The mixing efficiency is an important characteristic of gas-liquid bioreactors as it will determine the bulk fluid and gas phase homogeneity, which will in turn affect the driving force for heat and oxygen mass transfer. Biological parameters such as growth rate, shear damage, pH and gas transfers will be controlled by the mixing performance. Different mixing behaviour has been observed around the loop of an airlift reactor. Fields and Slater (1983) observed that mixing consisted of the combined effects of local mixing in the riser, downcomer and top and bottom flow reversal sections. Axial dispersion occurs in the riser and downcomer due to differences between the gas-liquid phase velocities (Chisti, 1989). Turbulent mixing occurs in the top (gas disengagement) section and a certain amount o f liquid backmixing will occur caused by recirculation, adding a final contribution towards the overall mixing pattern (Fields and Slater, 1983). Therefore, Blenke (1985) described two fundamental mixing effects: the longitudinal mixing which occurred in each circulation due to the velocity profile, turbulence, dead spaces and molecular diffusion and backmixing due to the recycling of the circulation flow. The axial dispersion model has been used to simulate the longitudinal mixing w hich occurs when the tracer is injected into an tower loop reactor and becom es hom ogeneously distributed (Merchuk, 1991). The dispersion model is based on the analogy between mixing in actual flow (plug flow) and diffusion-like eddy movement superimposed on the plug flow. Taylor's (1954) one dimensional diffusion model has been extensively used to model axial dispersion in single phase flows and was shown by Blenke (1979) to describe the dispersion due to single circulation in an unaerated Jet-loop reactor. The em pirical description of mixing .assumes a single loop circulation is equivalent to flow through a pipe with uniform liquid velocity, U^c, and axial dispersion coefficient, Dl, so that the tracer concentration, C at a point x in the loop at time t is given by:
5C 5^C 5 C
= 1-32
By assuming 'open' boundary conditions Frohlich et al. (1991a) expressed a solution to the dispersion model for airlift reactors using the dimensionless Bodenstein number :
B o l ( n -8)' 4 0
where the Bodenstein number is calculated from:
1.33
Bol = 1-34
where Ulc is the mean liquid velocity , H is the height of the column and Dl is the liquid phase dispersion coefficient (ms*^). The Bodenstein number is the ratio of convective to
diffusive transport rates which decreases with enhanced backmixing (Fields and Slater. 1983). The equation (1.33) can also be expressed in terms of the Peclet number (Pe)
^LC ^
Pe = - g - 1.35
where D is the height of the liquid (unaerated)
Blenke (1979) dem onstrated that the model can be applied to a loop reactor if the summation of dispersion traces for n complete circulations around the loop is described by:
B ol ( n -0)^
4 0 1.36
Therefore the overall liquid phase axial dispersion coefficient ( D l ) can be obtained by fitting the equation to the experimental response of the reactor to a pulse of tracer with Bo or Pe number as the fitting parameter. Variations of this type of equation in terms o f the open boundary conditions for airlift reactors have been made by Van der Laan (1958), M urakami et al. (1982) and W am ecke et al. (1985). Most significantly was the model proposed by M erchuk and Y unger (1990) that considered that both the riser and downcomer were plug flow sections and the gas separator (top section) represented a well mixed stage.
O f the few m ixing studies that exist in the literature the overall dispersion coefficient of the vessel has been used to characterise the mixing performance. The zones of an airlift reactor are hydrodynamically different, hence the dispersion coefficients would also be expected to be different. Verlaan et al. (1986) used the Peclet number from the dispersion model to describe the mixing performance in the individual sections. The dimensionless Peclet number is similar to the Bodenstein number and can be defined from the axial dispersion model in a similar manner. The Peclet number for the whole reactor was found to increase with gas flow rate. The same trend was found for the individual zones. In Newtonian fluids the zones were found to be in an order of Pcdowncomer > Periser > Pctop-section- Chisti (1989) described the fully backm ixed state o f continuous flow reactors as Pe < 0.1 and plug flow behaviour was described as Pe >20. In N ew tonian fluids Pcoveraii in airlift vessels (external and internal loop) was 30 - 80. Verlaan et al. (1989) showed that the Bodenstein number for the riser o f a pilot plant external loop reactor with a 50 mM potassium chloride solution was between 30 - 40 and 40 - 50 in the downcomer, with values o f 10 in the gas-disengagement section. This indicated that the liquid flow behaved like plug flow with superimposed dispersion and that plug flow could not be assumed in the top section. Frohlich et al. (1991a) studied the mixing perform ance o f a pilot plant (4m^) concentric loop airlift reactor and used the Bodenstein number (Bo) to describe the mixing performance. They found that the Bo
diminished with increasing gas velocity in tap water and ethanol solution, thus indicating improved mixing performance. In tap water the presence of antifoam produced a slight increase in Bo with superficial gas velocity and hence a decrease in the dispersion coefficient. Therefore, increasing gas velocity produces a reduction in Bo and enlarges the axial dispersion coefficient. Fields and Slater (1983) also studied the increase in Bo with water from the addition of antifoam and the decrease in Bo with ethanol addition. They attributed these changes to reflect the respective increase and decrease in liquid velocity. Gas disengagement from the water surface in the top section was enhanced by the addition of antifoam and hindered for smaller bubbles from the addition of ethanol. Thus the effect of additives may be partially attributed to changes in turbulence in the head section.
When a tracer is injected into a loop reactor if will circulate around the vessel and be mixed into the liquid phase, and the tracer concentration will reduce to a uniform value throughout the vessel (Onken and Weiland, 1983, Van't Riet and Tramper, 1991). The time that this process involves is described as the mixing time and can be used to characterise the mixing process. It is a measure of the homogeneity of components of the broth, such as microbes, dissolved oxygen and substrate concentrations. However, the mixing time is largely dependent on the measuring method applied and should therefore be considered as a relative measure of mixing performance and not an absolute one (Guy
et al., 1986a). Mixing time is defined as the time between the beginning of a mixing operation and the moment when the fluid reaches a required degree of homogeneity (Onken and Weiland, 1983, Siegel et a i , 1988). The degree of homogeneity is defined as the relative deviation of the tracer concentration of the pulse, C, at some time after injection from the equilibrium concentration after complete mixing, C@.
C e - C
Homogeneity = —p — 1.37
Normally the mixing time is measured for 90, 95 or 99% homogeneity. Various tracer methods have been used, the most popular is pH. An acid or base pulse is injected into the reactor and detected by one or more pH electrodes. Other methods include flow followers which contain radio transmitters, radioactive tracers, and electrolyte tracers (Van't Riet and Tramper, 1991).
M ost o f the mixing studies with airlift reactors have produced data o f mixing times to describe overall mixing performance of the reactor. M ixing time has been dem onstrated to depend on the superficial gas velocity, volume o f the vessel, column diameter ratio, and liquid properties (Weiland, 1984). Pandit and Joshi (1983) found that determ ination o f the mixing time allowed an understanding of the liquid phase flow pattern, effect o f surface active agents, change in bubble diam eter and gas holdup. M ixing time was found to decrease steeply with an increase in gas superficial velocity whereas at higher gas velocities (generally above 0.06 ms'O, the mixing time decreased at
a slower rate. This has been noted by many workers and Margaritis and Sheppard (1981) related this to the change in flow regime, from bubbly to churn turbulent regime, as described in section 1.4.2.
Russell (1989) found that the ratio of the mixing to circulation time of the pilot scale airlift reactor with baker's yeast broth remained constant with increasing gas velocity from 0.015 to 0.2 ms’ '. This indicated that the mixing time process was predom inated by the bulk circulation of the liquid rather than axial dispersion due to ascending bubbles. This was also proposed by Weiland (1984).
The liquid mixing time has been shown to decrease with increasing liquid height above the draft tube, to a height above which no further improvement is observed (Chisti, 1989, Russell et a i , 1994, Sukan and Vardar-Sukan, 1987, and W eiland, 1984). This indicated the existence of two distinct zones in the top section. Chisti (1989) used dyes to demonstrate the existence o f the two zone flow model. When the top section height was above a certain critical height the two zone model existed, whereby the bulk o f the recirculating liquid flowed through the lower region, bypassing the upper region. As the liquid level above the draft tube reduced, the circulating flow moved through the entire top section. The decline in mixing time with increasing top section height defined the region of the top section where no upper section exists. As the top section increased up to the critical height the residence time of circulating liquid in the turbulent top section increased, and the rate of pulse dispersion was enhanced. This showed the importance of the top section hydrodynamics to the overall mixing performance of the reactor. Popovic and Robinson (1993) showed similar effects in a pilot scale external loop reactor with CMC solutions as the mixing time improved with increasing dispersion height in the riser.
Decreasing the ratio of downcomer to riser cross sectional area was found by W eiland (1984) to improve mixing in an airlift reactor. This was due to a larger difference in the liquid velocities o f the two sections and increased mixing in the top section. M ixing time has been shown to increase with an increase in draft tube height (Onken and W eiland, 1983, Sukan and Vardar-Sukan, 1987 and Russell et a i , 1994). Onken and W eiland (1983) explained that the increase in draft tube height increases the length o f the circulation path. This extends the distance that the tracer pulse has to travel between the end sections of the vessel where the bulk of the dispersion is suggested to take place and hence, prolongs the mixing time.
Liquid properties influence the mixing time as studied by Pandit and Joshi (1983). M ixing time increased in the presence o f electrolytes, such as sodium sulphate and sodium chloride. The average bubble size was found to be small and so an increase in gas holdup and a decrease in the terminal rise velocity was expected. This resulted in a increase in liquid circulation and hence an increase in mixing time. The mixing time increases as the viscosity or the shear thinning properties o f the liquid increase (Guy et a l , 1986b). However, Russell (1989) observed that the mixing time decreased from the
increase o f apparent viscosity during a P. chrysogenum fermentation in a pilot scale airlift reactor. This was accounted for by the improved liquid circulation and increased turbulence due to the formation of large bubbles, as the viscosity of the broth increased. Glennon et al. (1988) observed a reduction of the Bo from the addition of xanthan gum (flow behaviour of 0.54) to a 300 L external loop airlift reactor when compared to water. This improved mixing performance was not associated with improved liquid circulation as liquid circulation was prolonged due to viscous drag. Glennon et al. (1988) suggested the improved mixing must have been due to improved axial dispersion coefficient leading to higher levels of dispersion in a single circulation. Fields et al. (1984) observed similar reductions o f the Bo with xanthan gum concentrations from 0.1 to 0.5% w/v as a function o f superficial gas velocity in a concentric pilot scale reactor. This was contributed to the disengagement of bubble slugs and the formation of slug flow in the downcomer from the coalescence of the small bubbles.
Van't Riet and Tramper (1991) provided data for the comparison of the mixing perform ance between stirred tanks, bubble columns and airlift reactors o f the same dimensions. The tip speed of the stirred tank was keep constant at 5 ms** whereas, the superficial gas velocity of the bubble column and airlift was compared from 0 .0 0 1 to 0.1 m s'K At the low gas velocities (0.001 ms'^), the stirred tank had the best mixing performance with mixing times of 18 s compared to 33 s and 131 s for the bubble column and airlift reactor respectively, at 0.01 m^ working volume. At high gas velocities (0.1 ms’i ) the airlift was preferable when the height/diameter ratio was 10. However, in the region between the highest and lowest gas velocities the difference between vessels was less distinct. At high gas velocities (0.05-0.1 ms'^), the bubble column had lower mixing times than the stirred tank of the same dimensions at all of the working volumes studied. The mixing times for the bubble column and stirred tank were 7 s and 18 s respectively for a working volume of 0.001 m^, and at 1227 m^ the mixing times were 97 s for the bubble column and 230 s for the stirred tank. This provided evidence that the circulatory flow o f bubbles in a bubble column produced greater mixing perform ance than the agitator o f a stirred tank.