Bruce D. Bowen

Fine particle deposition in smooth parallel-plate channels

Abstract The effect of electrical double-layer interactions on the rate of deposition of uniform spherical particles from an aqueous suspension in laminar flow through a smooth parallel-plate channel was measured experimentally using a radioactive tracer technique. The results obtained under initial conditions (negligible surface coverages) were compared to those predicted using a previously published theoretical model. It was found that for the deposition of negatively charged silica particles onto a positively charged plastic substrate, especially at intermediate counterion concentrations, good quantitative agreement between theory and experiment was obtained by assuming that the process was mass-transfer controlled. However, for negative particles and negative channel walls, although the theory provided an accurate qualitative description of the experimental results, the measured deposition rates were always much greater than those predicted theoretically. The evidence suggests that the primary cause of this discrepancy is the failure of the model to account for surface heterogeneity, which could result in preferential deposition onto areas of locally favorable potential or geometry. It was also found that, under the conditions of the present experiments, the release of deposited particles from the channel surface was negligible. Thus, the declining rate of accumulation with time observed in most runs could only be attributed to a diminishing rate of particle deposition.

Fine particle deposition in laminar flow through parallel-plate and cylindrical channels

Abstract The deposition of colloidal particles from a suspension in steady fully developed laminar flow onto the walls of a channel is rationalized as equivalent to mass transfer in the bulk with a first-order reaction at the walls. The resulting extended Graetz problem is solved for both parallel-plate and cylindrical channels. Through the use of confluent hypergeometric functions combined with asymptotic techniques, an evaluation of the resulting series solutions is made possible which is more accurate than all previous solutions, especially for the deposition of colloids and for cylindrical channels. Simple Leveque-type asymptotic solutions are also obtained for the case of large Peclet numbers, and when the reaction rate constant is infinite, these reduce to the corresponding well-established results for convective diffusion.

Mammalian cell retention devices for stirred perfusion bioreactors

Within the spectrum of current applications for cell culture technologies, efficient large-scale mammalian cell production processes are typically carried out in stirred fed-batch or perfusion bioreactors. The specific aspects of each individual process that can be considered when determining the method of choice are presented. A major challenge for perfusion reactor design and operation is the reliability of the cell retention device. Current retention systems include cross-flow membrane filters, spin-filters, inclined settlers, continuous centrifuges and ultrasonic separators. The relative merits and limitations of these technologies for cell retention and their suitability for large-scale perfusion are discussed.

Stabilization of emulsions by fine particles II. capillary and van der Waals forces between particles

Abstract The effective surface tension (free energy per unit area) of a planar oil/water interface completely covered with a closely-packed monolayer of identical spherical particles is determined as a function of contact angle. The surface tension diminishes as contact angle increases from 0° to 90° or decreases from 180° to 90°. Preliminary experimental results show this general trend. A theoretical study is made of the capillary forces acting between the interfacial spherical particles which stabilize oil/water emulsion droplets. Applying a two-dimensional cell model, the oil/water meniscus immediately surrounding a given particle of a closely-packed monolayer structure is assumed to have circular symmetry. Changes in interfacial areas between the oil, water and solid occur when an isolated surface particle becomes a member of the monolayer structure. For the simplified model used here the accompanying energy change due to interfacial tension yields a repulsion between the surface particles for all contact angles. By applying the well-known Derjaguin method of determining the interaction of particles at close separation, the van der Waals attraction between adjacent spheres in the monolayer is calculated as a function of the contact angle. The magnitudes of the capillary and van der Waals energy per particle are smaller by three or four orders of magnitude than the depth of the energy well in which an isolated solid sphere is trapped at the oil/water interface.

Capillary interaction of spherical particles adsorbed on the surface of an oil/water droplet stabilized by the particles. Part II

Abstract We develop a conical-cell model for determining the capillary interaction between identical spherical particles forming a monolayer adsorbed at variable packing on the surface of an oil-in-water (Pickering) emulsion droplet. Each adsorbed particle is assigned a cone-shaped section of the droplet volume. The vertex of the cone is located at the center of the droplet and the axis of the cone passes through the center of the adsorbed particle. A typical adsorbed particle is surrounded by an oil/water interfacial shell having circular symmetry about the axis of the cone. The shape of the oil/ water interface is obtained by solving the Young—Laplace equation. It is required that the volume of the dispersed phase in the droplet, which is contained in the cone, does not change on adsorption of the monolayer of particles. The interfacial energy assigned to a single adsorbed particle and its surrounding oil/water interface situated within its cone is determined. The capillary interaction is obtained by subtracting the corresponding interfacial energy when capillary interaction between the adsorbed particles is ignored. One method of obtaining interfacial energy without capillary interaction between the particles is based on the model of Menon, Nagarajan and Wasan, described in part I (S. Levine and B.D. Bowen, Colloids Surfaces, 59 (1991) 377). With this choice of interfacial energy without particle interactions, the capillary interaction is small and attractive. The leading term is identical with that obtained in Part I, by developing further the model of Menon, Nagarajan and Wasan. This term is proportional to the fourth power of the particle radius and diminishes as the inverse square of the separation between the particles. The use of the conical-cell model yields an additional term which is expressed in terms of the difference between the so-called effective (macroscopic) interfacial tension, due to the layer of adsorbed particles, and the conventional (microscopic) tension of the oil/water interface without particles. Although our result is consistent with the order of magnitude of the capillary interaction found with an earlier cylindrical-cell model, which was intended to apply to a very large droplet, the latter gave an incorrect capillary repulsion between the adsorbed particles.

Streaming potential in the hydrodynamic entrance region of cylindrical and rectangular capillaries

Previous analyses of streaming potential in capillaries have ignored the region of flow development that occurs near the entrance of all ducts. A new theory is presented which accounts for the influence of the hydrodynamic entrance region on streaming potential measurements under conditions where the capillary dimensions are large relative to the double-layer thickness. First, a general theory is formulated for capillaries having an arbitrary cross-sectional shape. Specific application is then made to the two ducts in most common experimental use; namely, cylindrical and rectangular capillaries. The results are given in terms of correction factors modifying the classical Helmholtz-Smoluchowski equation which applies when the capillaries are sufficiently long.

Optimization of an Acoustic Cell Filter with a Novel Air-Backflush System

Increasing worldwide demand for mammalian cell production capacity will likely be partially satisfied by a greater use of higher volumetric productivity perfusion processes. An important additional component of any perfusion system is the cell retention device that can be based on filtration, sedimentation, and/or acoustic technologies. A common concern with these systems is that pumping and transient exposure to suboptimal medium conditions may damage the cells or influence the product quality. A novel air‐backflush mode of operating an acoustic cell separator was developed in which an injection of bioreactor air downstream of the separator periodically returned the captured cells to the reactor, allowing separation to resume within 20 s. This mode of operation eliminated the need to pump the cells and allows the selection of a residence time in the separator depending on the sensitivity of the cell line. The air‐backflush mode of operating a 10L acoustic separator was systematically tested at 107 cells/mL to define reliable ranges of operation. Consistent separation performance was obtained for wide ranges of cooling airflow rates from 0 to 15 L/min and for backflush frequencies between 10 and 40 h−1. The separator performance was optimized at a perfusion rate of 10 L/day to obtain a maximum separation efficiency of 92 ± 0.3%. This was achieved by increasing the power setting to 8 W and using duty cycle stop and run times of 4.5 and 45 s, respectively. Acoustic cell separation with air backflush was successfully applied over a 110 day CHO cell perfusion culture at 107 cells/mL and 95% viability.

Two-dimensional analysis of protein transport in the extracapillary space of hollow-fibre bioreactors

The two-dimensional porous medium model (PMM) has been applied to predict the redistribution of protein in the extracapillary space (ECS) of hollow-fibre bioreactors (HFBRs) during open-shell and closed-shell operations. The time-dependent convection-diffusion equation describing protein transport was coupled with the quasi-steady lumen and ECS pressure equations through a relationship between the osmotic pressure and the concentration of protein. Model simulations of closed-shell operation with radial lumen pressure gradients imposed at the inlet and outlet of the fibre bundle showed significant axial as well as radial polarisation of ECS protein. Experiments were carried out to determine the ECS protein distributions that arise during HFBR inoculation. The PMM predictions were generally in better agreement with the experimental data than those obtained using a one-dimensional Krogh cylinder model (KCM). Although the experiments demonstrated significant angular variations of concentration, believed to be due to non-uniform fibre distribution, the angularly and radially averaged concentration profiles were generally well represented by the PMM. Differences between the theoretical and experimental results can be explained by natural convection effects caused by vertical gradients of protein concentration and fluid density.

Two-dimensional analysis of fluid flow in hollow-fibre modules

A new model of hollow-fibre membrane devices has been developed in which the lumen and shell sides of the fibre bundle are treated as two interpenetrating porous regions. Darcys law and fluid continuity are combined to give a set of two-dimensional partial differential equations governing the hydrodynamics within these devices. The computational domain corresponds to the real dimensions of a hollow-fibre cartridge and hence macroscopic radial gradients, which exist during some operations, can be taken into account. The effects of fibre expansion under wet conditions are also included. The model was used to analyse fluid flow in several different configurations, including the closed-shell mode, dead-end and cross-flow filtration as well as counter-current and co-current contacting. The effects of the membrane and shell-side hydraulic permeabilities on the volumetric flow rates and spatial flow distribution were investigated and the predictions were compared with those of one-dimensional models based on the Krogh cylinder approximation. The new model can be readily extended to incorporate solute transport, gravitational effects, non-idealities of cartridge design or local variations of system parameters.

Transport of fluid and solutes in the body I. Formulation of a mathematical model

A compartmental model of short-term whole body fluid, protein, and ion distribution and transport is formulated. The model comprises four compartments: a vascular and an interstitial compartment, each with an embedded cellular compartment. The present paper discusses the assumptions on which the model is based and describes the equations that make up the model. Fluid and protein transport parameters from a previously validated model as well as ionic exchange parameters from the literature or from statistical estimation [see companion paper: C. C. Gyenge, B. D. Bowen, R. K. Reed, and J. L. Bert. Am. J. Physiol. 277 ( Heart Circ. Physiol. 46): H1228-H1240, 1999] are used in formulating the model. The dynamic model has the ability to simulate 1) transport across the capillary membrane of fluid, proteins, and small ions and their distribution between the vascular and interstitial compartments; 2) the changes in extracellular osmolarity; 3) the distribution and transport of water and ions associated with each of the cellular compartments; 4) the cellular transmembrane potential; and 5) the changes of volume in the four fluid compartments. The validation and testing of the proposed model against available experimental data are presented in the companion paper.