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2.9.3.1 R heological m easurem ent

Many types of rheometer have been used to study the rheology of fermentation broths. These include capillary viscometers (Bjorkman, 1987, Blakebrough et al.,

1978b), concentric cylinders (Ghildyal et al., 1987, W ittier et a i, 1983), cup and bob viscom eters (Banks, 1977), cone and plate viscometers (Charles, 1978) and impeller viscometers (Kemblowski and Kristiansen, 1986, Roels et al., 1974, Bongenaar et al.,

1973). However, it has been reported that problems can be encountered when studying fermentation broth rheology with all of these rheometers. Standard rotational viscometers such as the concentric cylinders and cup and bob systems are versatile and widely used. Yet, there are associated problem s with these systems which include the tendency to cause gravity settling of suspended particles, and phase separation such as the formation of less dense layers next to the rotating surface. Also large particles such as pellets can be the same size as the measuring gap o f the instrument which causes destruction of the particles in the shear field (Kemblowski and Kristiansen, 1986, Banks, 1977). These problems were overcome by Roels et al. (1974) and Bongenaar et al. (1973) by using an impeller viscometer shaped like a Rushton turbine where the flow regime was similar to a standard fermenter. Kemblowski and Kristiansen (1986) successfully used a six vane impeller rheometer to analyse the rheology of Aureobasidium pullulans and claimed the method was more successful than other conventional methods. However, the impeller viscom eters were constrained by the narrow shear range required for analysis under lam inar flow conditions. Also, the complex flow pattern established by the impeller viscom eter does not allow straightforward calculation o f shear rate. W arren (1994) studied the rheology o f three A c tin o m y c e te sp, A. roseorufa, S. rim osus and S. erythraea and found no obvious benefit using impeller systems instead of conventional rotational viscometers.

For this study a concentric cylinder was chosen against an impeller viscometer due to the difficulty in requiring laminar flow conditions. This transpired with low viscosity broths which occurred in the earlier stages of the S. erythraea fermentations. Also, A llen and R obinson (1990) found good agreem ent betw een the rheological measurements of Streptomyces levoris broths from pipeline, helical and rotating cylinder rheom eters and suggested that slip effects were not significant problem s in these rheometers. Hence, the rheom eter used for this study was a Rheomat 115 rotational viscom eter (Contraves AG, Zurich, Switzerland) with a plug in 7/7 module operating system and a concentric cylinder (M S-0/115) measuring unit with quick release coupling. M easurem ents were made at room tem perature as M etz et al. (1979) reported that viscosity for mycelial suspensions was only slightly dependent on temperature and that it was not necessary to maintain a constant sample temperature during rheological analysis. Rheological measurements were made immediately after each sample was withdrawn

from the fermenter. The cup was filled with 20 mL of broth, the cylinder bob put in place and rotated for 10 seconds at the highest speed (step 15) to degas the broth (Metz et a i,

1979). Torque readings were then recorded as the speed was reduced to step 1. To m inimise settling, readings were taken in a short time (5 seconds) of reaching each impeller speed setting. M easurement readings for each speed step were translated into shear stress using the table supplied by Contraves. The shear rate step range was from 24.3 to 3680 s‘k The values of shear stress and shear rate were then used to determine the power law constants for determining the rheological behaviour of the sample. The power law relationship is:

X = K t" 2.18

where

X = shear stress (Pa) y = shear rate (s~^)

K = consistancy index (Pa.s") n = flow behaviour index (-)

Values o f n and K were found from the slope and y axis intercept respectively, o f a log - log plot o f the shear stress versus shear rate. For continuity of rheological studies, the use o f a single rheom eter for all measurements throughout the work was desired. However, the mechanical breakdown of the Contraves rheomat 115 resulted in the use of a B ohlin cup and bob rheom eter to analyse the samples from one S. erythraea

ferm entation. The bob dimensions were 0.045 m x 0.025 m with an annular gap of 0.001 m. The shear rate range was from 0.02 to 1000 S'k

2 .9 .3 .2 A p p aren t viscosity

Investigators have used the concept of an average shear rate for air agitated vessels to calculate the apparent viscosity from the equation below:

t l a = 7 = K ( Y a r ‘

2.19

fa

where

M'a = apparent viscosity (Pa.s)

X = shear stress (Pa) Ya = shear rate (s~^)

K = consistency index (Pa.s") n = flow behaviour (-)

where the average shear rate (was proportional to the superficial gas velocity, :

Ya = C U ^ 2 .2 0

However, large variations existed in the value of C from 5000 (Nishikawa et al. (1977) from heat transfer coefficient measurements), 2800 (Schumpe and Deckwer, 1987) to 1500 (H enzler, 1980) which were all for bubble columns. Hence, C histi (1989) questioned the applicability of these correlations especially as the shear rate could vary by three fold depending on which value of C was chosen. Allen and Robinson (1991) also explained that it was uncertain whether the value of C was independent o f column diam eter, sparger type, or rheological properties. Also, it was unclear whether the average shear rate estimated from stationary point positions within the bubble column were relevant to other areas of the vessel. Therefore, the use of these correlations from bubble colum n systems was difficult to use for the 'average' shear rate o f an airlift reactor, especially when the bubble column has no net liquid flow and as an airlift reactor has distinct liquid flow direction. In the airlift reactor the shear rate in simple terms would be a function of the relative velocity between both the bubbles and liquid, and between the liquid and the column wall. The liquid circulation in simple terms is mostly a result of the density difference between gas holdup in the riser and downcom er and the gas holdup is determined by the superficial gas velocity. Also, the flow direction change in the vessel provides resistance to liquid flow. Thus a relationship between shear rate and liquid circulation velocity exists. Shi et a l (1990) used this analogy to obtain a correlation of average shear rate from the superficial gas velocity for an external loop reactor. The variable parameter of this correlation was only the superficial gas velocity and so, it was not applicable to this study as it could not be used to distinguish the average shear rate betw een the operating conditions o f conventional aeration and, com bined aeration and propeller operation. Therefore, the Blasius correlation for estim ating shear stress at a vessel wall (Russell, 1989, W ood and Thom pson, 1986, Boysan et a l , 1988) was used in this study for estimating the maximum shear stress of the reactor. The Blasius correlation for wall shear stress is a function of the liquid linear velocity as shown below;

x„ = Î PlU > .0 7 9 2,21

where

= shear stress at the wall (Pa) Urn = mean liquid linear velocity (ms~^) Re = Reynolds number

Hence, the experim ental m easurements o f liquid linear velocity in the riser and dow ncom er were used to calculate shear stress for the different airlift reactor configurations used in this study. Although this led to an estimate of the maximum shear stress and not an 'average' value, it did enable a comparison between the shear stress and apparent viscosity to be made between the aerated and, combined aerated and propeller operated airlift reactor configurations. As the Blasius correlation was only applicable to Newtonian broths, Russell (1989) used the correlation of W ilkinson (1960) for non- Newtonian broths shown below:

= i P lU „ a (R e)-" 2 .2 2

where

Re = generalised Reynolds number

a,b = function of generalised flow behaviour (n )

where values for a and b were given by Wilkinson (1960) and tabulated in appendix 8.0. The generalised Re was given by :

R .' -

K 8" - ' where

D = diameter of the flow channel (m) K'= generalised consistency index (Pa.s") n' = generalised flow behaviour (-)

and the n' was equal to n (flow behaviour) for a power law fluid and the value of K' obtained from the equation below:

K' = K 3n-h 1 2.24

4n

Therefore, for each measurement interval using the non-Newtonian broths, the liquid linear velocity o f the riser and downcomer, rheological flow characteristics (n & K) and the broth density were used to calculate the generalised Re and then, the wall shear stress of the riser and downcomer. In all cases the Re were less than 10^ which met the Blasius correlation criterion. The calculated shear stresses of the riser and downcomer were then used to calculate the corresponding apparent viscosity from the equation below:

M-a - ₁ 2.25

K J

A comparison of the apparent viscosity between reactor configurations using the value of the wall shear stress from the riser was complicated by the liquid linear velocity, as it was

influenced by the different cross sectional area ratios of the reactor configurations. Hence, apparent viscosity was estimated from the mean wall shear stress of the vessel obtained from the average o f the values from the riser and dow ncom er so a more meaningful comparison could be made between the reactor configurations. An example of apparent viscosity calculation is demonstrated in appendix 8.0.

Apparent viscosity estimation for the stirred tank used the estimation of apparent shear rate from the method of Metzner and Otto ( 1957) :

Ya ~ ^ 2.26

where

N = rotational speed of the impeller (s~*) kj = average shear rate constant (-)

where Metzner et a l (1961) obtained at value of kg for multiple rotating Rushton turbines of 11.4 for a pseudoplastic fluid (0.14 > n < 0.7) which was used in this study. Hence, the apparent viscosity was calculated from the equation below:

Ha = 7 = K ^ = K ( k , N r ‘

2.27

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