Scaling of heat transfer and temperature distribution in granular flows in rotating drums.

Accurate prediction of the time required to heat up granular materials to a target temperature is crucial for several processes. However, we do not have quantitative models to predict the average temperature or the temperature distribution of the particles. Here, we computationally investigate the scaling of heat transfer in granular flows in rotating drums. Based on our simulations, which include a wide range of system and material properties, we identify the appropriate characteristic time that is used to derive equations that predict the particles' average temperature and the particles' temperature distribution.

Shear distribution and variability in the USP Apparatus 2 under turbulent conditions.

Computational analysis is used to examine the hydrodynamic environment within the USP Apparatus II at common operating conditions. Experimental validation of the computational model shows that the simulations of fluid motion match the dispersion of dye observed in experiments. The computations are then used to obtain data that cannot be easily measured with experiments, specifically the distribution of shear forces within the media and along the wall. Results show that the shear environment is highly non-uniform. Increasing the paddle speed from 50 to 100 rpm does not improve shear homogeneity within the apparatus. Experiments show that this uneven distribution of hydrodynamic forces is a direct cause of dissolution testing variability. This variability is large enough to cause for type II dissolution test failures, i.e., failures are a result of a vulnerability of the testing method rather than a problem with a dosage form. Future development of new dissolution tests should include evaluations of the hydrodynamic environments to eliminate this potential source of failure that is unrelated to product quality.

Sampling and characterization of pharmaceutical powders and granular blends.

We use a variety of experimental results to illustrate issues and challenges involved in the sampling and characterization of pharmaceutical mixtures. Accurate and reliable characterization of granular mixtures is hindered by both the complexity of granular systems and the lack of validated and reliable sampling technology and techniques. Both sampling tools and sampling protocols are critically important for accurate characterization. Using cohesive and free-flowing powders and four thief probe designs, we reveal a large potential for extremely misleading results as well as severe disturbance of the granular bed. We also discuss results from several experiments designed to test the validity of various sampling protocols by varying parameters such as sampling location and frequency of sampling. These experiments illustrate the importance of effective sampling procedures to achieve the best and most efficient results.

Effects of blender rotational speed and discharge on the homogeneity of cohesive and free-flowing mixtures.

The roles of blender rotational speed and blender discharge on the homogeneity of free-flowing art sand and of a cohesive placebo formulation were investigated in the tote blender. For three practical operating speeds, 6, 10, and 14 RPM, spanning the entire range of commercial equipment, the homogeneity of the free-flowing mixture was independent of rotational speed and blender size. On the other hand, the homogeneity of the cohesive pharmaceutical powder mixture was dependent on vessel rotational speed in a complex fashion, with 10 RPM producing a better final mixture than either 5 or 15 RPM. The homogeneity of the free-flowing sand mixture was preserved when discharged into a vertical bin, while the homogeneity of the fine pharmaceutical powder mixture significantly improved after discharge from the tote blender.

Noise to order.

Patterns in natural systems abound, from the stripes on a zebra to ripples in a riverbed. In many of these systems, the appearance of an ordered state is not unexpected as the outcome of an underlying ordered process. Thus crystal growth, honeycomb manufacture and floret evolution generate regular and predictable patterns. Intrinsically noisy and disordered processes such as thermal fluctuations or mechanically randomized scattering generate surprisingly similar patterns. Here we discuss some of the underlying mechanisms believed to be at the heart of these similarities.

Attraction of minute particles to invariant regions of volume preserving flows by transients.

We find that tracer material can be concentrated into invariant regions of flows due exclusively to transient effects, as are produced when tracers temporarily become more buoyant than the surrounding fluid. This can occur either as a single event, e.g., if the tracer is initially weakly buoyant, or under periodic forcing, e.g., when external effects (such as solar heating) change the tracer density periodically. We study both cases in experiments, in a model, and in direct numerical simulations of laminar flow in a stirred tank. Focusing occurs for very small tracer size and inertia in flows that are instantaneously strictly volume conserving.

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.

Computational and experimental investigation of flow and particle settling in a roller bottle bioreactor.

It is shown that cell settling is a key factor affecting the performance of roller bottle bioreactors. The two-dimensional cross-sectional flow at the center of a roller bottle is simulated using a finite difference method, and the settling behavior of cells is simulated using particle dynamics algorithms and validated experimentally using fluorescent particles. The settling behavior of particles in the roller bottle flow is studied using both steady and time dependent rotation rates. Under steady flow conditions the flow is divided into two regions: one where the particles settle to the wall and one where the particles remain suspended indefinitely. The relative size of these two regions depends on the ratio of the settling velocity to the rotation rate of the bottle. For unsteady flows generated by periodic changes of the bottle rotation direction, the settling of cells is accelerated significantly, leading to complete deposition in just a few turns of the bottle.

Batch uptake of lysozyme: effect of solution viscosity and mass transfer on adsorption.

In this study, solid-phase adsorption by macroporous and hyper-diffusive resins was investigated in a batch uptake adsorption system to quantify solid-phase diffusion rates as a function of bulk phase viscosity. The performance of chromatographic resins used for adsorption of proteins is dependent on several factors including solid and liquid-phase diffusivity, boundary layer mass transfer, and intraparticle mass transfer effects. Understanding these effects is critical to process development and optimization of both packed and fluidized bed adsorption systems. The macroporous resin used here was Streamline SP, and the hyper-diffusive resin was S-HyperD LS. Both have been frequently used in fluidized bed adsorption of proteins; however, factors that affect uptake rates of these media are not well quantified. Adsorption isotherms were well represented by an empirical fit of a Langmuir isotherm. Solid-phase diffusion coefficients obtained from simulations were in agreement with other models for macroporous and hyper-diffusive particles. S-HyperD LS in the buffer system had the highest uptake rate, but increased bulk phase viscosity decreased the rate by approximately 50%. Increases in bulk phase viscosity increased film mass transfer effects, and uptake was observed to be a strong function of the film mass transfer coefficient. Uptake by Streamline SP particles was slower than S-HyperD in buffer, due to a greater degree of intraparticle mass transfer resistance. The effect of increased film mass transfer resistance coupled with intraparticle mass transfer resistances at an increased bulk phase viscosity resulted in a decrease of 80% in the uptake rate by Streamline SP relative to S-HyperD.

Effect of oxygen limitations on monoclonal antibody production by immobilized hybridoma cells.

The productivity of an immobilized cell biocatalyst is often limited by the amount of oxygen that reaches cells located at interior regions of the biocatalyst. These diffusive limitations depend on a multitude of factors including the oxygen supply, the cellular uptake kinetics, and the cell density of the material. Large cell densities, which are desired for high productivity, are also likely to reduce the percentage of cells that receive an adequate supply of oxygen. To develop a better understanding of how different conditions affect biocatalyst behavior, a computational model of immobilized hybridoma cells was developed. The model accounts for oxygen diffusion and consumption, cell proliferation and death, and monoclonal antibody production. This model assumes that cellular productivity is limited only by the supply of oxygen and that the growth media is continually replenished so that nutrient levels remain high and wastes are eliminated. Biocatalyst performance is evaluated by monitoring the amount of monoclonal antibody produced by the cells. Model predictions agree with experimental measurements reported in the literature and indicate that for long operation time the supply of oxygen, biocatalyst size, and cell kinetics have a significant effect on biocatalyst performance, whereas the initial cell loading has only a relatively small effect. Under typical culture conditions, we find that oxygen penetrates to a maximum depth of about 0.4 mm. Accordingly, cells immobilized farther than this threshold distance receive an insufficient supply of oxygen.

A simple correlation for predicting effective diffusivities in immobilized cell systems.

A simple correlation method has been developed to predict effective diffusivities of small molecules in heterogeneous materials such as immobilized cell systems. This correlation uses a single diffusivity measurement at one cell volume fraction to predict diffusivities for any other volume fraction of cell. The method has been applied to 20 sets of published diffusivity measurements in immobilized cell systems and accurately predicts affective diffusivities of molecules for the full range of cell fractions. It may also be used to predict effective diffusivities in heterogeneous materials in which the diffusivity of a molecule in each phase and the volume fraction of each phase are known. (c) 1996 John Wiley & Sons, Inc.

Monte Carlo simulation of diffusion and reaction in two-dimensional cell structures.

Diffusion and reaction processes control the dynamics of many different biological systems. For example, tissue respiration can be limited by the delivery of oxygen to the cells and to the mitochondria. In this case, oxygen is small and travels quickly compared with the mitochondria, which can be considered as immobile reactive traps in the cell cytoplasm. A Monte Carlo theoretical investigation quantifying the interplay of diffusion, reaction, and structure on the reaction rate constant is reported here for diffusible particles in two-dimensional, reactive traps. The placement of traps in overlapping, nonoverlapping, and clustered spatial arrangements can have a large effect on the rate constant when the process is diffusion limited. However, under reaction-limited conditions the structure has little effect on the rate constant. For the same trap fractions and reactivities, nonoverlapping traps have the highest rate constants, overlapping traps yield intermediate rate constants, and clustered traps have the lowest rate constants. An increase in the particle diffusivity in the traps can increase the rate constant by reducing the time required by the particles to reach reactive sites. Various diffusive, reactive, and structural conditions are evaluated here, exemplifying the versatility of the Monte Carlo technique.

Chaos, symmetry, and self-similarity: exploiting order and disorder in mixing processes.

Fluid mixing is a successful application of chaos. Theory anticipates the coexistence of order and disorder-symmetry and chaos-as well as self-similarity and multifractality arising from repeated stretching and folding. Experiments and computations, in turn, provide a point of confluence and a visual analog for chaotic behavior, multiplicative processes, and scaling behavior. All these concepts have conceptual engineering counterparts: examples arise in the context of flow classification, design of mixing devices, enhancement of transport processes, and controlled structure formation in two-phase systems.