Article pubs.acs.org/IECR
Bubble Rise Velocity in a Fiber Suspension Wen-Hui Zhang,* Xiaoya Jiang, and Weitao Du Tianjin Key Lab of Pulp and Paper, College of Material Science & Chemical Engineering, Tianjin University of Science & Technology, Tianjin 300457, China ABSTRACT: Since a fiber suspension is opaque and fibers are prone to flocculate, it is difficult to measure the bubble rise velocity in a fiber suspension. In this study, a low-cost method combining an imaging technique with a conductivity technique is developed to estimate the rise velocity of single bubbles in a fiber suspension. The bubble velocity in a bleached kraft hardwood fiber suspension is investigated at the mass concentration of 0.2−1.0% (oven dry) and at the superficial velocity of 0.01 to 0.04 m/s. Finally, an empirical correlation among the bubble drag coefficient, Reynolds number (based on bubble size and water viscosity), and crowding number is developed for the fiber suspension.
1. INTRODUCTION Rise velocity (generally termed as terminal rise velocity in a stagnant liquid and slip velocity in a moving liquid) of gas bubbles in liquid or multicomponent media has become an important focus of research in many industrial and natural processes. Bubble rise velocity is an important design parameter, which decides the gas phase residence time or the contact time for interfacial transport. Bubble rise in liquid or multicomponent media is affected by many factors viz. bubble characteristics (size and shape), liquid properties (density, viscosity, surface tension, etc.), and operation conditions (temperature, pressure, and gravity).1,2 Though bubble rise velocity has been widely investigated for several years,3−10 little attention has been focused on the fiber suspension system.11,12 In the papermaking process, gas bubbles and their interaction with other substances in fiber suspensions may cause many problems related to pumping, dewatering, stock filtration, and sheet formation. Hence, gas removal is a very important part of the papermaking process. In the flotation deinking process, the behavior of a bubble not only decides the gas phase residence time but also affects the collision probability of bubble-ink particle. In the oxygen delignification process, though significant delignification can occur in the mixer during a short residence time, the bulk delignification is also important in high-aspect ratio columns. The bulk delignification is greatly dependent on the bubble-pulp contact time, which is also affected by bubble rise velocity.13 Hence, it is important for design and control, but little data for bubble rise velocity in fiber suspensions are available due to the complexity of the wood fiber suspension. A fiber suspension system is a complex system due to two main reasons. The first one is swelling, which means that a dry fiber can absorb water and swell to several times its normal size. The second one is flocculation. Fibers can flocculate even at mass fractions as low as 0.3% and form continuous fiber networks at mass fractions as low as 1%.14 Since bubble size and bubble rise velocity can be determined simultaneously, the imaging method is a powerful tool to study bubble behavior in a fluid.15 In fiber suspensions, a flash X-ray radiography method is often applied to visualize air flows due to its ability to penetrate the opaque fiber suspension.16,17 © XXXX American Chemical Society
However, in addition to high cost and stringent health and safety, the measurement accuracy is also affected by reactor size and the consistency of the fiber suspension. Recently, Haapala et al.11 applied submersed backlight illumination in a pressurized bubble column and a high-speed CMOS camera to study the local bubble rise velocity and hydrodynamic drag in papermaking process waters. However, this method may not be suitable for high consistency (i.e., more than 0.4 wt %) due to low penetration of the light. As far as we know, since fiber flocculation can lead to the heterogeneous distribution of fiber concentration or floc size, it is more practical to measure the average bubble rise velocity based on a long distance. In this paper, the aim of the study is to develop a low-cost method to measure bubble rise velocity in a fiber suspension at the mass concentration of 0.2−1.0 wt % and obtain the experimental data for the validation of multiphase CFD models in white waters or flotation deinking system. The new method combines an image technique with a conductivity technique and can determine bubble rise velocity and bubble size at the same time. Bubble size and bubble rise velocity for a bleached kraft hardwood fiber suspension are experimentally investigated in an upflow column. Finally, a simple empirical correlation among the bubble drag coefficient, Reynolds number, and crowding number14 is developed.
2. EQUIPMENT AND MATERIALS A schematic diagram of the experiment is shown in Figure 1. The main components of the experiment include a stirred degassing tank, a centrifugal pump, an electromagnetic flow meter, and a test column. The test column is constructed of a 0.1 m ID Plexiglas tube that is 1.6 m in height. The diameter of the top part is 0.3 m. The distributor, which is located 0.15 m from the bottom of the column, is a perforated plate containing 19 holes of 8 mm diameter arranged in an equilateral rectangular configuration. Received: December 17, 2012 Revised: May 26, 2013 Accepted: May 26, 2013
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degassing tank, which can lead to horizontal flow at the top of the tank to minimize bubble residence time. All things can avoid bubbles from entering the test column. The rough bubble size is controlled by stainless steel tubes of different sizes, whose inner diameters are in the range of 0.5−6 mm. It is not necessary to control the exact bubble size, since bubble rise velocity and bubble size are determined at the same time. In this work, taking into account the fiber flocculation, we consider that it is better to measure the bubble rise velocity based on a long distance. The measurement system is designed as follows. A single bubble is released by a stainless steel tube, whose surface is coated with insulating paint. The inner wall of the stainless steel tube is connected to the conductivity measurement system with a sampling rate of 500 Hz. When a bubble is formed at the tip of the tube and the inner wall of the stainless steel tube is in contact with gas, the conductivity signal is at a low level. When the bubble is just released at the tip and the inner wall is in contact with fiber suspension, the conductivity signal is at a high level. Hence, the bubble generation time can be detected by the sudden change of the conductivity signal. In other words, when one bubble is released, the conductivity signal will change from the low level to the high level. The bubble rises along the column to the top outlet, where it is captured by a transparent Plexiglas plate. The bubble size measurement device is shown in Figure 2. The bubble terminal
Figure 1. Schematic diagram of the experiment.
A bleached kraft hardwood pulp is used in this study. Tap water is used as the liquid phase. The dry pulp sheet is soaked for 6 h and is beaten to 35° SR in a Valley beater. Then, the pulp is washed several times and centrifuged to about 27% consistency (oven dry weight). Finally, it is stored at 5 °C in the form of wet pulp. Before the experiment, the wet pulp is disintegrated in a laboratory hydropulper until all fiber bundles are dispersed. Additional tap water is added to adjust the mass fraction of the fiber suspension. The fiber morphology is analyzed by a fiber tester (model 912, Lorentzen & Wettre Co. Ltd., Sweden). The average length and the average diameter of fibers is 0.72 mm and 23.8 μm respectively. Fiber coarseness, defined as weight per fiber length, is 108.8 μg/m in this study. Figure 2. Schematic diagram of the measurement device for bubble size estimation.
3. MEASUREMENT AND ANALYSIS METHOD All experiments in this study are carried out under atmospheric pressure, and the temperature is about 27 ± 1 °C. During the test, the fiber suspension is pumped into the test column from the bottom. Then it leaves the test column from the top, goes into the stirred degassing tank, and returns to the test column finally. The velocity is adjusted by a valve in the range of 0.01 to 0.04m/s (based on the column area). After the flow is stable and no bubble is detected in the test column, a single bubble is generated by a syringe through a special stainless steel tube and the position is 0.2m above the distributor. To make sure that only one single bubble is released, three requirements must be met. First, gas is delivered by hand carefully from a syringe to the stainless steel tube. The conductivity signal changes only once during an experiment if only one bubble was released, which will be explained later. Second, the measurement time interval is greater than the time for the fiber suspension traveling along the column or hydraulic retention time. Third, it is also important to separate bubbles from the pulp suspension in the degassing tank to keep bubbles from entering the column. The pulp suspension flows into the degassing tank through an immersion tube and the export is on the wall of the immersion tube. In addition, there is an inclined plate in the
time, detected by a CCD camera (Beijing Join Hop Image Technology Ltd., OK-AM 1530, resolution: 1024 × 1024 pixels, sampling rate: 25 Hz) on the top view, is determined when the bubble collides with the capture plate. A 100 W high efficient light is used for illumination at an angle of 45° to the capture plate. In most cases, the plate can capture bubbles. However, once the plate fails to capture a bubble, it needs to wait for a given period to measure the next bubble. The period is larger than the hydraulic residence time. The distance between the release and the capture of a bubble is 128 cm, which is long enough to minimize the effect of the local concentration differences and bubble acceleration on the velocity measurement. In the study, we assume that the flow is uniform along the column and bubble rise trajectory in the pulp suspension is linear. Though bubble trajectory will deviate from the straight line even in the pure water, the linear hypothesis could be accepted in the statistics. Because the image sampling and the conductivity signal sampling is carried out simultaneously, bubble velocity could be calculated by the distance and B
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Figure 3. Bubble slip velocity at different mass concentrations and at different superficial velocities of fiber suspensions. (a) C = 0.2 wt %; (b) C = 0.4 wt % ; (c) C = 0.6 wt %; (d) C = 0.8 wt %; and (e) C = 1.0 wt %.
effect of pressure difference along the column and the pressure from the peristaltic pump on bubble size could be ignored. The main image analysis algorithm is described as follows: (1) Image binarization. Bubble difference images are binarized using Otsu’ method.18 A bubble difference image is obtained by subtracting an image from a reference image without bubbles. (2) Parameter estimation for candidate objects. The projected area, A, is measured by counting the number of square pixels in a candidate object and the perimeter, P, is calculated by 8connectivity chain code. (3) Bubble recognition. Bubble is determined by the shape factor ((4πA)1/2/P). In this paper, we suggest that a candidate object is regarded as a bubble when the shape factor is greater than 0.8.19 (4) Bubble size estimation. Bubble equivalent diameter is defined as De = (D12D2)1/3. Here, D1 is the major axis length, and D2 is the minor axis length.
the difference between the generation time and the terminal time. The captured bubble could be sucked by a peristaltic pump to an observation chamber (60 × 90 × 20 mm). The sucking tube was filled with water before a bubble is sucked and this ensures that no bubble but the captured bubble is sucked into the tube. During sucking, the velocity must be slow, otherwise it will lead to bubble breakup. Bubble images are recorded by a CCD camera at a sampling rate of 25 Hz and a 100W trichromatic light is used as backlight source. The image sequences are analyzed automatically with an image analysis algorithm to determine bubble size. The image analysis algorithm includes a bubble recognition method since fibers may be sucked into the observation chamber especially at high concentration of fiber suspension. Here, we assume that the C
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4.2. Correlation for Bubble Rise Velocity in Fiber Suspensions. The drag coefficient based on the force balance around a bubble moving in fluid5 can be given as
4. RESULTS AND DISCUSSION 4.1. Bubble Rise Velocity in Fiber Suspensions. Pelton and Piette12 used a Plexiglas cylinder (i.d. = 70 mm) to study bubble escape probability in quiescent wood fiber suspensions. The bubble escape probability had been used to evaluate the network strength of fiber suspensions. However, since the settling property of the fiber suspension may lead to heterogeneous distribution of fiber concentration or floc size along the column, the method cannot estimate the bubble rise velocity well in fiber suspensions. For this reason, it is better to estimate the bubble rise velocity in a moving fluid. Figure 3 shows the bubble slip velocity at different mass concentrations and at different superficial velocities of fiber suspensions. The bubble slip velocity is the bubble rise velocity relative to the superficial velocity of the fiber suspension. From the figure, it is generally shown that bubble slip velocity increases as bubble size increases. When the mass concentration is low (i.e., no more than 0.6 wt %), bubble slip velocity curves are almost the same at three superficial velocities of fiber suspension. However, when the mass concentration continues to increase, bubble slip velocity curves are almost the same only at higher superficial velocities and the slip velocities of small bubbles are nearly zero at low superficial velocity. All of these may be derived from the fiber flocculation. Kerekes et al.14,20 introduced a crowding number (or crowding factor) to describe the fiber flocculation, which is defined as the number of fibers in a volume swept out by the mean fiber length. This parameter is given by Nc =
Cd =
4g Δρde 3ρp us 2
where Δρ = ρp − ρa ≈ ρp, ρp is apparent density of fiber suspension, de is equivalent bubble diameter, us = ub − up, is bubble slip velocity, and up is superficial velocity of fiber suspension. In short, the drag coefficient of a bubble can be estimated by (4gde)/(3us2). In the literature,22 the flow behavior of the fiber suspension can be fitted to a Herschel−Bulkley model. The shear stress, τ, can be defined as τ = τy + kγn = μpγ. where τy is yield stress, which is always used to estimate the network strength of fiber suspension.23 Apparent viscosity fiber suspension, μp, can be given as (τy + kγn)/γ·. Ansley and Smith24 postulated that the drag could consist of two components: one due to the viscosity and the other due to yield stress in Bingham plastic fluids. The researchers25−27 introduced three dimensionless parameters (the generalized Reynolds number, the Bingham number, and the yield number) to correlate with the drag coefficient. However, it is not easy to measure rheology property of fiber suspensions.28 Wide gap size and enough rough wall is needed to overcome the depletion layer. The selection for gap size or rough wall may be dependent on the floc size or the fiber suspension consistency. Since the data obtained by different methods is significantly different,28 water viscosity is used for calculating the Reynolds number (Re* = ρpusde/μw) in this study. As far as we know, the consistency of fiber suspension and the fiber property (such as fiber length, fiber coarseness) have a great effect on rheology of fiber suspension (such as τy, k, and n). Bennington et al.23 found that the yield stress is accurately correlated with the volume concentration of fiber suspension. Bennington and Kerekes29 adopt an indirect approach to measure the shear viscosity of the semibleached kraft (SBK) softwood fiber suspension. In their study, they found that the apparent viscosity strongly depends on the third power of mass concentration of fiber suspension. Based on the above considerations, a correlation among Re*, Nc, and Cd is developed to express the relationship of bubble slip velocity, bubble size, and fiber suspension consistency. In practical situations, a bubble surface is sufficiently contaminated and almost no-slip surface is attained. In the study, since the bleached kraft hardwood pulp is diluted by tap water, the bubble surface may be retarded partially. The drag coefficient of a bubble with an immobile interface in newton fluids can be predicted as a function of bubble Reynolds number (Re = ρLubde/μL)2.
π L2 L2 Cm ≈ 0.5Cm ω ω 6
where L is the length-weighted average length of the pulp fibers (m), Cm is the oven dry mass concentration (kg/m3), and ω is the fiber coarseness (weight per unit length of fiber, kg/m). Kerekes and Schell20 introduced a critical value, that when Nc ≈ 60, fiber suspensions have about three contact points per fiber and fibers form a rigid network. Martinez et al.21 introduced a “gel crowding factor” Nc ≈ 16 and “gel” represents the formation of an incipient continuous phase, but mechanical strength has not yet developed. In this study, when mass concentration is no more than 0.6 wt % (corresponds to Nc < 16), the fiber suspension behaves as essentially dilute21 and has no yield stress. If the concentration continues to increase (corresponds to Nc > 16), the fiber suspension starts to form a continuous phase, and bubble movement needs to overcome the network strength of fiber suspension. Hence, at low concentration, the apparent viscosity of fiber suspension increases slowly, which leads to a slow change of the bubble slip velocity with bubble size; when the concentration is beyond the critical value, the apparent viscosity increases rapidly due to the formation of fiber network, which cause a significant change of the bubble slip velocity with bubble size. In addition, the critical bubble size for the zero slip velocity at low superficial velocity of fiber suspension is greater than that at high superficial velocity, which may be caused by the heterogeneous distribution of fiber concentration or floc size at low superficial velocity in the test column. Moreover, since fiber suspension can be regarded as Herschel-Bulkley fluid22 and the velocity gradient around a bubble is greater at high flow rate, the bubble can overcome the initial resistance more easily at high flow rate.
Cd =
24 (1 + 0.1935Re 0.6305), 20 ≤ Re ≤ 260 Re
log10 Cd = 1.6435 − 1.1242 log10 Re + 0.1558(log10 Re)2 , 260 ≤ Re ≤ 1500
The ratio of the bubble diameter to column diameter is less than 0.05 in this study, and the wall effect on the rise of single bubble may be ignored.30 D
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Figure 4. Bubble drag coefficient curves with respect to Re* at different Nc at the flow rate of 0.02 and 0.04 m/s. (a) Nc = 4.8 for C = 0.2 wt %; (b) Nc = 9.5 for C = 0.4 wt %; (c) Nc = 14.3 for C = 0.6 wt %; (d) Nc = 19.1 for C = 0.8 wt %; (e) Nc = 23.8 for C = 1.0 wt %.
5. CONCLUSION A new low-cost method is developed to estimate the bubble rise velocity in a fiber suspension. The method combined a conductivity technique with an image technique. The bubble rise (slip) velocity in a bleached kraft hardwood fiber suspension is investigated. The results showed that when the mass concentration of the fiber suspension is low, which corresponds to Nc < 16, bubble slip velocity curves are almost the same at three superficial velocities of fiber suspension. However, when the concentration continues to increase, bubble slip velocity curves are almost the same only at higher superficial velocities and bubble slip velocities of small bubbles are nearly zero at low superficial velocity. Hence, it is better to measure the bubble rise velocity at high concentration under high flow conditions, in order to minimize the effect of the heterogeneous distribution of fiber consistency or floc size along the column. An empirical correlation for Re*, Nc, and Cd is developed, when the mass concentration of fiber suspension is from 0.2 to 1.0 wt % and the superficial velocity of fiber
In this study, an empirical correlation for the experiment data at high superficial velocities (0.02 and 0.04 m/s) can be expressed as ln Cd = A + B ln Re* + C(ln Re*)2 , 200 < Re* < 1000, 4.8 < Nc < 19.1
where A = 16.26, B = −3.9010−4Nc3 + 1.97 × 10−2Nc2 − 1.68 × 10−1Nc − 5.15, and C = −0.142B − 0.323. Figure 4 shows the bubble drag coefficient curves with respect to Re* in the range of 200−1000 at different Nc. The blue solid line is the calculated value and the solid point is the experimental data. At low concentration, there is a minimum value for bubble drag coefficient as Re* increases; however, bubble drag coefficient decreases with Re* at high concentration. It is also shown that the calculated value fits well to the experimental data. E
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(18) Otsu, N. A Threshold Selection Method from Gray-Level Histograms. IEEE T. Syst. Man Cy. 1979, SMC-9, 62. (19) Bailey, M.; Gomez, C. O.; Finch, J. A. Development and Application of an Image Analysis Method for Wide Bubble Size Distributions. Miner. Eng. 2005, 18, 1214. (20) Kerekes, R. J.; Schell, C. J. Characterization of Fibre Flocculation by a Crowding Factor. J. Pulp Pap. Sci. 1992, 18, 32. (21) Martinez, D. M.; Buckley, K.; Jivan, S.; Lindstrom, A.; Thiruvengadaswamy, R.; Olson, J. A.; Ruth, T. J.; Kerekes, R. J. Characterizing the Mobility of Papermaking Fibres During Sedimentation. The Science of Papermaking: Transactions of the 12th Fundamental Research Symposium; The Pulp and Paper Fundamental Research Society: Bury, U.K., 2001. (22) Gomez, C.; Derakhshandeh, B.; Hatzikiriakos, S. G.; Bennington, C. P. J. Carbopol as a Model Fluid for Studying Mixing of Pulp Fibre Suspensions. Chem. Eng. Sci. 2010, 65, 1288. (23) Bennington, C. P. J.; Kerekes, R. J.; Grace, J. R. The Yield Stress of Fibre Suspensions. Can. J. Chem. Eng. 1990, 68, 748. (24) Jossic, L.; Magnin, A. Motion of Spherical Particles in a Bingham Plastic. AIChE J. 1967, 13, 1193. (25) Beaulne, M.; Mitsoulis, E. Creeping Motion of a Sphere in Tubes Filled with Herschel−Bulkley Fluids. J. Non-Newtonian Fluid Mech. 1997, 72, 55. (26) Atapattu, D. D.; Chhabra, R. P.; Uhlherr, P. H. T. Creeping Sphere Motion in Herschel-Bulkley Fluids: Flow Field and Drag. J. Non-Newtonian Fluid Mech. 1995, 59, 245. (27) Jossic, L.; Magnin, A. Drag and Stability of Objects in a Yield Stress Fluid. AIChE J. 2001, 47, 2666. (28) Derakhshandeh, B.; Kerekes, R. J.; Hatzikiriakos, S. G.; Bennington, C. P. J. Rheology of Pulp Fibre Suspensions: A Critical Review. Chem. Eng. Sci. 2011, 66, 3460. (29) Bennington, C. P. J.; Kerekes, R. J. Power Requirements for Pulp Suspension Fluidization. Tappi J. 1996, 79, 253. (30) Krishna, R.; Urseanu, M. I.; van Baten, J. M.; Ellenberger, J. Wall Effects on the Rise of Single Gas Bubbles in Liquids. Int. Comm. Heat Mass Transfer. 1999, 26, 781.
suspension is 0.02 and 0.04 m/s. The correlation can be only given by ln Cd = A + B ln Re* + C(ln Re*)2 for 200 < Re* < 1000 and 4.8 < Nc < 19. Here, A = 16.26, B = −3.90 × 10−4Nc3 + 1.97 × 10−2Nc2 − 1.68 × 10−1Nc − 5.15, and C = −0.142B − 0.323.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +86 022 60602199. Fax: +86 022 60601854. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial supports by National Natural Science Foundation of China (No. 31000284).
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REFERENCES
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