Expansion and hydrodynamic properties of β-cyclodextrin polymer/tungsten carbide composite matrix in an expanded bed

The expansion and hydrodynamic properties of matrix are significant for expanded bed adsorption (EBA) processes. A series of new composite matrices CroCD-TuC are studied and estimated in an expanded bed. It is found that the heavier matrix is better suited for high operation fluid velocity than the lighters. Although the Richardson–Zaki equation can well correlate the bed voidage with fluid velocity for all CroCD-TuC matrices tested, the modifications are proposed to improve the accuracy of theoretical predictions of correlation parameters, including terminal settling velocity (U_t) and expansion index (n). Residence time distributions (RTDs) are determined, and the Bodenstein number (Bo) and axial dispersion coefficient (D_ax) are employed to analyze the liquid mixing in the expanded bed. It is found for CroCD-TuC matrices, both parameters notably changed with the variation of fluid velocity and viscosity. Furthermore, D_ax is an intuitive parameter estimating the bed stability on various operating conditions, and also a restriction on developing the matrix for high operation fluid velocity. The comparison of the hydrodynamic properties on different matrices reveals that CroCD-TuC 3 and CroCD-TuC 4 seem superior to other matrices in hydrodynamic properties, making them promising matrices for further use. The correlations as the functions of fluid velocity and viscosity have been established which may provide beneficial information for practical applications of CroCD-TuC matrices in EBA processes.     

Evaluation of new high-density ion exchange adsorbents for expanded bed adsorption chromatography

New adsorbents Q HyperZ and CM HyperZ composed of hydrogel-filled porous zirconium oxide particles were evaluated for expanded bed adsorption applications in the present work. The HyperZ adsorbents have wet density of 3.16 g ml(-1), particle size of 44.5-100.8 microm and average sphere diameter of 67 microm. The bed expansion as the function of flow velocity and fluid viscosity was measured and correlated with Richardson-Zaki equation. The suitable expansion factor was considered less than 2.5, while the corresponding flow velocity was about 450 cmh(-1). Liquid mixing in the bed was determined to evaluate the stability of expanded bed. The Bodenstein numbers tested were higher than 40 and the axial mixing coefficients (D(ax)) were between 0.5 and 9.7x10(-6)m(2)s(-1), which demonstrated that a stable expanded bed could be formed under suitable operation conditions. Bovine serum albumin (BSA) and lysozyme were used as model proteins to estimate the adsorption capacities of Q and CM HyperZ, respectively. The maximum equilibrium adsorption of Q and CM HyperZ could reach 45.7 and 27.2 mg g(-1) drained adsorbents, respectively. It was found that yeast cells had little influence on the adsorption capacities of the two adsorbents tested. The dynamic adsorption capacity of BSA at 10% breakthrough with Q HyperZ was 35.9 mg g(-1) drained adsorbent at flow velocity of 100 cm h(-1) for packed bed adsorption. The values for expanded bed adsorption were 34.4 mg g(-1) drained adsorbent at flow velocity of 200 cm h(-1), 33.6 mg g(-1) drained adsorbent at 300 cm h(-1) and 31.7 mg g(-1) drained adsorbent 400 cm h(-1). The results demonstrated that Q HyperZ and CM HyperZ are suitable for expanded bed adsorption of biomolecules.     

Nd-Fe-B alloy-densified agarose gel for expanded bed adsorption of proteins

Novel dense composite adsorbents for expanded bed adsorption of protein have been fabricated by coating 4% agarose gel onto Nd-Fe-B alloy powder by a water-in-oil emulsification method. Two composite matrices, namely Nd-Fe-B alloy-densified agarose (NFBA) gels with different size distributions and densities, NFBA-S (50-165 microm, 1.88 g/ml) and NFBA-L (140-300 microm, 2.04 g/ml), were produced. Lysozyme was used as a model protein to test the adsorption capacity and kinetics for the NFBA gels modified by Cibacron blue 3GA (CB-NFBA gels). Liquid-phase dispersion behavior in the expanded beds was examined by measurements of residence time distributions, and compared with that of Streamline SP (Amersham-Pharmacia Biotech, Sweden). The dependence of axial mixing in the expanded beds on flow velocity, bed expansion degree. settled bed height, and viscosity of liquid phase was investigated. Breakthrough curves of lysozyme in the expanded beds of the CB-NFBA gels were also examined. The dynamic binding capacity at 5% breakthrough was 23.3 mg/ml matrix for the CB-NFBA-S gels, and 16.7 mg/ml matrix for the CB-NFBA-L, at a flow velocity of 220 cm/h. The results indicate that the NFBA gels are promising for expanded bed adsorption of proteins.     

Enhanced performance of expanded bed chromatography on rigid superporous adsorbent matrix

Rigid spherical macroporous adsorbent beads with surface hydroxyl groups were prepared by cross-linking of cellulose. These beads had diameter in the range 100-200 microm and a mean pore size of about 3 microm with about 60% pore volume. The matrix (bulk density approximately 1600 kg m(-3)) could be expanded into a stable bed and used for protein chromatography. Chromatographic runs were performed on a 10 mm diameter column under non-retaining and retaining conditions on the prepared matrix (called Celbeads) and performance of the runs was measured in terms of the height equivalent to a theoretical plate (HETP). The HETP curves in both packed and expanded bed modes followed profiles typical of macroporous adsorbents, i.e. increasing and levelling with velocity. Unimpaired performance of the matrix at increasing flow-rates permitted expanded bed elution of adsorbed solutes without loss of efficiency in terms of purification factor and product concentration. As a model system, Celbeads was used to purify lactate dehydrogenase from porcine muscle homogenate by dye-affinity chromatography. The prepared matrix provided about 100 theoretical plates per meter for the enzyme system at a linear flow velocity of 1.27 cm x min(-1) in an expanded bed elution mode, and gave enzyme yields of 100% with a purification factor of 31 using an optimized procedure. The adsorbent could be cleaned in place with 5 M urea and used repeatedly without loss of performance.     

Macroporous copolymer matrix. IV. Expanded bed adsorption application

Macroporous crosslinked hydroxyethyl methacrylate-ethylene dimethacrylate copolymeric beads (HEG beads) were synthesized by suspension polymerization in the presence of a pore generating agent. These beads were coupled to alpha-cyclodextrin through a urethane spacer. These modified copolymer beads (affinity-HEG beads) so prepared were evaluated for their suitability in expanded bed chromatography. The optimum thickness of the distributor plate for stable expanded bed for use in expanded bed adsorption (EBA) was established. The affinity-HEG beads are comparable in density to Streamline diethyl amino ethane (DEAE) and exhibit better mechanical stability at higher superficial velocity under fluidization. The affinity-BEG beads were used as affinity chromatography matrices for the purification of cyclodextrin glycosyltransferase. Feeding of 5-fold diluted fermented broth to the column containing affinity-HEG beads of settled bed height 7.5 cm (I.D. 26 mm and length 42 cm) at double bed expansion resulted in a sharp breakthrough curve of alpha-cyclodextrin glycosyltransferase (CGTase). The adsorbed enzyme was eluted from the bed in 50 mM Tris-HCl buffer containing 10 mM CaCl2 at 25 degrees C in packed bed configuration.     

Pellicular expanded bed matrix suitable for high flow rates

A new type of expanded bed matrix with a heavy core of stainless steel covered with an agarose layer was prepared. Two bead size fractions, the smaller one (32-75 microm diameter) having a single particle core and the larger (75-180 microm diameter) with an agglomerate of stainless steel particles constituting the core, were chosen for further characterisation. The dispersion behaviour was determined both in packed bed and expanded bed modes by the retention time distribution method (RTD) and compared with the Streamline matrix (Amersham Pharmacia Biotech). The comparison turned out in favour of the new matrix. Flow rates as high as 3000 cm/h were used with the larger fraction, giving stable expanded beds with good mass transfer properties. The matrices were mechanically stable without any tendency to crack or peal, even after prolonged use.     

Fluidisation and dispersion behaviour of small high density pellicular expanded bed adsorbents

The fluidisation and dispersion properties of various agarose-based expanded bed matrices--small high density stainless steel cored prototypes and standard commercial types--were studied in 1-cm diameter expanded bed contactors in which fluid entering the column base is locally stirred. In all cases, fluidisation behaviour was poorly predicted from the Richardson-Zaki correlation, with experimentally determined values of the expansion index being considerably higher than the theoretical values. The resons for these discrepancies are discussed in detail and the validity of applying this widely used correlation for characterisation of expanded bed systems is questioned. Residence time distribution studies using acetone tracers, demonstrated that in comparison to existing commercial supports, the small pellicular prototype materials generally possessed far superior hydrodynamic properties, which augurs well for their future employment in expanded bed chromatographic separations.     

Characterization and evaluation of a macroporous adsorbent for possible use in the expanded bed adsorption of flavonoids from Ginkgo biloba L.

The suitability of the use of macroporous adsorbent Amberlite XAD7HP in expanded bed adsorption processes for the isolation of flavonoids from crude extracts of Ginkgo biloba L. has been assessed. The expansion and hydrodynamic properties of expanded beds were investigated and analyzed. The bed expansion as a function of operational fluid velocity was measured and correlated with the Richardson–Zaki equation. Theoretical predictions of the correlation parameters (the terminal settling velocity u_t and exponent n) were improved by modifying equations in the literature. Residence time distributions (RTDs) were studied using acetone as a tracer. Three measures of liquid phase dispersion (the height equivalent of theoretical plate, Bodenstein number and axial distribution coefficient) were investigated and compared to values previously obtained with commercial EBA adsorbents developed for protein purification. A suitable bed expansion ratio was found to be 1.25 times the settled bed height, which occurred at a corresponding flow velocity of 183 cm/h. For an initial settled bed height of 42 cm, the mean residence time of liquid in the expanded bed was around 28 min. Under these flow conditions, the axial mixing coefficient D_ax was 7.54 × 10⁻⁶ m²/s and the Bodenstein number was 28; the number of theoretical plates (N) was 19 and the height equivalent of a theoretical plate (HETP) was 2.77 cm. Rutin trihydrate was used as a model flavonoid for the characterization of the adsorption properties of Amberlite XAD7HP. Adsorption was observed to reach equilibrium within 3 h with 70% of the adsorption capacity being achieved within 30 min. The estimated maximum equilibrium adsorption capacity for rutin was estimated to be 43.0 mg/(g resin) when the results were fitted to Langmuir isotherms. The adsorption performance was not seriously impaired by the physical presence of G. biloba leaf powders. Assessment of the kinetics of the adsorption of rutin revealed that the rate constant for adsorption was only reduced by 15% in the presence of leaf powders at a concentration of 50 mg/mL. The results demonstrated that Amberlite XAD7HP should be suitable for expanded bed adsorption of flavonoids from crude extracts of G. biloba L.     

Drag and Torque on Clusters of N Arbitrary Spheres at Low Reynolds Number

Hydrodynamics of particle clusters suspended in viscous fluids is a subject of considerable theoretical and practical importance. Using a multipole expansion of the flow velocity in a series of spherical harmonics, Lamb's fundamental solution of the Stokes flow outside a single sphere is generalized in this work to the case of N nonoverlapping spheres of arbitrary size with slip boundary conditions. The expansion coefficients are found by transforming the boundary conditions to the Lamb form and by transforming the spherical coordinates and solid spherical harmonics centered at different spheres. The problem is reduced to the solution of the linear system of equations for the expansion coefficients, which is carried out numerically. Based on the developed theory, the relation between the hydrodynamic and gyration radius of fractal-like aggregates with different structure is established. In another application, an asymptotic slip-regime dependence of the aggregate hydrodynamic radius on the Knudsen number and the number of particles is found by performing calculations of drag forces acting on the gas-borne fractal-like and straight chain aggregates. A good agreement is shown in comparing predictions of the described theory with available experimental and theoretical results on motion of various small sphere clusters in viscous fluid. Copyright 2000 Academic Press.     

The optimized Rouse-Zimm theory of excluded volume effects on chain dynamics

Based on the optimized Rouse-Zimm (ORZ) approximation to the Kirkwood diffusion equation, we investigate the effects of excluded volume interactions on the single chain dynamics. By incorporating the nonuniformly expanded moments of interbead distances into the expressions for the diffusion and structure matrices appearing in the ORZ diffusion equation, we obtain the general relaxation spectrum for flexible chains that is valid over the range from theta; solvents to good solvents. The present theory involves four parameters: the Kuhn statistical length b(0), the bead number N, the excluded volume parameter z, and the hydrodynamic interaction parameter h(*). These model parameters are determined from structural data of polymers with the aid of the quasi-two-parameter theory. The set of relaxation times of ORZ normal modes calculated with these bead-and-spring model parameters enables the theoretical prediction of various frictional and dynamical properties of polymers within a unified framework. The present ORZ theory generalizes the Ptitsyn-Eizner-type approaches by incorporating the nonuniform chain expansion effect into the structure matrix as well as the diffusion matrix.     

一种球形纤维素/钛白粉扩张床吸附剂的研究--组成对性能的影响

采用反相悬浮再生法 ,以超细钛白粉颗粒作增重剂 ,包埋于纤维素骨架之中 ,经环氧氯丙烷活化后与二乙胺连接 ,制得一种球形扩张床吸附剂 .研究表明 ,吸附剂的密度、机械强度和孔结构可以随钛白粉用量的变化而改变 ;钛白粉颗粒的掺入有利于基质的活化 ,活化后环氧基含量可达 2 2 0 μmol mL .吸附剂具有良好的扩张床性能 ,扩张床中的蛋白质吸附行为与填充床中相似 ,吸附容量为 4 8 9mg牛血清白蛋白 mL吸附剂     

Particle circulation and oxygen mass transfer in an immobilized cell bioreactor

Two important considerations in the design of an aerobic particulate immobilized cell bioreactor are the provision of sufficient oxygen to maintain the desired metabolism of the immobilized organism, and the biomass holdup (which is proportional to the number of immobilized cell particles in the reactor). The Circulating Bed Reactor, a reactor developed for use with those forms of immobilization that result in particles of essentially neutral buoyancy, operates with an expanded bed of circulating particles. The particle number density attainable in such a reactor has been found to be dependent upon the circulation cell aspect ratio, the individual particle properties, the static bed voidage of the particles, and the superficial gas velocity. The oxygen mass transfer characteristics have been found to be dependent upon the circulatory nature of the system, the particle (solids) holdup, the particle porosity, and the superficial gas velocity.     

Particle size and density distributions of two dense matrices in an expanded bed system

The size and density distributions of two commercial media, that is, Streamline particles and 6% agarose coated steel beads (6AS), in an expanded bed system has been studied with a glass column (26 mm I.D.) modified by side ports. The Streamline particles have a broad size distribution but a relatively uniform density, while the 6AS beads have both broad size and density distributions. The effect of liquid-phase flow velocity, liquid viscosity and settled bed height on the particle size and density distributions is investigated. It is found that the radial mean particle size and density of the two matrices are uniform, while axial classifications are obvious in the expanded beds. For the Streamline, the volume-weighted mean particle size decreases linearly with increasing expanded bed height. For the 6AS beads, however, the mean particle size is even in the axial direction, but the particle density decreases exponentially with the increase of bed height. Moreover, the mean particle size of the Streamline or the density of the 6AS beads is well expressed as a function of the normalized bed height (that is, the ratio of the distance from bed bottom to the expanded bed height). The liquid flow-rate, liquid viscosity and settled bed height influence the mean axial size or density distribution by affecting the expanded bed height.     

Numerical simulation of the hydrodynamics of an inverse liquid–solid fluidized bed using combined Lattice Boltzmann and smoothed profile methods

Knowledge of an inverse fluidized-bed fluid hydrodynamics is advantageous in optimal adjustment and designing high-efficiency beds. In the present study, a combination of a single relaxation time collision operator lattice Boltzmann method (LBM) and the smoothed profile method (SPM) is employed to simulate the hydrodynamics of an inverse liquid–solid fluidized bed comprising circular monodisperse and polydisperse particles in a rectangular channel. A numerical instance of inverse fluidization involving 231 particles is illustrated to show the capability of the combined methods. Moreover, comparison of the numerical results is performed with the Ergun equation and the Richardson–Zaki correlation. The comparison demonstrates that the present model can simulate the fluid flow behavior in an inverse fluidized bed. Several different models were also presented to investigate the effect of different fluid properties and size of particles in the bed. Simulations indicate that the more the superficial liquid velocity, the higher the porosity of the bed. The present simulations show that porosity of the bed increases by increasing the particles size, and also the vertical velocity of the bed decreases with an increase in liquid viscosity. Finally, polydisperse particle systems are also simulated. The results show that porosity in an inverse fluidized bed comprising polydisperse particles is more than that of a monodisperse particle bed.     

Structure-transport analysis for particulate packings in trapezoidal microchip separation channels

This article investigates the efficiency of particulate beds confined in quadrilateral microchannels by analyzing the three-dimensional fluid flow velocity field and accompanying hydrodynamic dispersion with quantitative numerical simulation methods. Random-close packings of uniform, solid (impermeable), spherical particles of diameter d(p) were generated by a modified Jodrey-Tory algorithm in eighteen different conduits with quadratic, rectangular, or trapezoidal cross-section at an average bed porosity (interparticle void fraction) of epsilon = 0.48. Velocity fields were calculated by the lattice Boltzmann method, and axial hydrodynamic dispersion of an inert tracer was simulated at Péclet numbers Pe = u(av)d(p)/D(m) (where u(av) is the average fluid flow velocity through a packing and D(m) the bulk molecular diffusion coefficient) from Pe = 5 to Pe = 30 by a Lagrangian particle-tracking method. All conduits had a cross-sectional area of 100d(p)(2) and a length of 1200d(p), translating to around 10(5) particles per packing. We present lateral porosity distribution functions and analyze fluid flow profiles and velocity distribution functions with respect to the base angle and the aspect ratio of the lateral dimensions of the different conduits. We demonstrate significant differences between the top and bottom parts of trapezoidal packings in their lateral porosity and velocity distribution functions, and show that these differences increase with decreasing base angle and increasing base-aspect ratio of a trapezoidal conduit, i.e., with increasing deviation from regular rectangular geometry. Efficiencies are investigated in terms of the axial hydrodynamic dispersion coefficients as a function of the base angle and base-aspect ratio of the conduits. The presented data support the conclusion that the efficiency of particulate beds in trapezoidal microchannels strongly depends on the lateral dimensions of the conduit and that cross-sectional designs based on large side-aspect-ratio rectangles with limited deviations from orthogonality are favorable.     

Gas holdup in three-phase immobilized-cell bioreactors

A number of studies in the published literature deal with gas holdup in three-phase reactors. However, very few address the cases in which the solid density approaches that of the liquid phases and in which low gas velocities are involved. These conditions are commonly encountered in immobilized-cell bubble columns and in fluidized-bed bioreactors. This paper reports the effect of gas and liquid velocity upon gas holdup and bed expansion in fluidized-bed bioreactors. For liquid-fluidization of low-density alginate beads in the absence of gas, the terminal sedimentation velocity (vT) of the particles is a constant, and expansion of the bed follows Richardson and Zaki’s correlation. In the presence of gas, however, the apparent terminal sedimentation velocity value is affected by the velocity of the gas and liquid phases. For gas velocities above a minimum value, the calculated value of vT depends on liquid velocity only, and a constant bed expansion was observed for a range of gas and liquid flow rates. For the gas-liquid interactions, a modified drift-flux model was found to be valid. For superficial gas velocities between 5 and 17 cm/min, the modified drift-flux velocity was observed to be a function of gas velocity, suggesting the prevalence of a coalescence regime.     

Molecular theory of barycentric velocity: monatomic fluids

The notion of barycentric velocity appears in irreversible thermodynamics and fluid mechanics, in which it is a field variable obeying the hydrodynamic equations or, more specifically, the momentum balance equation, which is coupled to the rest of hydrodynamic equations. Therefore, its behavior is not known until the hydrodynamic equations are solved for the flow problem of interest. Unlike diffusion fluxes, heat fluxes, or stresses, it does not have its own constitutive relation similar to Fick's law, Fourier's law, and Newton's law of viscosity. In this work, the constitutive equation is derived for it. In parallel to the phenomenological notion of barycentric velocity, the notion of mean fluid velocity appears in statistical mechanics of irreversible dynamic processes according to the theory of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)], and plays the same role of the phenomenological counterpart. In this work, we investigate the statistical mechanical meanings of the mean fluid velocity of a fluid in flow beyond its formal connection with the barycentric velocity. We show that it consists of two components; the center-of-gravity velocity of the packet of fluid molecules, which may be identified with the barycentric velocity in the phenomenological theory, and the diffusive contribution of its collective modes relative to the center of gravity. If the fluid is uniform in space or if the packet of fluid mass is rigid, the diffusive component vanishes. The statistical mechanical (molecular theory) formula for the mean fluid velocity provides the constitutive relation for it in terms of density and temperature gradients present in the fluid in flow. The constitutive relation obtained for the mean fluid velocity can be an important component in the theory of transport processes in liquids. Its significance to fluid mechanics is briefly discussed.     

加压流化床流化性质的实验与模拟研究

在二维射流流化床装置中,考察了压力对颗粒和气泡运动的影响规律.通过使用摄像技术详细的记录了压力下气泡的行为,并对其进行了分析,由此解决了较高压力下测量流态化性质较为困难的问题.数值研究通过CFD双欧拉模型模拟了带有V形分布器和中心射流的二维流化床内压力对气泡大小、床的膨胀率和射流深度的影响.实验和理论结果表明,在加压状态下,射流气速和分布板气速对气泡的产生、大小及形状有不同的影响.在较高的操作压力下,射流气速增加,气泡变长;分布器气速增大,气泡则变大;射流高度随着分布器气速的增加而降低.模拟结果与实验数据吻合较好,由此该模型为研究较高操作压力下射流流化床流化性质提供了有利的工具.     

Variations of particle size and bed voidage distributions in expanded bed during transient operation processes

Changes in bed expansion are frequently encountered during an expanded bed adsorption, such as during the initial bed expansion, feed loading and washing processes. We have here studied the changes of local particle size distribution and bed voidage of an expanded bed in the initial bed expansion process as well as those during the changes in mobile phase viscosity, which imitated feed loading and column washing processes. Using a glass column modified with three side sampling ports and Streamline AC as the solid phase, experimental measurements on a series of operation moments during the transient processes were carried out by sampling the particles from within the column at different axial positions. In the initial bed expansion process, the gradual formation of an axial classification from a settled bed to a stable expanded bed was first displayed. By changing the mobile phase from water to 10% (w/w) glycerol solution or vice versa, the variations in both the particle size distribution and bed voidage corresponding to the increase or decrease of the bed height caused by the changes of the mobile phase viscosity were examined as well. The transient changes of the local particle size distribution and bed voidage first occurred in the bed bottom and then progressed from bottom to top along the axial direction. However, the changes of bed voidage at different axial positions were not unidirectional. That is, by changing the mobile phase to the high-viscosity glycerol solution, a constant increase of the bed voidage was observed in the bed bottom, while a distinct decrease of the bed voidage before its increase was involved at the middle and top positions. This is ascribed to the compression effect caused by the upward movement of the lower part particles.     

Adsorption Strategy of Plasmid DNA Nanoparticulate: Preparative Purification by a Simple Custom Expanded Bed Column

This paper summarizes the critical examination of the hydrodynamic performance of the NBG expanded bed contactor operated with streamline-DEAE adsorbent under various operating conditions for expanded bed adsorption of plasmid DNA nanoparticles from alkaline lysate. The purification process is not RNase-free. In this study, a rapid and efficient scaleable purification protocol obtaining, plasmid DNA nanoparticles (average size of 40 nm) with a high purity level for use as therapeutic agent in customized NBG expanded bed columns was developed. This technique allows efficient levels of binding to the column media and vector purification without centrifugation or filtration steps. Residence time distribution (RTD) studies were exploited to achieve the optimal condition of plasmid DNA nanoparticle (pDNA) recovery upon anion exchange adsorbent in this contactor. In addition, the purification experiments were carried out in the expanded bed columns with settle bed height of 6.0 ± 0.2 cm. NaCl gradient elution enabled the isolation of supercoiled plasmid from low-Mr RNA, cDNA and plasmid variants. Subsequently dynamic binding capacity of the adsorbent was calculated while these values decreased with increase in flow velocity. Moreover, the effect of pH upon the performance of this recovery process and the feedstock volume upon the expanded bed anion exchange purification was investigated. The results demonstrated that separation of low-Mr RNA from plasmid DNA isoforms in the range of pH between 5.5 and 7.5 is achievable in this column. The yield of recovery of pDNA in optimal condition was higher than 88.51% which was a superior result in one-pass frontal chromatography. The generic application of simple customized NBG expanded bed column and its potential for the purification and recovery of plasmid DNA as a nanoparticulate bioproduct is strongly discussed.