Specific Energy Dissipation Rate Research Articles

Bubble Size Distribution and Void Fraction in the Wake Region Below a Ventilated Gas Cavity in Downward Pipe Flow

The aim of this study was to develop a population balance model to predict the resultant bubble size distribution and gas void fraction in the wake region below a ventilated cavity in down-flowing liquid inside a pipe. The model includes (1) the gas entrainment process from the ventilated cavity; (2) fluid flow and specific energy dissipation rate in the wake region, comprising both wall-jet and recirculation-vortex zones; (3) bubble breakup and coalescence events, determined by a critical Weber number criterion and bubble interaction and film drainage times, respectively; and finally (4) gas void fraction in the wake and recirculation of gas back into the base of the ventilated cavity. The model predictions are compared with experimental measurements for an air–water system. The model successfully predicts the length of the wake region and the gas void fraction within it, and the average and resultant bubble size distributions immediately downstream of the wake. The average bubble diameter was of the order 2–3 mm for each of the cases studied. In applying the model, attention was focused on the specific energy dissipation rate distribution between the wall-jet and recirculating-vortex zones within the wake. As part of the analysis Fluent computational fluid dynamics simulation was carried out and the results from this work are also presented in the paper.

Suspension of Microcarriers for Cell Culture with Axial Flow Impellers

The suspension characteristics, the agitator speed, Njs, and the mean specific energy dissipation rate, ( e ¯ T )js, required to just fully suspend ∼20% wet weight Cytodex 3® microcarrier beads have been studied using a range of different diameter Chemineer HE-3 hydrofoils, a pair of Ekato InterMIG impellers and a six-blade mixed-flow impeller in a baffled vessel of 19.2 l operating volume containing phosphate buffer saline solution. Flat and modified tank bases were used. Njs values were observed to be in the range of 50 to 90 rev min−1. The use of Zwietering's correlation using existing literature geometric suspension parameters, S, to predict Njs would give values up to 50% higher. The low Njs values obtained in the experiments are attributed to the very small particle–liquid density difference (40 kg m−3), which eased the lifting of the particles from the tank bottom, compared to those studied previously. Also, it was found that at Njs, it took up to about 40 min to suspend all particles as the upper surface of the initially settled bed was scoured away. Previous work has not reported such a long-term phenomenon. With the liquid/particle properties used in this study, the three-blade hydrofoil HE-3 impeller of D/T = 0.39 in a cone-and-fillet based tank was marginally the most efficient; that is, it had the lowest ( e ¯ T )js of ∼0.5 x 10−3 W kg−1. However, ( e ¯ T )js was less than 1 x 10−3 Wkg−1 in most cases with the different size HE-3 hydrofoils, which implies that these geometries would probably be suitable for application in shear-sensitive animal cell culture systems using such microcarriers.

Mixing Studies Related to the Cleaning of Molten Aluminium

AbstractMolten aluminium is traditionally “cleaned” by a chlorine‐based fluxing gas. This gas also has to provide the motive power for mixing. Recently, mechanical agitation with solid fluxes has been considered as a replacement for environmental reasons. Here, these two methods of mixing are compared using particle image velocimetry (PIV), decolourisation for homogenisation and power measurement for comparison of efficiencies. A geometrically scaled‐down vessel was used, with air to mimic “chlorine” fluxing and with water as the working fluid. At equivalent mean specific energy dissipation rates, $ \bar \varepsilon $T, maximum velocities are higher and mixing times are shorter with an impeller. This improved performance is achieved with the impeller without causing surface gas entrainment, the latter being detrimental to fluxing.

Break-up, coalescence and catastrophic phase inversion in turbulent contactors

When a low concentration of immiscible phase is dispersed, break-up in the impeller region controls the drop size. The traditional application of Kolmogoroff's theory of local isotropic turbulence has been moderately successful in relating equilibrium drop sizes to the physical properties and the turbulent flow, with low power number impellers giving smaller drops at equal mean specific energy dissipation rates, ε ̄ T. However, to explain the reduction in drop size at equal ε ̄ T on scale-up, the concept of intermittency must be introduced leading to a scale-up rule close to constant tip speed. With increasing concentration, coalescence generally becomes important and drop sizes increase. Modelling of coalescence involves collision frequency and coalescence efficiency. The latter is dependent on the type of drop interface, the establishment of which type for a particular system being difficult. The difficulty is compounded since in clean systems, at concentrations of the aqueous phase >∼20% by volume, droplets of oil appear in the aqueous drops whilst the converse is not found. At sufficiently high concentrations, where the concept of collision frequency is questionable, catastrophic phase inversion (CPI) occurs because coalescence becomes so high. Anything that enhances coalescence, e.g. surfactants, particles that bridge interfaces, wettable surfaces, bulk flow patterns, encourages CPI to occur at lower concentrations of dispersed phase. Satisfactory models for CPI are not available.

The Impact of Fluid Mechanical Stress on Saccharomyces Cerevisiae Cells During Continuous Cultivation in an Agitated, Aerated Bioreactor; its Implication for Mixing in the Brewing Process and Aerobic Fermentations

The introduction of mechanical agitation or re-circulation of CO 2 from the headspace to facilitate the natural CO 2 -driven mixing in anaerobic brewing fermentations has the potential to cause damage to yeast cells through increased hydrodynamic stress. In addition, such damage has been reported in aerobic yeast fermentations. Here, a reproducible, duplicate series of aerobic, carbon-limited, continuous culture yeast fermentations have been carried out up to approximately 340 h. In the first series, mean specific energy dissipation rates, e ¯ T from ∼4.5 × 10 –2 to ∼6.0 W kg −1 were used, the former mimicking for approximately 20 h the maximum level found in anaerobic fermentations at the large scale and the latter a higher value than that usually found in aerobic fermentations. In the second, e ¯ T was held at ∼4.5 x 10 −2 W kg −1 and two aeration rates (1 and 3 vvm) were used. Both values are very high for brewing, even if headspace CO 2 recirculation is used. The latter value is also high for aerobic fermentations. In all cases, the dissolved oxygen level was held constant by gas blending at 40% of saturation. At e ¯ T > ∼4.5 W kg −1 , a transient effect on the cells as measured by multi-parameter flow cytometry was found, but all other measured parameters, including mass spectrometry and classical microbiological data, showed that, statistically, there was no effect on cellular morphology or physiology. For all other conditions of agitation and aeration, all measured parameters remained constant. This study indicates that the potentially deleterious effects of agitation or CO 2 gas recirculation can be largely discounted with respect to brewing fermentations and for more intense aerobic fermentations up to ∼6 W kg −1 and 3 vvm.

Studies on the Impact of Mixing in Brewing Fermentation: Comparison of Methods of Effecting Enhanced Liquid Circulation

Mixing during beer production by natural CO2 evolution has been enhanced at the bench scale by headspace gas recirculation to the base of a 3.5l cylindroconical fermenter or by mechanical agitation in a 4l fermenter. Standardized lager fermentations were used to compare the two methods at a range of mean specific energy dissipation rates ( e ¯ T , W kg−1), including ∼5 × 10−2W kg−1. The latter corresponds approximately to the maximum e ¯ T found at the production scale (∼400m3) due to natural CO2 evolution. The work has shown that gas recirculation is a viable technique that avoids the loss of volatiles found if mixing is enhanced by sparging a separate gas such as nitrogen. For both types of mixing, it was found that e ¯ T resulted in increased yeast growth and fermentation rates and an alteration in the balance of key volatile compounds, with, in general, an enhanced formation of higher alcohols and a suppression of the formation of esters. However, with gas recirculation this enhanced performance was limited to an e ¯ T of ∼5 × 10−2Wkg−1 because of the tendency for excessive foaming at higher recirculation rates, whilst values up to ∼2.5 × 10−1W kg−1 proved effective under agitated conditions. On comparison, at an e ¯ T of ∼5× 10−2W kg−1, the two modes of operation gave similar results, although gas recirculation produced a slightly increased fermentation rate. The possible reasons for this are briefiy discussed. Both methods seem to have the potential for reducing fermentation time and enhancing reproducibility, especially at the small scale.

Optimising activated sludge growth rate by intensifying hydrodynamic forces

AbstractIn this study a Couette device was used to examine the influence of hydrodynamic forces on the overall behaviour of activated sludge. The specific growth rate of activated sludge increased with increasing specific energy dissipation rate, reaching a maximum rate at an energy input of approximately 40 m2 s−3, beyond which any further increases resulted in a reduction in the overall growth. At levels above about 250 m2 s−3 the specific growth rate was negligible. Experimental growth rates in the range 0.04–0.20 h−1 were obtained, depending on the energy input levels and substrate (glucose) concentration. A theoretical model successfully predicted both the decrease in the floc radius and microbial activity with increasing energy input into the system, and when combined was able to provide a reasonable prediction for the optimum specific energy dissipation rate to maximise the specific growth rate.© 2003 Society of Chemical Industry

Study Of Micromixing in a Stirred Tank Using a Rushton Turbine: Comparison of Feed Positions and Other Mixing Devices

The consecutive-competing iodide–iodate reaction scheme has been used to study micromixing phenomena in a baffled vessel of 0.29 m diameter agitated by a Rushton turbine. It has been confirmed that, by using successive injections, this reaction scheme is very efficient for such a study. Four agitator speeds giving mean specific energy dissipation rates, e T from ∼0.2 to ∼ 1.2 Wkg −1 have been used, with sub-surface feeding at one of four points. For a given speed, addition at each of these four points gave different local values of e ¯ T, ranging from less than e ¯ T very close to the top of the liquid to much greater close to the impeller. The point closest to the impeller was chosen to be such that feeding was estimated to be at the point of maximum e T. For the maximum speed, the segregation index, as a measure of the amount of ’waste product’, was ∼20% with feed at the top of the liquid (as preferred industrially because of its convenience). This ’waste’ was reduced to ∼5% by feeding at the point of maximum e T close to the impeller. A comparison was also made with results reported in the literature using the same reaction for two new devices developed for improved micromixing. By feeding at the carefully chosen position close to the impeller, the results with the Rushton turbine were as good as or better than with the special devices even at the comparatively low e ¯ T of ∼ l.2 Wkg−1. It was estimated that the maximum local specific energy dissipation rate was ∼70 times the mean, in reasonable agreement with a very recent study where the same pair of reactions and LDV were both used.

Recent Studies on Agitated Three-Phase (Gas–Solid–Liquid) Systems in the Turbulent Regime

Earlier work using Rushton turbines and down-(MFD) and up-(MFU) pumping, 45°-pitched blade turbines at relatively low concentrations of solids of different size and density in vessels up to 1.8 m diameter enabled correlations to be developed for predicting the minimum speed for solid suspension, NJSg. Further work has been conducted with these impellers and with two modern impellers, a Scaba 6SRGT, a typical hollow-blade radial flow impeller, and a typical up-pumping, axial flow, wide-blade hydrofoil, the Lightnin’ A315, in a vessel of 0.45 m diameter with solids up to 40% by weight. The earlier correlations were validated for the new higher concentration conditions. In all cases, increases in solids concentration increased NJSg and the specific energy dissipation rate required to suspend solids, (ɛT)JSg On the other hand, the large increase (up to two orders of magnitude) in mixing time found at solids concentration >∼15% by weight in two phase systems at NJSg as compared with the case without solids, is essentially eliminated in the three-phase case. At low gassing rates, QGv (vvm), down-pumping impellers achieve suspension and relatively good vertical solids distribution at the lowest (ɛT)jsg-However, with increased QGv UP to 3 vvm, NJSg and (ɛT)JSg increase rapidly, solids maldistribution develops, the flow pattern is very unstable and gross torque fluctuations occur. For the 6SRGT, the operation is very stable and although NjSg and (ɛT)JSg are both high they are insensitive to QGv This high value of (ɛT)JSg may not be a disadvantage if high rates of gas–liquid mass transfer are required. For both the 6MFU and especially the A315(U), the flow pattern, NJSg and (ɛT)JSg are again all very insensitive to QGv and a good vertical solids distribution is maintained. For the A315(U) at high QGv values, (ɛT)JSg is the least amongst the impellers tested, so that wide-blade, up-pumping axial flow hydrofoils are considered to be the optimum impeller when just physical suspension is required or solid–liquid reactions are rate limiting.

Mixing of Three-Phase Systems at High Solids Content (up to 40% w/w) Using Radial and Mixed Flow Impellers.

A liquid-gas-solid system has been studied at higher solids concentration (up to 40% by wt) and gas flow rates (up to 2 vvm) than previously. Two different radial flow impellers (Scaba 6SRGT and a standard Rushton turbine) and a six-bladed mixed flow impeller with pitch angle of 45°, either in its downward (6MFD) or upward pumping (6MFU) mode were used. Power input, mixing time, the speed to achieve complete suspension of the solids (ungassed and gassed) as well as the amount of suspended solids and the height of the liquid-solid interface were measured. In addition, a new technique for measuring the amount of suspended solids in two-phase systems was extended successfully to three phases. When compared to the situation without solids, the mixing time, t m , in the solid-liquid case at the higher solid concentrations was much greater, as previously reported, but for the three-phase case, the increase was relatively small, especially with the Scaba and 6MFU impellers. In general, the power and speed required to suspend the solids increased with increasing solids concentration but once suspended, with the Scaba and the 6MFU impellers, even the highest solids concentration and gas flow rates only required a very small further increase. It has recently been proposed (Pantula and Ahmed, 1997) that by maintaining constant agitator torque on gassing, solids suspension would be sustained. The present work showed this to be broadly valid for the 6SRGT and the 6MFU but not for the Rushton and the 6MFD impellers. Overall, the most stable impeller, requiring the least specific energy dissipation rate for solids suspension and gas dispersion under the most demanding conditions, was the 6MFU.

Agitation induced mycelial fragmentation of Aspergillus oryzae and Penicillium chrysogenum

Given the impact of mycelial morphology on fermentation performance, it is important to understand the factors that influence it, including agitation-induced fragmentation. The successful application of the energy dissipation/circulation function (EDC) to correlate fragmentation of Penicillium chrysogenum with agitation intensity and with different impeller types [5] has already been demonstrated. The EDC function takes into account the specific energy dissipation rate in the impeller swept volume and the frequency of mycelial circulation through that volume. In order to explore whether the EDC function can be used more generally to correlate fragmentation of different filamentous species, the present study extended the concept to agitation-induced, off-line fragmentation of Aspergillus oryzae grown in chemostat culture. The work shows that at EDC values off-line greater than that in the chemostat, fragmentation with different impellers can be correlated with the EDC. For EDC values less than those used in the chemostat, fragmentation did not occur. The earlier results of Jüsten et al. [5] with Penicillium chrysogenum are also reconsidered and found to behave similarly.

The Transition from Homogeneous to Heterogeneous Flow in a Gassed, Stirred Vessel

Much ’old’ work has been undertaken studying gas-liquid systems in stirred reactors (Nienow1). However, this ‘old’ work has generally been limited to specific ungassed energy dissipation rates, ( ɛ T ) 0 , up to ∼2 Wkg −1 and gas flow rates of up to ∼2 vvm (or superficial gas velocity, ν s , of −1 ). Recent developments have led to the need to operate modern reactors at much higher values of ɛ T and ν s . This preliminary study reports work under such conditions and also builds on studies at very high gas velocities in bubble columns. Under such conditions, a transition from homogeneous to heterogeneous flow occurs. The results show that under well dispersed conditions, the transition occurs at lower gas velocities for the coalescence-inhibited solutions in comparison to water. Possible reasons for these findings and for the formation of large bubbles at this transition are discussed. A simple model on the basis of a gas volume balance is proposed which matches the trend. The impact of the intense operating conditions on a range of other mixing parameters is also reported.

Dependence of mycelial morphology on impeller type and agitation intensity

The influence of the agitation conditions on the morphology of Penicillium chrysogenum (freely dispersed and aggregated forms) was examined using radial (Rushton turbines and paddles), axial (pitched blades, propeller, and Prochem Maxflow T), and counterflow impellers (Intermig). Culture broth was taken from a continuous fermentation at steady state and was agitated for 30 min in an ungassed vessel of 1.4-L working volume. The power inputs per unit volume of liquid in the tank, P/V(L), ranged from 0.6 to 6 kW/m(3). Image analysis was used to measure mycelial morphology. To characterize the intensity of the damage caused by different impellers, the mean total hyphal length (freely dispersed form) and the mean projected area (all dispersed types, i.e., also including aggregates) were used. [In this study, breakage of aggregates was taken into account quantitatively for the first time.]At 1.4-L scale and a given P/V(L), changes in the morphology depended significantly on the impeller geometry. However, the morphological data (obtained with different geometries and various P/V(L)) could be correlated on the basis of equal tip speed and two other, less simple, mixing parameters. One is based on the specific energy dissipation rate in the impeller region, which is simply related to P/V(L) and particular impeller geometrical parameters. The other which is developed in this study is based on a combination of the specific energy dissipation rate in the impeller swept volume and the frequency of mycelial circulation through that volume. For convenience, the function arising from this concept is called the "energy dissipation/circulation" function.To test the broader validity of these correlations, scale-up experiments were carried out in mixing tanks of 1.4, 20, and 180 L using a Rushton turbine and broth from a fed-batch fermentation. The energy dissipation/circulation function was a reasonable correlating parameter for hyphal damage over this range of scales, whereas tip speed, P/V(L), and specific energy dissipation rate in the impeller region were poor. Two forms of the energy dissipation/circulation function were considered, one of which additionally allowed for the numbers of vortices behind the blades of each impeller type. Although both forms were successful at correlating the data for the standard impeller designs considered here, there was preliminary evidence that allowing for the vortices would be valuable. (c) 1996 John Wiley & Sons, Inc.

Study of hydrodynamics in microcarrier culture spinner vessels: A particle tracking velocimetry approach

Three-dimensional particle tracking velocimetry (3-D PTV), a modern, quantitative, visualization tool, has been applied to the characterization of the flow field in the impeller region of cell culture reactor vessels. The experimental system used here is a 250-mL microcarrier spinner vessel. The studies were conducted at three different agitation rates, 90, 150, and 210 rpm, corresponding to healthy, mildly damaging, and severely damaging shear intensities, respectively. The flow can be classified into three regions: a predominantly tangential (azimuthal) flow generated by the impeller; a trailing vortex region coming off the impeller tip; and a converging flow region close to the center of the vessel. The latter two are the regions of highest velocity gradients. Energy dissipation rates due to mean velocity gradients were also calculated to characterize the impeller stream. Local specific energy dissipation rates > 10,000 erg/(cm(3)sec) . have been measured. It is proposed that the critical regions for microcarrier culture damage due to impeller hydrodynamics are the trailing vortex region and the high energy converging flow region. Graphical representation of the mean velocity flow fields and the distribution of energy dissipation rates in the impeller region are also presented here. The merits of using the dissipation function (measure of specific energy dissipation rate) as a possible scale-up parameter are also discussed. (c) 1996 John Wiley & Sons, Inc.

Comparative bioparticle and hydrodynamic characteristics of conventional and tapered anaerobic fluidized-bed bioreactors

By maintaining the same operational conditions of one conventional fluidized-bed bioreactor (CFB) and two tapered fluidized-bed bioreactors (TFBs), the performance of the TFBs with taper angles of 5 ° and 2.5 ° were found to be superior to that of the CFB with a taper angle of 0 °. Experimental results together with statistical analyses showed that the bioparticle and hydrodynamic characteristics of the TFBs were significantly different from those of the CFB. Also, bioparticle stratification occurred in the three bioreactors. The biofilm thickness (δ) and the specific biomass (β) of the three bioreactors varied in the following decreasing order 5 ° > 2.5 ° > 0 ° under the same volumetric loading. Meanwhile, the specific energy dissipation rate (ω) and the bioparticle washout rates (W = 0.214 ± 0.219; 0.537 ± 0.493 g BAC dm−3day−1) of the two TFBs were considerably lower than that of the CFB (W = 1.086 ± 0.916 g BAC dm−3 day−1). A lower ω value results in increases in δ and β, and a lower dry density of the biofilm (ρd). Accordingly, the performance enhancement with TFBs should be related to their lower ω and W, thicker δ and larger β values. © 2000 Society of Chemical Industry

Comparing Impeller Performance for Solid-Suspension in the Transitional Flow Regime with Newtonian Fluids

Particle suspension in Newtonian fluids of viscosities from 0.01 to 1 Pa s have been studied using Rushton turbines, pitched blade turbines, Chemineer HE-3 and Lightnin’ A310 hydrofoils (all pumping downwards), and Ekato Intermig agitators. By comparison to the turbulent system (Ibrahim and Nienow, 19961), at high viscosity, there was less random particle movement across the base prior to suspension. On the other hand, once the agitation speed, N, was high enough to achieve supension, i.e., N = Njs, particles remained longer in suspension after a reduction lo N < Njs, though eventually with little or no hysterisis. Suspension at high viscosity was achieved with a lower mean specific energy dissipation rate, (eT)js, when using large D/T impellers whether of the radial or axial type. Thus, at Re > 3000, the optimum overall configuration was a D/T of about 0.4 with the downward pumping HE-3 and pitched blade turbines, whilst at Re < 3000, the optimimum was the HE-3 at a D/T of about 0.5. The performance of dual Intermigs with D/T ratios of ∼ 0.6 dramatically improved as the viscosity increased to 0.1 Pa s, and the single Intermig was the most efficient impeller at 1 Pa s. The Zwietering equation was found unsuitable for prediction of Njs at low Re.

The influence of impeller type on mean drop size and drop size distribution in an agitated vessel

In most work on agitated liquid–liquid dispersions, Rushton turbines have been used. Here, mean drop size and drop size distributions are reported for six different impellers covering 3 generic types over a range of mean specific energy dissipation rates. Both viscous and non-viscous dispersed phases have been used at concentrations by volume of 1 and 5%. It has been found that at the same mean specific energy dissipation rate, low power number impellers (whether of the so-called “ultra-high shear” or “high flow” type) all produced similar sized drops at equilibrium which were much smaller than those found with two “high shear”, high power number impellers, i.e., the standard Rushton turbine and another six-blade disc impeller. By considering the energy dissipation rate to be confined to the impeller swept volume, these equilibrium drop size could be approximately correlated. The low power number impellers also achieved that equilibrium more rapidly and the drop size distributions in the dispersions produced by them were narrower than those formed when agitated by the Rushton turbine and the other six-blade disc impeller. However, further analysis of the flow in the impeller region and the inclusion of advanced coalescence models would appear to be required in order to enhance the interpretation of these results.

Suspension and Liquid Homogenization in High Solids Concentration Stirred Chemical Reactors

In many crystallization processes and other solid-liquid reactors, solids are present in high concentrations. Often these reactors are operated in the semi-batch mode and the purity, productivity and selectivity of the reaction (and in the case of precipitation and crystallization, the size distribution and morphology too) depends on the relative rates of mixing (or homogenization) compared to chemical reaction. It has usually been assumed that, provided the solids are all fully suspended, the rate of mixing is similar to that found in single-phase systems. Recent extensive work carried out by the above team at The University of Birmingham with support from DuPont has analysed the processes of homogenization and particle suspension. It has shown that, for typical industrial conditions, there is a range of operating conditions in which the solid particles at high concentration are fully suspended but have a clear liquid layer above them in which the local specific energy dissipation rate appears to be very low. Under these conditions, the mixing time may be two or more orders of magnitude longer than in the single phase case. This paper describes the phenomenon, analyses its importance, develops a physical model and proposes ways of overcoming the problem.

Product concentration profile in strained reacting fluid films

The product concentration profile that develops as a result of an instantaneous bimolecular reaction when contacting semi-infinite strained reactant solution films, is modelled and analysed. Analytical solutions to reactant and product concentrations are presented for which initial reactant concentrations, reactant diffusivities, and product diffusivity can be independently and arbitrarily chosen. The validity of the model for finite geometry is thoroughly discussed. It is shown that the product concentration profile may differ significantly depending on diffusivities and reactant concentrations, even for cases when almost the same amount of product is produced. The maximum product concentration is constant in time but varies with diffusivities and reactant concentrations in a quite complicated fashion. Under certain conditions the maximum product concentration may even decrease when initial reactant concentrations or reactant diffusivities are increased. Dimensionless concentration profiles and the maximum concentration are invariant with mixing intensity. The influence of mixing is fully incorporated into the length and time scales. The actual real time to form a certain amount of product is inversely proportional to the square root of the specific local energy dissipation rate. The implications of model results on fast complex reactions are discussed.

Influence of fermentation conditions and scale on the submerged fermentation of Aspergillus awamori

Aspergillus awamori is an interesting fungus for the industrial production of enzymes. To generate essential information, fermentations with this organism (CBS 115.52) were performed under various conditions. The ratio of the biomass production to the sum of biomass production and carbon dioxide production in time is used for deriving the yield and maintenance coefficient. This ratio can be used to estimate the biomass concentration from the CO 2 production on line as well. Pellets were the dominant morphology for most of the fermentations performed. The hairy length of the pellets first increased with time and then decreased. At a comparable specific energy dissipation rate, in the larger scale fermenters, pellets had a larger hairy length than in the smaller. The fraction of pellet biomass in the total biomass decreased with time at the beginning of the fermentations (0–20 h) and then reached a more or less stable value. Both counting the number of pellets during the fermentations and observing pellets under agitated but nongrowth conditions indicated that formation and breakage of pellets hardly occurred under the studied conditions.