (cm) Co Feed suspension concentration (wt.%) Dp50 50% cut size (µm) Dp̅ Mass median diameter (µm) E Total collection efficiency (–) Er Radial electrostatic field strength (V/cm) fcΔDp, ffΔDp Particle size distributions of coarse and fine sides, respectively (–) I Electrostatic current (mA) l Inlet height (cm) M, mc, mf Mass of particles on the feed suspension, collected particles in coarse and fine sides, respectively (g) N Number of particle rotations (–) q Charge of particles (C) Q Inlet flow rate (cm3/s) R Mean radius of the conical section in hydrocyclone (cm) Ri Radius of center electrode (cm) t Feed suspension waiting time (h) tx, tθ Time of the particles to reach the collecting wall in radial and tangential direction, respectively (m/s) T Feed suspension temperature (°C) uo Velocity of fluid medium (m/s) V Volume of hydrocyclone's conical section vr,vre,vrc Particle total radial velocity, particle radial velocity contributed by centrifugal force and electrostatic force, respectively (cm/s)
Greek letters Δη Partial separation efficiency (–) ΔV Applied electrostatic potentials (V) μo Fluid viscosity (g/cm s) ρp, ρf Particle and fluid density, respectively (g/cm3) μe Particle electrostatic mobility (cm2/V.s) σ Surface charge density (C/cm2) ζ Zeta potential (mV)
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