Characterization of mixing in shaker table containers

Mixing in shaker table beakers is studied using dye dispersion to measure mixing times. Experimental conditions range from the laminar regime into the turbulent mixing. Different flow patterns occurring in the beakers are reported for the mixing. The transition Reynolds number is determined. Rotational speed of the table, volume of material to be mixed, and viscosity of the material are studied as to their effects on mixing time. A graphical mixing time correlation is provided which is useful for the translation of mixing from laboratory scale to pilot scale.     

Computational and experimental investigation of flow and fluid mixing in the roller bottle bioreactor

The fully three-dimensional velocity field in a roller bottle bioreactor is simulated for two systems (creeping flow and inertial flow conditions) using a control volume-finite element method, and validated experimentally using particle imaging velocimetry. The velocity fields and flow patterns are described in detail using velocity contour plots and tracer particle pathline computations. Bulk fluid mixing in the roller bottle is then examined using a computational fluid tracer program and flow visualization experiments. It is shown that the velocity fields and flow patterns are substantially different for each of these flow cases. For creeping flow conditions the flow streamlines consist of symmetric, closed three-dimensional loops; and for inertial flow conditions, streamlines consist of asymmetric toroidal surfaces. Fluid tracers remain trapped on these streamlines and are unable to contact other regions of the flow domain. As a result, fluid mixing is greatly hindered, especially in the axial direction. The lack of efficient axial mixing is verified computationally and experimentally. Such mixing limitations, however, are readily overcome by introducing a small-amplitude vertical rocking motion that disrupts both symmetry and recirculation, leading to much faster and complete axial mixing. The frequency of such motion is shown to have a significant effect on mixing rate, which is a critical parameter in the overall performance of roller bottles.     

Radial and longitudinal compartmental analysis of gas transport during high-frequency ventilation

A model of gas exchange by low-tidal-volume (VT), high-frequency ventilation (HFV) is presented, based on the physical principles of dispersion. These are the nonuniformity of the velocity profile and the nonreversible mixing of fluid components in a diffusive manner. A numerical method was used to incorporate these principles into a quantitative model. The airways of a symmetrically bifurcating bronchial-tree model were partitioned in the radial direction into two concentric layers representing the kinematic dispersion by nonuniformity of the velocity profile. Mixing between the layers was invoked in proportion to the diffusivity and local dimensions. The effects of frequency (f), VT, shape of the velocity profile, and bronchial-model configuration were tested in the model, with favorable comparison to available experimental data. The model predicts that for a frequency-dependent velocity profile, the rate of tracer exchange is proportional to the square root of f and to the square of VT-V0, where V0 is a constant small volume under which gas exchange was nil. Intracycle asymmetric mixing is predicted to have a stronger effect on gas exchange than asymmetric velocity profile. Gas exchange when turbulent-flow regime is assumed is predicted to be less for the higher VT values than with laminar flow and with mixing by molecular diffusivity. This model was found to be didactic, flexible, and capable of modeling combinations of factors affecting either one of the two fundamental processes of dispersion.     

Hydrodynamics and Gas Dispersion Characterization in a System Equipped with a New Gas‐Inducing Impeller

A new agitation system, called Turboxal, used for the oxygenation and the mixing of wastewater biological treatment tanks has been studied. The interactions between the shell and the three impellers which compose the Turboxal have been analyzed by single‐phase flow patterns. The pumping capacity and the power consumption have also been measured. In addition, the gas dispersion regimes have been analyzed in the tank and in the shell. Finally, the effect of the interaction and the effect of the position of the different agitators on the limit of the flooding regime have been determined.     

Computational fluid dynamics modeling of the paddle dissolution apparatus: Agitation rate,mixing patterns,and fluid velocities

The purpose of this research was to further investigate the hydrodynamics of the United States Pharmacopeia (USP) paddle dissolution apparatus using a previously generated computational fluid dynamics (CFD) model. The influence of paddle rotational speed on the hydrodynamics in the dissolution vessel was simulated. The maximum velocity magnitude for axial and tangential velocities at different locations in the vessel was found to increase linearly with the paddle rotational speed. Path-lines of fluid mixing, which were examined from a central region at the base of the vessel, did not reveal a region of poor mixing between the upper cylin-drical and lower hemispherical volumes, as previously speculated. Considerable differences in the resulting flow patterns were observed for paddle rotational speeds between 25 and 150 rpm. The approximate time required to achieve complete mixing varied between 2 to 5 seconds at 150 rpm and 40 to 60 seconds at 25 rpm, although complete mixing was achievable for each speed examined. An analysis of CFD-generated velocities above the top surface of a cylindrical compact positioned at the base of the vessel, below the center of the rotating paddle, revealed that the fluid in this region was undergoing solid body rotation. An examination of the velocity boundary layers adjacent to the curved surface of the compact revealed large peaks in the shear rates for a region within∼3 mm from the base of the compact, consistent with a ‘grooving’ effect, which had been previously seen on the surface of compacts following dissolution, associated with a higher dissolution rate in this region.     

Activated sludge process performance using a multistage tower aeration tank

This study's objective was to clarify both experimentally and theoretically whether a vertical multistage tower aeration tank system is advantageous as compared with a completely mixed system, particularly with respect to purification efficiency, sludge settleability, and excess sludge production. In comparing the two systems: (1) purification efficiency in the multistage tower aeration system with partial fluid mixing with a large Peclet number was higher than in a corresponding completely mixed system for all applied organic loadings; (2) the multistage tower aeration system had some definite advantages with respect to sludge settleability and excess sludge production; (3) the activated sludge system's higher performance with partial fluid mixing was shown quantitatively with the axial dispersion model in conjunction with growth kinetics which involved rapid uptake such as biosorption and subsequent oxidative biodegradation processes of organic substances. (c) 1993 John Wiley & Sons, Inc.     

Asymptotic worst-case mixing in simple demographic models of HIV/AIDS.

The majority of published modeling work regarding the impact of mixing patterns among subgroups on the spread of HIV infection assumes either that the overall population size remains constant, the aggregate immigration to the population occurs at a constant annual rate, or that no immigration occurs and the population in question declines due to HIV or other causes. In this paper, immigration rates are modeled as simple functions of population size and may be interpreted as aggregate birth rates. This assumption implies asymptotic exponential growth in the disease-free population as long as per capita birth rates exceed per capita mortality rates. The introduction of HIV infection to such a population may change this situation, and the asymptotic population growth rate can be reduced substantially as a result. The specific manner in which this occurs depends in part upon difficult to observe mixing patterns among those with different sexual activity rates. Rather than attempting to explicitly model a variety of mixing patterns, a bound on the impact of worst-case mixing is produced, where "worst case" refers to the mixing pattern that maximizes the asymptotic prevalence of infection, which is equivalent to minimizing the asymptotic population growth rate. These new techniques are illustrated with a numerical example.     

Quantitative measurements of mixing intensity in shake-flasks and stirred tank reactors. Use of the Mixmeter, a mixing process analyzer

A new mixing probe has been developed which measures the motions of the fluid during mixing as pressure fluctuations and converts the measurements into a mixing signal (MS). The MS is the root mean square (RMS) pressure fluctuation in the 1-64Hz range as determined by a sensitive pressure sensor and a digital signal processor specifically designed for the purpose. The MS is a measure of the actual mixing flow of the fluid rather than a measurement of the input motions or energies into the reactor system (e.g. RPM, torque or power). In other studies, the MS has been measured as a function of mixing speed in numerous sized reactors from 10 to 1000l, and provides consistent and reproducible measurements. The MS increases monotonically as a function of mixing speed, with a change of slope corresponding to the transition from laminar to turbulent mixing regimes. Maps of MS as a function of location in the reactor are useful in understanding stirred tank reactor design and performance. Quantitative measurements of mixing are especially useful during process development as a tool to increase the success of scale-up during the transition from process development to manufacturing. Measurements at a fixed location in a given reactor are useful in understanding changes in mixing that occur during the course of a given process, and are useful in manufacturing situations where validated documentation of lot-to-lot consistency of mixing is required (e.g. pharmaceutical manufacturing). In addition, the probe has been used to measure mixing in vessels with vibrational mixers with similar results. The probe has been successfully used in feedback loops to control either mixing speed or vibrational mixing amplitude in order to maintain constant mixing of the fluid during processing. With this system it is possible to maintain constant mixing over a wide range of fluid volumes in a given reactor, and, for instance, to compensate for changes in viscosity throughout the course of the process. Adaptations of this system for the measurement of mixing in shake-flasks is described in this paper.     

The Emergence of Urban Land Use Patterns Driven by Dispersion and Aggregation Mechanisms

We employ a cellular-automata to reconstruct the land use patterns of cities that we characterize by two measures of spatial heterogeneity: (a) a variant of spatial entropy, which measures the spread of residential, business, and industrial activity sectors, and (b) an index of dissimilarity, which quantifies the degree of spatial mixing of these land use activity parcels. A minimalist and bottom-up approach is adopted that utilizes a limited set of three parameters which represent the forces which determine the extent to which each of these sectors spatially aggregate into clusters. The dispersion degrees of the land uses are governed by a fixed pre-specified power-law distribution based on empirical observations in other cities. Our method is then used to reconstruct land use patterns for the city state of Singapore and a selection of North American cities. We demonstrate the emergence of land use patterns that exhibit comparable visual features to the actual city maps defining our case studies whilst sharing similar spatial characteristics. Our work provides a complementary approach to other measures of urban spatial structure that differentiate cities by their land use patterns resulting from bottom-up dispersion and aggregation processes.     

Fundamental Procedures for Determining Ergosterol Content of Decaying Plant Material by Liquid Chromatography

Portions of published procedures for measurement of ergosterol content of decomposing plants were examined for their influence upon ergosterol yield. Common methods of treatment of plant samples prior to sterol extraction (e.g., oven drying, freezing, lyophilization) led to reduced recoveries of ergosterol (ca. 20 to 80%). The least destructive method was direct placement and storage in methanol. Photoconversion of ergosterol is not likely to cause losses during analysis, but losses are likely if there is insufficient mixing during neutral-lipid partitioning from base-hydrolysis reagents. Homogenization (two times for 2 min) and refluxing (2 h) in methanol were equally effective in extracting ergosterol. Direct extraction in base-hydrolysis reagents was less effective (by ca. 40%).     

Characterization of mixing in a novel wavy-walled bioreactor for tissue engineering

The wavy-walled bioreactor (WWB) possesses a novel geometry comprised of walls with sinusoidal waves that mimic baffles in an effort to promote mixing. This geometry provides a unique hydrodynamic environment suitable for the cultivation of mammalian cells and tissues and the investigation of fluid mechanical effects on cell and tissue growth and development. In the present study, mixing in WWB was characterized and compared to that in a conventional spinner flask (SF). The key parameters included in this characterization were mixing time, residence time distribution (RTD), and dissolved oxygen concentration during engineered cartilage tissue cultivation. Factors that influenced mixing in WWB included wave amplitude, agitation rate, and the ratio of the impeller diameter to the tank diameter (D/T). Data obtained from RTD and acid base neutralization studies confirmed the presence of different mixing zones in WWB. A theoretical comparison of WWB to a baffled spinner flask (BSF) using computational fluid dynamics (CFD) modeling predicted that while enhanced mixing was achieved in wavy-walled and BSF bioreactors, the shear stresses applied on tissue constructs were 15% lower in WWB. Improved mixing was achieved in WWB compared to the SF at similar D/T ratios, verified by improved oxygen transport and increased dispersion. However, for lower D/T ratios mixing in WWB was not necessarily improved. This study demonstrated the importance of characterization of mixing by showing the impact of even minor changes in bioreactor geometry and operating conditions.     

Computation Confirms Contraction: A Molecular Dynamics Study of Liquid Methanol,Water and a Methanol-Water Mixture

It may be questioned whether potential models that have been developed independently for two different pure compounds would behave properly when used in computer simulations of mixtures of these compounds. Since they are optimized for the pure compounds there is no guarantee whatsoever that the terms describing the interaction between dissimilar molecules are correct. If the simulational and experimental values of several thermodynamical properties of the mixture relative to those of the pure compounds agree closely, however, this strongly indicates that no separate optimizations need be carried out for the mixtures. Here we present the results of isothermal-isobaric Molecular Dynamics simulations of liquid methanol, water and equimolar methanol-water mixtures, using simple point charge models. The potential parameters of the models for the pure liquids had been independently optimized. No adjustment of parameters was made for the mixture, but nonetheless the experimental volume contraction and excess enthalpy upon mixing were reproduced almost perfectly.     

Growth dynamics of a methylotroph (Methylomonas L3) in continuous cultures. I. Fast transients induced by methanol pulses and methanol accumulation

The dynamic behavior of the Ribulose Monophosphate-type Methylomonas L3 in continuous cultures was studied, using methanol pulses to induce fast transients in steady-state cultures of single (methanol) and mixed (methanol plus formaldehyde) substrates. In several experiments, the methanol-uptake rate (MUR) profiles displayed negative MUR values for a time period following the methanol pulse, and significant amounts of methanol disappeared immediately following the pulse. These phenomena suggested the accumulation of methanol in the cells upon pulsing, apparently due to an active transport system. Accordingly, and in order to estimate the potential of the transport system for methanol accumulation, accumulation profiles were calculated for several pulse experiments. The calculations are based on a methanol balance and experimentally determined values of the cell volume and the true transient biomass yields. It is calculated that methanol accumulates up to 200-fold to very high intracellular concentrations. The accumulation is calculated to be much higher in single- (methanol) substrate cultures of low dilution rate than in cultures of high dilution rate or of mixed substrates. The specific growth rate immediately following the methanol pulse decreased in single-substrate cultures and increased in mixed-substrate ones. The biomass yield decreased after the methanol addition in all experiments; however, the drop was less severe in the mixed-substrate experiments. It is also suggested that formaldehyde as a methanol cosubstrate may be an effective means of providing more stable biomass yields and growth rates in reactors with imperfect mixing, and of protecting the reactor against accidentally induced methanol accumulation.     

Backmixing and mass transfer in the design of immobilized-enzyme reactors

The effects of dispersion and mass transfer resistance on the degree of conversion in an immobilized-enzyme reactor have been considered theoretically. It is assumed that the immobilized enzymes obey a Michaelis–Menten relationship and backmixing can be characterized by a dispersion model. For two extreme cases (perfect mixing and piston flow), approximate equations are obtained, which can be readily used to evaluate the effect of mass transfer on degree of conversion. Numerical solutions are obtained for other intermediate cases. Design charts are given which set practical limits of enzyme reactor design.     

Effects of reactant heterogeneity and mixing on catabolite repression in cultures of Saccharomyces cerevisiae

An experimental study was conducted into the effect of reactant heterogeneity on glucose-fed continuous cultures of S. cerevisiae, The heterogeneity was altered by varying mixing intensity in the nutrient entry region within a static mixing device. Experimental results confirm simulation predictions based upon a simple growth model, showing that mixing in the entry region can govern macroscopic culture behavior. Specifically, at high dilution rates, the biomass concentration was reduced by mixing patterns that increased the size of regions where glucose exceeded the threshold for catabolite repression. Because the size of such repressive regions is not uniquely determined by reactant segregation, the authors argue that in biological systems (and others involving a threshold response) an alternative measure of mixing quality should be used. Conclusions are drawn concerning the simulation of biological reactors for design purposes, and the importance of nutrient delivery systems to reactor performance.     

Mixing analysis of PCS slurries in a horizontal scraped surface bioreactor

Horizontal rotating reactors offer many advantages for enzymatic hydrolysis of viscous biomass slurries; however, they do not provide homogenous mixtures since motion is only in the angular direction. Multi-directional mixing is important for dispersing enzymes and carrying products away from reaction sites. The objective here was to experimentally quantify mixing times and axial dispersion coefficients in a horizontal rotating bioreactor. Mixing times were of the same order as reaction times, indicating that enzymatic hydrolysis could be as much controlled by diffusion and mixing effects as by the complex reaction mechanism. The dispersion coefficient for the highest solids slurry was 20× less than the lowest solids slurry, which is indicative of the difference in free water and the magnitude change of viscosity with relatively small addition of solids. The slow mixing times and low dispersion may be an acceptable tradeoff with significantly lower power requirements compared to a conventional vertical reactor.     

Modeling the hydraulic effect of transverse deep zones on the performance of short-circuiting constructed treatment wetlands

Short-circuiting, which occurs when a large fraction of water traveling through a system exits well before the residence time, reduces the performance of constructed treatment wetlands. Recent field and laboratory observations have shown that short-circuiting within vegetated marsh areas results from narrow, continuous fast flowpaths that experience longitudinal dispersion but do not exchange fluid with slow flowing regions of dense vegetation on either side. Based on these observations, this paper develops an analytic stream tube model with dispersion to represent flow through the marsh areas of a short-circuiting constructed treatment wetland under steady flow conditions. The model also includes transverse deep zones, which rapidly dissipate fast flowpath momentum and introduce lateral mixing through wind-driven circulation. Modeled results reveal that a transverse deep zone that replaces a portion of a wetland marsh can offset the adverse impact of short-circuiting flowpaths through two separate mechanisms. First, lateral mixing can dilute the water that has traveled through a fast flowpath. Second, deep zones reduce the probability that fast flowpaths align throughout the entire wetland. The model results suggest that deep zones may improve wetland performance when properly sized and located, even when they do not directly contribute to contaminant removal.     

A mechanical approach to the longitudinal dispersion of gas flowing in human airways

The aim of this work is to contribute to elucidating the mechanism underlying gas mixing in the human pulmonary airways. For this purpose, a particular attempt is made to analyse the fluid mechanical aspects of gaseous dispersion using bolus response methods. The experiments were performed on five normal subjects by injection of 10 cm3 bolus of He, Ar and SF6 into the latter part of the inspired airstream, in such a way that the whole bolus entered the inspiratory flow and was recovered during the following expiration. The results, presented in a logarithmic plot of dimensionless variance (dispersion of the output bolus) against the Peclet number, show that gaseous dispersion is only slightly dependent on the nature of the tracer gas but is strongly related to flow velocity. This is in agreement with the theory of turbulent or disturbed dispersion; however, it seems that Taylor laminar dispersion does not play a significant role in the airways.     

Effect of small flow reversals on aerosol mixing in the alveolar region of the human lung.

It has been suggested that irreversibility of alveolar flow combined with a stretched and folded pattern of streamlines can lead to a sudden increase in mixing in the lung. To determine whether this phenomenon is operative in the human lung in vivo, we performed a series of bolus studies with a protocol designed to induce complex folding patterns. Boli of 0.5- and 1-microm-diameter particles were inhaled at penetration volumes (V(p)) of 300 and 1,200 ml in eight subjects during short periods of microgravity aboard the National Aeronautics and Space Administration Microgravity Research Aircraft. Inspiration was from residual volume to 1 liter above 1 G functional residual capacity. This was followed by a 10-s breathhold, during which up to seven 100-ml flow reversals (FR) were imposed at V(p) = 300 ml and up to four 500-ml FR at V(p) = 1,200 ml, and by an expiration to residual volume. Bolus dispersion and deposition were calculated from aerosol concentration and flow rate continuously monitored at the mouth. There was no significant increase in dispersion and deposition with increasing FR except for dispersion between 0 and 7 FR at V(p) = 300 ml with 0.5-microm-diameter particles, and this increase was small. This suggested that either the phenomenon of stretch and fold did not occur within the number of FR we performed or that it had already occurred during the one breathing cycle included in the basic maneuver. We speculate that the phenomenon occurred during the basic maneuver, which is consistent with the high degree of dispersion and deposition observed previously in microgravity.     

Flow Pattern and Mixing in the Multi‐Turbine Agitated Bioreactor Filled with Poly(γ‐Glutamic Acid) Solution

We investigated the flow pattern and mixing behavior of a poly(γ‐glutamic acid) (γ‐PGA) solution in a bioreactor equipped with two Rushton turbines by simulation and experiment. Computational fluid dynamics (CFD) is used to solve the three‐dimensional hydrodynamics in the bioreactor and to obtain the flow patterns and tracer concentration at every point. The flow circulation patterns by inter‐impeller clearance and viscosity and their effects on overall mixing time were studied. Based on the results we can conclude that the impeller clearance should not be larger than 0.2 D for the efficient mixing under non‐aerated condition when the liquid viscosity is above 20 cp, which corresponds to concentrations of 20 g/L or above for γ‐PGA.