气泡碰撞导致气泡破碎研究

Chemical Engineering Science 62 (2007) 1741–1752 www.elsevier.com/locate/ces Bubble coalescence at sieve plates: II. Effect of coalescence onmass transfer. Superficial area versus bubble oscillations Mariano Martín∗, Francisco J. Montes, Miguel A. Galán Departamento de Ingeniería Química y Textil, Universidad de Salamanca, Pza. de los Caídos 1-5, 37008 Salamanca, Spain Received 22 May 2006; received in revised form 5 December 2006; accepted 9 December 2006 Available online 27 December 2006 Abstract Bubble columns are among the most used equipments for gas–liquid mass transfer processes. This equipment’s aim is to generate gas dispersions into a liquid phase in order to improve the contact between phases. Bubble coalescence has always been one of their greatest problems, since it reduces the superficial gas–liquid contact area. However, bigger bubbles can oscillate, and these oscillations increase the mass transfer rate by means of modifying the contact time as well as the concentration profiles surrounding the bubble. In the present work, the coupled effect has been studied by means of two-holed sieve plates with diameters of 1.5, 2 and 2.5mm each, close enough to allow the coalescence and separated enough to avoid it. The results show that although coalescence decreases mass transfer rate from bubbles the deformable bubble generated can, in certain cases, balance the decrease in mass transfer rate due to the reduction in superficial area. This fact can then be used to avoid the harmful effect of coalescence on the mass transfer rate. Empirical and theoretical equations have also been used to explain the phenomena. � 2007 Elsevier Ltd. All rights reserved. Keywords: Oscillating bubbles; Hydrodynamics; Bubble columns; Coalescence; Mass transfer 1. Introduction Common equipments used for mass transfer operations are bubble columns and stirring tank reactors. Bubble columns have advantages like simple operation, maintenance and construc- tion and high mass transfer rates. The main disadvantage is the coalescence process which is very difficult to avoid (Shah et al., 1982). The coalescence process has been studied in the central region of the bubble column, where bubble break-up and coa- lescence processes reach an equilibrium which determines the bubble mean diameter, responsible for the superficial area avail- able for transport phenomena between the gas phase and the liquid phase (Prince and Blanch, 1990; Camarasa et al., 1999; Pohorecki et al., 2001). In the lower region of the bubble column, the coalescence depends on the dispersion device. Sieve plate design is usually carried out according to simple rules of thumb (Walas, 1990), ∗ Corresponding author. Tel.: +34 923294479; fax: +34 923294574. E-mail address: mariano.m3@usal.es (M. Martín). 0009-2509/$ - see front matter � 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.12.019 so that typical separation between orifice centres ranges from 2.5 to 4 times the orifice diameter (Walas, 1990; Perry and Green, 2001). The bubble diameter depends on the orifice diam- eter and is usually between 3 and 4 times the orifice diameter, determined by the gas flow rate (Miller, 1974) and the phys- ical properties of the working fluids (Sherwood et al., 1975); (Bhavaraju et al., 1978). As a result, bubble coalescence over the plate may occur if the gas flow rate is high and the separation between two orifices is small along with the effect of the physical properties of the liquid on the bubble size, which also determines the coalescence processes in the central region of the column. Furthermore, the mass transfer between phases improves the efficiency of the coalescence process. The mass transfer mod- ifies the surface tension since it modifies the solute concentra- tion in the gas–liquid interphase. The solute usually reduces the surface tension. Leshansky (2001) studied the effect of the direction of mass transfer on the liquid drainage and thus on the coalescence rate. In case of mass transfer from the dispersed phase to the continuum phase, the surface tension in the liquid film is lower than that of the external film. This superficial 1742 M. Martín et al. / Chemical Engineering Science 62 (2007) 1741–1752 tension gradient generates a tangential force in the inter- phase which modifies the radial movement of the liquid film, Marangoni effect, and accelerates the drainage process, reduc- ing the drainage time. As a result, the bubble coalescence rate is enhanced by the mass transfer. The coalescence effectiveness is increased (Leshansky, 2001; Saboni et al., 2002). The formation of bigger bubbles, due to coalescence, has two effects on the hydrodynamics with an important result in the mass transfer. On the one hand, there is a reduction in the superficial area available, the main reason for considering coalescence as a harmful process in mass transfer operations (Shah et al., 1982). On the other hand, the increment in the bubble size also increases the deformability of the bubbles and their oscillating amplitudes. Oscillating bubbles improve the mass transfer rate due to the modification of the contact times and the concentration profiles surrounding the bubbles (Montes et al., 1999; Martín et al., 2006). In case of drops, an increment in the mass transfer rates immediately after coalescence, has been reported, followed by a rapid fall to zero, rebound to an intermediate value and finally decay to the level expected for an undisturbed drop, with the result of a net decrease in the mass transfer rate (Defrawi and Heideger, 1978). The aim of the present work is to determine if the decrease in the rate of mass transfer due to the reduction in superficial area can be balanced with the increase due to the oscillatory behaviour of the bubbles in both Newtonian and non-Newtonian fluids. 2. Theoretical considerations The coalescence of bubbles is a complex process with several results in the hydrodynamics of the bubble column as far as mass transfer processes are concerned. When two bubbles get closer, like those about to coalesce, there will be a reduction in the concentration gradient in the vicinity of the bubble surfaces. Sherwood number drops from 2, due to molecular diffusion, to 1.98 when the distance between centres is a hundred times the sphere bubble radius, to 1.6 if the former distance is 4 times the bubble radius and in case bubbles touch each other, the Sherwood number reaches a minimum value of 1.386 (Skelland, 1974). The coalescence between bubbles reduces the contact area between the gas phase and the liquid phase, which can be un- derstood as a disadvantage, since the aim of the dispersion is to increase and to improve that contact. Surface area of a bub- ble resulting from a coalescence process is less than twice the superficial area of a single bubble. The real contact area de- pends on the final shape of the bubble. However, bigger bubbles are, within some limits, more de- formable than the little ones (Clift et al., 1978), and their oscillation amplitudes are also bigger than those of small bub- bles. The relationship between the oscillation amplitude and the bubble size is difficult to determine since bubble oscilla- tion amplitude depends on the liquid turbulence but increases greatly from zero as soon as the bubble oscillation behaviour changes from a rigid bubble to an oscillating bubble (Montes et al., 1999). These oscillations increase the mass transfer since the contact times and the concentration profiles surrounding bubbles are modified by the oscillatory process (Montes et al., 1999; Martín et al., 2006). Apart from the experimental measurements, empirical equa- tions (Shah et al., 1982) as well as theoretical ones (Montes et al., 1999; Martín et al., 2006) are used to study the coupled phenomena exposed. For Newtonian fluids, typical empirical volumetric mass transfer coefficient correlations are Eqs. (1) (Akita and Yoshida, 1974) taken from Shah et al. (1982) and (2) Kawase et al., (1987): kLa = 0.6 · ( DL D2T )( �L DL )0.5 · ( gD2T �L � )0.62 · ( gD3T �2L )0.31 · �1.1G , (1) kLa = 0.452 · ( DL D2C ) · ( �L DL ) 1 2 · ( gD2C�L � ) 3 5 · ( uGDC �L ) 3 4 · ( u2G gDC ) 7 60 . (2) The superficial gas velocity, uG, is defined as the gas flow rate in the cross-sectional area of the column. From Higbie’s theory (Shah et al., 1982), kL = ( 4 ·DLUB �db ) 1 2 . (3) According to Sidemann (Sidemann et al., 1966), the gas hold- up can be determined as the relation between the superficial gas velocity, uG, and the bubble rising velocity, UB : �G = uG UB . (4) The rising velocity of the bubbles, UB , can be expressed as follows (Shimizu et al., 2000): UB = [ 2.14 · � �Ldeq + 0.505 · gdeq ]0.5 . (5) The specific superficial area is calculated as a = 6 · �G deq . (6) For rigid bubbles, the Sherwood number is given by (Bird et al., 1992) NSh = 2√ � N 1 2 Pe. (7) If the system contains oscillating bubbles, the Sherwood number can be calculated for an oscillatory period as M. Martín et al. / Chemical Engineering Science 62 (2007) 1741–1752 1743 (Montes et al., 1999) NSh = 2√ � N 1 2 Pe [ In1 + In2 A �2n N 1 2 We ] , (8) where In1 and In2 are constants that depend on the bubble geometry: In1 = 3 4� √ 2 ∫ � 0 ∫ � 0 N (�) �r �� [ F 2n + ( �Fn �� )2] 12 × sin � d� dt, (9) In2 = 38� ∫ � 0 ∫ � 0 N(�) �r �� [ F 2n + ( �Fn �� )2] 12 sin � d� dt. (10) These equations are valid for every oscillation mode, where the radial derivative in the normal direction to the bubble surface is given by �r �� (�, t)= 1‖ cos[�+ tan−1(�n)]‖ , (11) and �n is the tangent to the interphase at each point of the bubble surface: �n = Fn + cos � dFn/d cos � sin � dFn/d cos �− Fn/ tan � (12) with Fn(q, t)= 1+ AF 1n(q, t)+ · · · , (13) F 1n = cos(t)Pn(cos �). (14) Pn(cos �) is the n degree Legendre polynomial and A, the am- plitude of the oscillation, is defined by (Schroeder and Kintner, 1965) A= dmax − dmin 2deq . (15) N(�) is a dimensionless geometrical function depending on the angular coordinate, �, of each point in the bubble surface defined by N(�)= sin 2 � (1− (3/2) cos �+ (1/2) cos3 �) 12 . (16) For non-Newtonian viscous fluids, some empirical correla- tions have been used, Eqs. (17) (Deckwer et al., 1981) and, (18) (Nakanoh et al., 1980) taken from Shah et al. (1982) and Eq. (19) (Godbole et al., 1984): kLa = 0.00315 · u0.59G · −0.84eff , (17) kLaD 2 C Di = 0.09 · ( �eff Di )0.5 · ( gD2C · �L � )0.75 · ( gD3C �2eff )0.39 · ( uG gDC )( 1+ C ( ub∞ · � dvs ))m−1 , (18) kLa = 8.35× 10−4 · u0.44G · −1.01eff . (19) The gas hold-up used in the calculation of the specific surface area can be determined by means of (Godbole et al., 1984) �G = 0.207 · u0.6G · −0.19eff . (20) The effective viscosity is defined by (Godbole et al., 1984) eff =m( ˙)n−1, (21) ˙= 5000 · uG. (22) For both inviscid and viscous fluids, an equation previously developed, Eq. (23) (Martín et al., 2006), has been used. The Sherwood number depends on the fluctuations of the area which modify not only the available surface area but also the concen- tration profile surrounding the bubble, so that the Sherwood number for a rigid bubble is modified by a term which calcu- lates that enhancement effect. For a rigid bubble freely rising that term is 1. In case of inviscid fluids, the integration time will be that of an oscillatory period, since there is no decay in the oscillation amplitude, while for viscous fluids it must be the time that a single bubble takes to reach the top of the liquid column. Sh= √ 2 � N 1 2 Pe · I 1 2 S , (23) IS = 1 T ∫ T 0 ∫ � 0 V ′�|n=1Fn [ F 2n + ( �Fn �� )2] 12 sin2 � d� dt, (24) V ∗� = 1 UB ( V (0) � + A ( −1 R2 · � sin � [ ��(1) �� − 2F (1)n ��(0) �� +F (1)n �2�(0) ��2 ])) . (25) 3. Materials and methods To determine the effect of the coalescence on the mass trans- fer rate, the combined effect of the oscillations and the spe- cific area reduction, two physical systems are used: air–water and air–1.4% carboxymethyl cellulose (CMC) in water. Since coalescence can be affected by the presence of solutes in the media, in this work coalescence will be obtained by means of the appropriate separation of holes bore in the sieve plates. The experimental set-up is shown in Fig. 1. The bubbles are generated in a bubble column with a cross- sectional area of 15×15 cm. A gas chamber divided into two is placed at the bottom of the bubble column. Each gas chamber is fed separately. On the top of the gas chamber a two-holed sieve plate is fixed. Each hole corresponds to the exit of each gas chamber so that two bubbles are generated in parallel. Total gas flow rates were 0.3×10−6, 0.6×10−6 and 1.4×10−6 m3/s. Stainless steel sieve plates are used as dispersion devices with two equal bore orifices of 1.5, 2 and 2.5mm in each plate with 1744 M. Martín et al. / Chemical Engineering Science 62 (2007) 1741–1752 Fig. 1. Experimental set-up. (1) High-speed video camera, (2) optical table, (3) bubble column, (4) fibre optic, (5) compressed air, (6) rotameter, (7) computer, (8) compressed nitrogen, (9) oxygen electrode. Table 1 Sieve plate configurations for mass transfer measurements Do (mm) Separation between holes (mm) Coalescence No coalescence 1.5–1.5 3 5.5 2–2 3.5 6 2.5–2.5 4 6.5 separations ranging from 3 to 6.5mm. The plate configurations used are reported in Table 1. For each orifice diameter, a small separation between holes and a bigger one are used in order to secure and avoid coalescence. The height of liquid over the plate is 8 cm. A high-speed video camera records the generated and ris- ing bubbles. Images are edited by means of MOTIONSCOPE� software. These images allow the calculation of the experimen- tal amplitudes of oscillation, using Eq. (15), as well as the spe- cific area. The mass transfer coefficient is calculated using the oxygen electrode method with an Oxi–92 Crison electrode. The transitory response of the oxygen electrode must be taken into account to determine the mass transfer coefficient (Rainer, 1990). The simplest model to analyse the oxygen transfer through the electrode membrane is assuming that there is one- dimensional diffusion perpendicular to the membrane. The process can be modelled, according to Fick’s Law, as follows: �Csensor �t =Ksensor(CO2 Liq − Csensor). (26) Csensor is the oxygen concentration inside the electrode and the value shown at the electrode LCD screen, Ksensor is the electrode constant and CO2 Liq is the oxygen concentration in the liquid phase. Oxygen transfer from bubbles to the liquid phase is given by �CO2 Liq �t = kLa(CO2 Gas − CO2 Liq), (27) where CO2 Gas is the oxygen concentration in the gas phase (Vandu and Krishna, 2004). The measure of the oxygen transfer from the bubbles injected in the liquid phase required previous deoxygenation of the liquid. The liquid is saturated with oxygen due to its contact with the atmosphere. So nitrogen will be injected to take the place of the oxygen in the liquid phase. Since it was useless saturating liquid phase with nitrogen before injecting the air, both previous Eqs. (26) and (27) have to be integrated taking CO2 Liq = CO2 ini = Csensor at t = 0, CO2 Liq = CO2 Gas + (CO2 ini − CO2 Gas) exp[−kLat], (28) Csensor = CO2 Gas − (kLa)(CO2 ini − CO2 Gas) exp[−Ksensort] Ksensor − kLa + Ksensor(CO2 ini − CO2 Gas) exp[−kLat] Ksensor − kLa . (29) To calculate Ksensor, the response time, td , is used. It is defined as the required time to achieve 63% of the total re- sponse (Van’t Riet, 1979). To carry out the calibration of the electrode a glass of water was saturated with oxygen and an- other glass was saturated with nitrogen (0% oxygen saturation), the concentration profile of oxygen was recorded versus time. The response time is calculated through td = −Ln(0.37) Ksensor . (30) Experimental result for Ksensor is 0.230 s−1. 4. Results and discusion Bubble oscillations depend on the physical properties of the liquid surrounding the bubble. In this study water, as inviscid fluid, and an aqueous solution of CMC (1.4%w/w CMC), as viscous fluid, are used. Small bubbles are generated no mat- ter which fluids behave as non-oscillating ones, while bigger bubbles oscillate (Clift et al., 1978). In a fermentation process, the liquid viscosity changes heavily. The liquid behaviour may switch from Newtonian to non-Newtonian. Viscosity absorbs some of the oscillation energy and thus the amplitude of oscilla- tion decreases (Valentine et al., 1965). Experimentally bubbles recorded in water show (Fig. 2) a more irregular and smoother shape than those generated in a more viscous fluid. M. Martín et al. / Chemical Engineering Science 62 (2007) 1741–1752 1745 Fig. 2. Bubbles rising in water (A,C) and in 1.4% CMC (B,D). (aA) (Do = 2mm, Sep = 4mm, Qc = 0.6 × 10−6 m3/s), (b) (Do = 2mm, Sep = 5mm, Qc = 0.6× 10−6 m3/s), (c) (Do = 2mm, Sep= 3.5mm, Qc = 0.6× 10−6 m3/s), (d) (Do = 2mm, Sep= 3.5mm, Qc = 0.6× 10−6 m3/s). Fig. 3. Non-coalescence system, air–water. Do = 2.5mm, Sep= 6.5mm and caudal 0.6× 10−6 m3/s. Time step: 5ms. 1746 M. Martín et al. / Chemical Engineering Science 62 (2007) 1741–1752 Fig. 4. Coalescence system, air–water. Do= 2.5mm, Sep= 4mm and caudal 0.6× 10−6 m3/s. Time step: 5ms. 4.1. Air–water system In Figs. 3 and 4 non-coalescence and coalescence processes are reported, respectively. Once the bubbles have detached from the orifice, the bubble shape is irregular, but their oscillations seem to be superficial waves around an unperturbed sphere. In the case of a bubble coming from the coalescence of two, the new bubble oscillates heavily, the velocity profiles surround- ing the bubbles are modified as well as the surface area, but the dispersion quality decreases. Figs. 5 and 6 represent the decrease in the specific area of the dispersion and the increase in the amplitude of oscillation of the bubbles. The specific area decreases by a third in most cases while the amplitude of the bubble doubled the values of the initial bubbles. Traditional theories have concluded that a decrease in the dispersion quality in terms of a decrease in specific area pro- duces a reduction in the mass transfer coefficient. This fact has been demonstrated in the case of medium size and big size bub- bles, when single bubbles generated from each orifice are big enough to be deformed by the hydrodynamics. Smaller bubbles cannot oscillate. Bubbles generated from 1.5mm orifice diam- eter are almost rigid meanwhile the bubbles resulting from the coalescence process are big enough to oscillate. In this case, the superficial area reduction can be balanced with the increase of the amplitude of the oscillation. Fig. 7 represents the compari- son between the volumetric mass transfer coefficients for coa- lescence systems and for non-coalescence systems. That figure shows the diffusion theory exposed in Skelland (1974). The Sherwood number for separated bubbles is 1.44 times bigger than that of close bubbles. The experimental mass transfer co- efficients also verify this relationship considering coalescence as the limit of the contact between the bubbles. Several empirical correlations together with the theoretical equations developed by Montes et al. (1999) and Martín et al. (2006) are used to test if the coupled effect of the increment of the oscillations and the reduction of the specific area can be predicted. Fig. 8 represents the experimental values and those predicted by Eqs. (1–3), (8) and (23). The experimental values are not well predicted because the bubble column works in a nearly stagnant regime so as to avoid the break-up of the coalesced bubble. However, empirical and theoretical equations can cope with both phenomena since their results are within the range predicted by the diffusion theory of approaching spheres of Skelland (1974). Mass transfer typical equations in the form of those given by several authors (Shah et al., 1982) show that coales