Intraparticle Peclet Number Research Articles

Protein and virus-like particle adsorption on perfusion chromatography media

The structural and protein adsorption characteristics of the perfusion chromatography matrix POROS® HS 50 are determined. Transmission electron microscopy shows a broad distribution of pore sizes with 100–500nm through-pores transecting a network of much smaller pores formed by aggregates of microgranules about 100nm in size. Dextran standards, proteins, and virus-like particles (VLPs) show size-exclusion behavior consistent with such a bimodal distribution of pore sizes. For non-binding conditions, the trends in height equivalent to a theoretical plate (HETP) as a function of mobile phase velocity and molecular size are consistent with perfusion suggesting that a fraction of the mobile phase between 0.0005 and 0.0008 flows through the particles. This small fraction provides little or no enhancement of intraparticle mass transfer for relatively small proteins (lysozyme and IgG) even at 1000cm/h, but can contribute substantially to transport for large proteins (thyroglobulin) and VLPs. Intraparticle concentration profiles during transient adsorption are determined by confocal microscopy in batch and flow systems. The profiles are spherically symmetrical indicating a dominance of diffusion for smaller proteins in both batch and flow systems but become highly asymmetrical and skewed in the direction of flow for thyroglobulin at 1000cm/h. Estimates of the convective enhancement of intraparticle transport for these conditions based on the confocal measurements are consistent with estimates of the intraparticle Peclet number and previously published models. Adsorption of VLPs, however, was found to be confined to a thin layer on the outer surface of the particles indicting that bound VLPs block access to the underlying pore network and suggesting that pores larger than those present on the resin studies are needed to take advantage of the effects of perfusion for the adsorption of large VLPs.

Characterization of Convection for Molecularly Imprinted Monolith

Convection of molecularly imprinted polymers monolith in LC mode was discussed in this paper. On the MIPs monolith reported here, a flat van Deemter plot of height equivalent to a theoretical plate (HETP) versus superficial velocity was observed. This typical behavior, similar to perfusion packings, suggests that the unique pore structure of the MIPs monolith allowed convection-enhanced mass transfer. Column parameters, e.g., external porosities, internal porosity, column permeability and equivalent sphere dimension, were obtained. Intraparticle Peclet number (λ) was used to characterize the convection in the monolith. In addition, a ratio of the numbers of transfer units, T, for diffusion in the micropores and through-pores has been introduced to quantify the relative importance of the contribution from convection and diffusion to mass transfer. The results show that the flow in a MIP monolith is extremely sensitive to pore size distribution and can be tuned by polymerization parameters.

Determination of the intraparticle electroosmotic volumetric flow-rate, velocity and Peclet number in capillary electrochromatography from pore network theory

The results obtained from the pore network model employed in this work, clearly show that the magnitudes of the intraparticle electroosmotic volumetric flow-rate, Q intrap, and velocity, 〈 v intrap, x 〉, in the pores of the charged porous silica particles considered in this study are greater than zero. The intraparticle Peclet number, Pe intra, of a solute in these charged porous silica particles would be greater than zero, and, in fact, the magnitude of the intraparticle Peclet number, Pe intrap, of lysozyme is greater than unity for all the values of the pore connectivity, n T, of the intraparticle pores and of the applied electric potential difference per unit length, E x , along the axis of the capillary column considered in this work. Furthermore, the values of the intraparticle electroosmotic volumetric flow-rate, Q intrap, and velocity, 〈 v intrap, x 〉, as well as the magnitude of the pore diffusion coefficient, D p, of the solute increase as the value of the pore connectivity, n T, of the intraparticle pores increases. The intraparticle electroosmotic flow can contribute significantly, if the appropriate chemistry is employed in the mobile liquid phase and in the charged porous particles, in (i) decreasing the intraparticle mass transfer resistance, (ii) decreasing the dispersive mass transfer effects, and (iii) increasing the intraparticle mass transfer rates so that high column efficiency and resolution can be obtained.

Modeling the velocity field of the electroosmotic flow in charged capillaries and in capillary columns packed with charged particles: interstitial and intraparticle velocities in capillary electrochromatography systems

Mass transfer systems based on electrokinetic phenomena (i.e., capillary electrochromatography (CEC)) have shown practical potential in becoming powerful separation methods for the biotechnology and pharmaceutical industries. A mathematical model has been constructed and solved to describe quantitatively the profiles of the electrostatic potential, pressure, and velocity of the electroosmotic flow (EOF) in charged cylindrical capillaries and in capillary columns packed with charged particles. The results obtained from model simulations (i) provide significant physical insight and understanding with regard to the velocity profile of the EOF in capillary columns packed with charged porous particles which represent systems employed in CEC, (ii) provide the physical explanation for the experimental results which indicate that the velocity of the EOF in capillary columns packed with charged porous particles is a very weak function (it is almost independent) of the diameter of the particles, and (iii) indicate that the intraparticle velocity, v p,i, of the EOF can be greater than zero. The intraparticle Peclet number, Pe int rap, for lysozyme was found to be greater than unity and this intraparticle convective mass transfer mechanism could contribute significantly, if the appropriate chemistry is employed in the mobile liquid phase and in the charged porous particles, in (a) decreasing the intraparticle mass transfer resistance, (b) decreasing the dispersive mass transfer effects, and (c) increasing the intraparticle mass transfer rates so that high column efficiency and resolution can be obtained. Furthermore, the results from model simulations indicate that for a given operationally permissible value of the applied electric potential difference per unit length, E x , high values for the average velocity of the EOF can be obtained if (1) the zeta potential, ζ p, at the surface of the particles packed in the column has a large negative magnitude, (2) the value of the viscosity, μ, of the mobile liquid phase is low, (3) the magnitude of the dielectric constant, ε, of the mobile liquid phase is reasonably large, and (4) the combination of the values of the concentration, C ∞, of the electrolyte and of the dielectric constant, ε, provide a thin double layer. The theoretical results for the velocity of the EOF obtained from the solution of the model presented in this work were compared with the experimental values of the velocity of the EOF obtained from a fused-silica column packed with charged porous silica C 8 particles. Systems with four different particle diameters and three different concentrations of the electrolyte were considered, and the magnitude of the electric field was varied widely. The agreement between theory and experiment was found to be good.

Modeling and simulation of protein adsorption in permeable chromatographic packings: a double linear driving force model

Permeable large-pore packings have many applications, particularly in perfusion chromatography for bioseparations. The major objectives of this paper are: (i) to develop a double linear driving force (LDF) model based on linear driving force approximations inside throughpores and microparticles to simulate dynamic nonlinear adsorption in columns having spherical permeable chromatographic packings with a bidisperse pore structure; and (ii) to analyze the performance of this simple model to simulate breakthrough and elution curves for bovine serum albumin adsorption on POROS Q/M large-pore particles (PerSeptive Biosystems, Cambridge, MA, USA), in comparison with a more realistic and difficult model (intraparticle diffusion/convection model) which is also presented in this paper. Model results obtained for several values of the intraparticle Peclet number, λ, resulting from the convective flow in the throughpores show the very reasonable performance of the double LDF model in simulating breakthrough and elution curves of proteins, particularly for higher values of λ. This finding is of relevance due to the remarkable saving in computation time afforded with the double LDF model.

Estimation of pore diameter for intraparticle fluid flow in bidisperse porous chromatographic particles

A quantitative method is developed and presented for estimating the mean pore diameter, d pore, that could allow intraparticle fluid flow in the macroporous region of adsorbent particles with a bidisperse porous structure packed in a column. The method is used to estimate the value of d pore that is required to obtain specified values of the fraction, F, of the column superficial fluid velocity that is flowing through the macroporous region of the adsorbent particles and the value of d pore that is required to obtain specified values of the intraparticle Peclet number, Pe intra.

Perfusion chromatography: performance of periodic countercurrent column operation and its comparison with fixed-bed operation

Abstract Simulation studies using mathematical models that describe the single-component adsorption of bovine serum albumin into spherical bidisperse perfusive and spherical bidisperse purely diffusive anion-exchange porous adsorbent particles in a single-column fixed-bed system and in a two-column periodic countercurrent system in which the adsorbent is equally distributed over two beds are presented. The total length of the two-column periodic countercurrent system is equal to the length of the single-column fixed-bed system, and studies are performed for different values of the intraparticle Peclet number, Pe intra , and of the microsphere diameter, d m . In the single-column fixed-bed system, the percentage utilization of the adsorptive capacity of the adsorbent increases as d m decreases and Pe intra increases. The results indicate that the two-column system under periodic countercurrent operation provides higher values for the percentage utilization of the adsorptive capacity of the adsorbent than all the values of the percentage utilization of the adsorptive capacity of the adsorbent obtained from the single-column fixed-bed system for all values of d m and Pe intra examined in this work. It is an interesting result that the percentage utilization of the adsorptive capacity obtained from a two-column periodic counter-current system having purely diffusive ( Pe intra = 0) adsorbent particles with the largest microsphere size, d m , studied in this work is found to be higher than the percentage utilization of the adsorptive capacity obtained from a single-column system that uses perfusive adsorbent particles with the smallest microsphere size, d m , and the largest intraparticle Peclet number, Pe intra , studied in this work. The simulation studies with the two-column periodic countercurrent system also provide the following interesting result: the factors of economic significance in the two-column system under periodic countercurrent operation, namely the time between column switches and the degree of saturation of the column removed, are nearly independent of the values of the microsphere diameter, d m , and the intraparticle Peclet number, Pe intra .

“Perfusion chromatography”. The effects of intra-particle convective velocity and microsphere size on column performance

A mathematical model describing the dynamic adsorption in columns with spherical bidisperse perfusive or spherical bidisperse purely diffusive adsorbent particles is presented and its solution is obtained numerically. The adsorption of bovine serum albumin on spherical anion-exchange porous particles was studied for different values of the intraparticle Peclet number, Pe intra, and of the microsphere diameter, d m. The results show a departure from spherical symmetry of the isoconcentration profiles of the adsorbate in the porous adsorbent particle as Pe intra increases. This spherical asymmetry increases the adsorbate availability in the pore fluid of the macroporous region and also increases the concentration of the adsorbate in the adsorbed phase in the upstream half of the spherical adsorbent particle. If, for example, the concentration profiles of the adsorbate in the adsorbed phase of the porous adsorbent particles could be determined experimentally and if these profiles show a departure from spherical symmetry, then this result could suggest that the porous adsorbent particles may have exhibited perfusion behavior under the conditions of operation of the column. The dynamic percentage utilization of the adsorptive capacity of the column increases as Pe intra increases and d m decreases. The percentage breakthrough to be selected for column switching is influenced by the magnitude of Pe intra because of its effect on the dynamic percentage utilization of the adsorptive capacity of the column.

Wrong-way behavior in packed-bed reactors with “large-pore” catalysts

The effect of intraparticle convection on the wrong-way behavior of a non-isothermal packed-bed reactor is analyzed. Transient one-dimensional heterogeneous models were used to calculate the dynamic responses of the system: the HT dc model, which takes into account both internal convective and diffusive fluxes and the HT d model, that includes only diffusional resistances inside the particle. The o-xylene oxidation to phthalic anhydride, described by a single first-order irreversible exothermic reaction was used as an example. For a sudden decrease in the feed temperature ( T 0), the HT dc model predicts an inverse temperature response along a wide range of inlet concentrations, which becomes more significant for rising C 0 values. Wrong-way behavior is also reported by the HT d model, for more severe operating conditions (high values of C 0 and T 0), where the temperature excursion can exhibit a sharp transient increase. It is also shown that, for the same operating conditions, the dynamic behavior of the packed-bed reactor depends on the intraparticle Peclet number, λ m, that accounts for the competition between convection and diffusion inside the catalyst particle.

The effect of intraparticle convection on conversion in heterogeneous isothermal fixed-bed reactors with large-pore catalysts for first-order reactions

Residence time distributions have been largely used in chemical engineering to make diagnosis of the ill-functioning of chemical reactors and to predict conversion in homogeneous isothermal reactors once the kinetic rate of reaction is known. The prediction is unambiguous for first-order reactions. In this paper, the impulse tracer response of isothermal heterogeneous fixed-bed reactors packed with large-pore catalysts, in which intraparticle convection occurs, is derived. From the impulse tracer response, the residence time distribution of the outer phase is calculated and used to predict the steady state conversion in the reactor for first-order reactions. The effect of intraparticle convection, measured by the intraparticle Peclet number λ for a given reaction-catalyst system, i.e. for a set of Damkhöler, Thiele, Biot and Peclet numbers (Da, ø, Bi m and Pe respectively) is to drive the conversion between the diffusion-controlled and the kinetic-controlled limits. The problem of scaling from batch to continuous packed beds is also addressed.

Peak resolution in linear chromatography: Effects of intraparticle convection

The quantitative relationship between separation performance and intraparticle convection in large-pore, permeable supports for chromatography is examined. A model for linear chromatography is used in the analysis for particles that contain both throughpores where diffusive and convective transport occur and purely diffusive micropores. The key concept is that of a convection-augmented intraparticle diffusivity, which depends only on the intraparticle Peclet number, λ. The separation performance is expressed in terms of both resolution and peak profiles at the column outlet. It is shown that, for given operating conditions, the separation enhancement obtained for intraparticle convection is dependent on the relative importance of throughpore and micropore diffusion rates. In the absence of micropore resistances, the resolution is always increased by intraparticle convection. The latter, however, is shown to have no effect on the separation performance when micropore diffusional resistances are dominant. Relationships necessary to assess the importance of these effects for linear chromatography conditions are provided.