Influence of vascular porosity on fluid flow and nutrient transport in loaded cortical bone

Load-induced fluid flow is a key factor in triggering bone modeling and remodeling processes that maintain bone mass and architecture. To provide an enhanced understanding of fluid flow in bone, unique computational models of a tibial section were developed. The purpose of the study was to examine the effects of incorporating vascular porosity on pore fluid pressure and resulting lacunocanalicular flow and to determine the role of load-induced fluid flow in tracer transport. Simulations revealed large local pressure gradients surrounding the vascular canals that were dependent on the magnitude and state (i.e., compressive or tensile) of the stress. Fluid velocity magnitudes were increased by over an order of magnitude in the dual-porosity model, relative to the single-porosity model. Fluid flow had a marked effect on tracer perfusion within the cortex. After 10 loading cycles, a 9-fold increase in tracer concentration, relative to diffusion alone, was observed in the compressive region where fluid exchange was greatest between the lacunocanalicular porosity and the vascular canals. Agreement was achieved between computational results and experimental investigations of electrokinetic phenomenon, tracer transport, cellular stimulation, and functional adaptation. The models produced substantial improvements in bone fluid flow simulation and underscored the significance of incorporating vascular porosity in models designed to quantify fluid pressure and flow characteristics within mechanically loaded cortical bone.     

An ex vivo model to study transport processes and fluid flow in loaded bone

Load-induced fluid flow has been postulated to provide a mechanism for the transmission of mechanical signals (e.g. via shear stresses, enhancement of molecular transport, and/or electrical effects) and the subsequent elicitation of a functional adaptation response (e.g. modeling, remodeling, homeostasis) in bone. Although indirect evidence for such fluid flow phenomena can be found in the literature pertaining to strain generated potentials, actual measurement of fluid displacements in cortical bone is inherently difficult. This problem motivated us to develop and introduce an ex vivo perfusion model for the study of transport processes and fluid flow within bone under controlled mechanical loading conditions. To this end, a closed-loop system of perfusion was established in the explanted forelimb of the adult Swiss alpine sheep. Immediately prior to mechanical loading, a bolus of tracer was introduced intraarterially into the system. Thereafter, the forelimb of the left or right side (randomized) was loaded cyclically, via Schanz screws inserted through the metaphyses, producing a peak compressive strain of 0.2% at the middiaphysis of the anterior metacarpal cortex. In paired experiments with perfusion times totalling 2, 4, 8 and 16 min, the concentration of tracer measured at the middiaphysis of the cortex in cross section was significantly higher in the loaded bone than in the unloaded contralateral control. Fluorometric measurements of procion red concentration in the anterior aspect alone showed an enhancement in transport at early stages of loading (8 cycles, 2 min) but no effect in transport after higher number of cycles or increased perfusion times, respectively. This reflects both the small size of the molecular tracer, which would be expected to be transported rapidly by way of diffusive mechanisms alone, as well as the loading mode to which the anterior aspect was exposed. Thus, using our new model it could be shown that load-induced fluid flow represents a powerful mechanism to enhance molecular transport within the lacunocanalicular system of compact bone tissue. Based on these as well as previous studies, it appears that the degree of this effect is dependent on tracer size as well as the mechanical loading mode to which a given area of tissue is exposed.     

Influence of interstitial bone microcracks on strain-induced fluid flow

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified.     

Fluid flow and convective transport of solutes within the intervertebral disc

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc.An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa.Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.     

Probing the tissue to subcellular level structure underlying bone's molecular sieving function

Transport of fluorescent probes between 300 and 2,000,000 Da was studied in mechanically loaded and unloaded ulnae of skeletally mature rats to characterize the permeability of the pericellular space of the lacunocanalicular system (LCS), and the microporosity of the bony matrix. The mineral matrix porosity allowed for penetration of the 300 Da probe but impeded transport of larger probes. The pericellular space of the LCS was permeable up to 10 kDa; above 10 kDa, diffusion was ineffective for transport through the pericellular space. Convective transport via load-induced fluid flow increased penetration of all probes up to 70 kDa. Above this threshold, probes were excluded from bone, both with and without loading. This exploratory study suggests that bone acts as a molecular sieve and that mechanical loading modulates transport of solutes through the pericellular space that links osteocytes deep within the tissue to the blood supply and to osteoblasts and osteoclasts on bone forming and resorbing surfaces. This provides support for the postulate of transport modulated bone remodeling in which osteocytes are influenced by and modulate the local permeability of their surroundings as a means for survival (Knothe Tate et al. 1998, [28]) and has profound implications for osteocyte viability and intercellular communication in bone.     

Modeling of neutral solute transport in a dynamically loaded porous permeable gel: implications for articular cartilage biosynthesis and tissue engineering

A primary mechanism of solute transport in articular cartilage is believed to occur through passive diffusion across the articular surface, but cyclical loading has been shown experimentally to enhance the transport of large solutes. The objective of this study is to examine the effect of dynamic loading within a theoretical context, and to investigate the circumstances under which convective transport induced by dynamic loading might supplement diffusive transport. The theory of incompressible mixtures was used to model the tissue (gel) as a mixture of a gel solid matrix (extracellular matrix/scaffold), and two fluid phases (interstitial fluid solvent and neutral solute), to solve the problem of solute transport through the lateral surface of a cylindrical sample loaded dynamically in unconfined compression with frictionless impermeable platens in a bathing solution containing an excess of solute. The resulting equations are governed by nondimensional parameters, the most significant of which are the ratio of the diffusive velocity of the interstitial fluid in the gel to the solute diffusivity in the gel (Rg), the ratio of actual to ideal solute diffusive velocities inside the gel (Rd), the ratio of loading frequency to the characteristic frequency of the gel (f), and the compressive strain amplitude (epsilon 0). Results show that when Rg > 1, Rd < 1, and f > 1, dynamic loading can significantly enhance solute transport into the gel, and that this effect is enhanced as epsilon 0 increases. Based on representative material properties of cartilage and agarose gels, and diffusivities of various solutes in these gels, it is found that the ranges Rg > 1, Rd < 1, correspond to large solutes, whereas f > 1 is in the range of physiological loading frequencies. These theoretical predictions are thus in agreement with the limited experimental data available in the literature. The results of this study apply to any porous hydrated tissue or material, and it is therefore plausible to hypothesize that dynamic loading may serve to enhance solute transport in a variety of physiological processes.     

Fluid pressure relaxation depends upon osteonal microstructure: modeling an oscillatory bending experiment.

When bone is mechanically loaded, bone fluid flow induces shear stresses on bone cells that have been proposed to be involved in bone's mechanosensory system. To investigate bone fluid flow and strain-generated potentials, several theoretical models have been proposed to mimic oscillatory four-point bending experiments performed on thin bone specimens. While these previous models assume that the bone fluid relaxes across the specimen thickness, we hypothesize that the bone fluid relaxes primarily through the vascular porosity (osteonal canals) instead and develop a new poroelastic model that integrates the microstructural details of the lacunar-canalicular porosity, osteonal canals, and the osteonal cement lines. Local fluid pressure profiles are obtained from the model, and we find two different fluid relaxation behaviors in the bone specimen, depending on its microstructure: one associated with the connected osteonal canal system, through which bone fluid relaxes to the nearby osteonal canals; and one associated with the thickness of a homogeneous porous bone specimen (approximately 1 mm in our model), through which bone fluid relaxes between the external surfaces of the bone specimen at relatively lower loading frequencies. Our results suggest that in osteonal bone specimens the fluid pressure response to cyclic loading is not sensitive to the permeability of the osteonal cement lines, while it is sensitive to the applied loading frequency. Our results also reveal that the fluid pressure gradients near the osteonal canals (and thus the fluid shear stresses acting on the nearby osteocytes) are significantly amplified at higher loading frequencies.     

Micromechanically based poroelastic modeling of fluid flow in Haversian bone

To explore the hypothesis that load-induced fluid flow in bone is a mechano-transduction mechanism in bone adaptation, unit cell micro-mechanical techniques are used to relate the microstructure of Haversian cortical bone to its effective poroelastic properties. Computational poroelastic models are then applied to compute in vitro Haversian fluid flows in a prismatic specimen of cortical bone during harmonic bending excitations over the frequency range of 10(0) to 10(6) Hz. At each frequency considered, the steady state harmonic response of the poroelastic bone specimen is computed using complex frequency-domain finite element analysis. At the higher frequencies considered, the breakdown of Poisueille flow in Haversian canals is modeled by introduction of a complex fluid viscosity. Peak bone fluid pressures are found to increase linearly with loading frequency in proportion to peak bone stress up to frequencies of approximately 10 kHz. Haversian fluid shear stresses are found to increase linearly with excitation frequency and loading magnitude up until the breakdown of Poisueille flow. Tan delta values associated with the energy dissipated by load-induced fluid flow are also compared with values measured experimentally in a concurrent broadband spectral analysis of bone. The computational models indicate that fluid shear stresses and fluid pressures in the Haversian system could, under physiologically realistic loading, easily reach the level of a few Pascals, which have been shown in other works to elicit cell responses in vitro.     

Interstitial fluid flow within bone canaliculi and electro-chemo-mechanical features of the canalicular milieu

Canalicular fluid flow is acknowledged to play a major role in bone functioning, allowing bone cells’ metabolism and activity and providing an efficient way for cell-to-cell communication. Bone canaliculi are small canals running through the bone solid matrix, hosting osteocyte’s dendrites, and saturated by an interstitial fluid rich in ions. Because of the small size of these canals (few hundred nanometers in diameter), fluid flow is coupled with electrochemical phenomena. In our previous works, we developed a multi-scale model accounting for coupled hydraulic and chemical transport in the canalicular network. Unfortunately, most of the physical and geometrical information required by the model is hardly accessible by nowadays experimental techniques. The goal of this study was to numerically assess the influence of the physical and material parameters involved in the canalicular fluid flow. The focus was set on the electro-chemo-mechanical features of the canalicular milieu, hopefully covering any in vivo scenario. Two main results were obtained. First, the most relevant parameters affecting the canalicular fluid flow were identified and their effects quantified. Second, these findings were given a larger scope to cover also scenarios not considered in this study. Therefore, this study gives insight into the potential interactions between electrochemistry and mechanics in bone and provides the rational for further theoretical and experimental investigations.     

Acinar flow irreversibility caused by perturbations in reversible alveolar wall motion.

Mixing associated with "stretch-and-fold" convective flow patterns has recently been demonstrated to play a potentially important role in aerosol transport and deposition deep in the lung (J. P. Butler and A. Tsuda. J. Appl. Physiol. 83: 800-809, 1997), but the origin of this potent mechanism is not well characterized. In this study we hypothesized that even a small degree of asynchrony in otherwise reversible alveolar wall motion is sufficient to cause flow irreversibility and stretch-and-fold convective mixing. We tested this hypothesis using a large-scale acinar model consisting of a T-shaped junction of three short, straight, square ducts. The model was filled with silicone oil, and alveolar wall motion was simulated by pistons in two of the ducts. The pistons were driven to generate a low-Reynolds-number cyclic flow with a small amount of asynchrony in boundary motion adjusted to match the degree of geometric (as distinguished from pressure-volume) hysteresis found in rabbit lungs (H. Miki, J. P. Butler, R. A. Rogers, and J. Lehr. J. Appl. Physiol. 75: 1630-1636, 1993). Tracer dye was introduced into the system, and its motion was monitored. The results showed that even a slight asynchrony in boundary motion leads to flow irreversibility with complicated swirling tracer patterns. Importantly, the kinematic irreversibility resulted in stretching of the tracer with narrowing of the separation between adjacent tracer lines, and when the cycle-by-cycle narrowing of lateral distance reached the slowly growing diffusion distance of the tracer, mixing abruptly took place. This coupling of evolving convective flow patterns with diffusion is the essence of the stretch-and-fold mechanism. We conclude that even a small degree of boundary asynchrony can give rise to stretch-and-fold convective mixing, thereby leading to transport and deposition of fine and ultrafine aerosol particles deep in the lung.     

A Model of Tracer Transport in Airway Surface Liquid

This study is concerned with reconciling theoretical modelling of the fluid flow in the airway surface liquid with experimental visualisation of tracer transport in human airway epithelial cultures. The airways are covered by a dense mat of cilia of length ∼ 6 μm beating in a watery periciliary liquid (PCL). Above this there is a layer of viscoelastic mucus which traps inhaled pathogens. Cilia propel mucus along the airway towards the trachea and mouth. Theoretical analyses of the beat cycle smithd, fulb predict small transport of PCL compared with mucus, based on the assumption that the epithelium is impermeable to fluid. However, an experimental study coord indicates nearly equal transport of PCL and mucus. Building on existing understanding of steady advection-diffusion in the ASL (Blake and Gaffney, 2001; Mitran,2004) numerical simulation of an advection-diffusion model of tracer transport is used to test several proposed flow profiles and to test the importance of oscillatory shearing caused by the beating cilia. A mechanically derived oscillatory flow with very low mean transport of PCL results in relatively little ‘smearing’ of the tracer pulses. Other effects such as mixing between the PCL and mucus, and significant transport in the upper part of the PCL above the cilia tips are tested and result in still closer transport, with separation between the tracer pulses in the two layers being less than 9%. Furthermore, experimental results may be replicated to a very high degree of accuracy if mean transport of PCL is only 50% of mucus transport, significantly less than the mean PCL transport first inferred on the basis of experimental results.     

RV instantaneous intraventricular diastolic pressure and velocity distributions in normal and volume overload awake dog disease models

Intraventricular diastolic right ventricular (RV) flow field dynamics were studied by functional imaging using three-dimensional (3D) real-time echocardiography with sonomicrometry and computational fluid dynamics in seven awake dogs at control with normal wall motion (NWM) and RV volume overload with diastolic paradoxical septal motion. Burgeoning flow cross section between inflow anulus and chamber walls induces a convective pressure rise, which represents a "convective deceleration load" (CDL). High spatiotemporal resolution dynamic pressure and velocity distributions of the intraventricular RV flow field revealed time-dependent, subtle interactions between intraventricular local acceleration and convective pressure gradients. During the E-wave upstroke, the total pressure gradient along intraventricular flow is the algebraic sum of a pressure decrease contributed by local acceleration and a pressure rise contributed by a convective deceleration that partially counterbalances the local acceleration gradient. This underlies the smallness of early diastolic intraventricular gradients. At peak volumetric inflow, local acceleration vanishes and the total adverse intraventricular gradient is convective. During the E-wave downstroke, the strongly adverse gradient embodies the streamwise pressure augmentations from both local and convective decelerations. It induces flow separation and large-scale vortical motions, stronger in NWM. Their dynamic corollaries on intraventricular pressure and velocity distributions were ascertained. In the NWM pattern, the strong ring-like vortex surrounding the central core encroaches on the area available for flow toward the apex. This results in higher linear velocities later in the downstroke of the E wave than at peak inflow rate. The augmentation of CDL by ventriculoannular disproportion may contribute to E wave and E-to-A ratio depression with chamber dilatation.     

A pulsed wire probe for the measurement of velocity and flow direction in slowly moving air

This report describes the theory and operation of a pulsed-probe anemometer designed to measure steady three-dimensional velocity fields typical of pulmonary tracheo-bronchial airflows. Local velocities are determined by measuring the transport time and orientation of a thermal pulse initiated at an upstream wire and sensed at a downstream wire. The transport time is a reproducible function of velocity and the probe wire spacing, as verified by a theoretical model of convective heat transfer. When calibrated the anemometer yields measurements of velocity accurate to +/- 5 percent and resolves flow direction to within 1 deg at airspeeds greater than or equal to 10 cm/s. Spatial resolution is +/- 0.5 mm. Measured flow patterns typical of curved circular pipes are included as examples of its application.     

Transport diffusivities of fluids in nanopores by non-equilibrium molecular dynamics simulation

We present a method to study fluid transport through nanoporous materials using highly efficient non-equilibrium molecular dynamics simulations. A steady flow is induced by applying an external field to the fluid particles within a small slab of the simulation cell. The external field generates a density gradient between both sides of the porous material, which in turn triggers a convective flux through the porous medium. The heat dissipated by the fluid flow is released by a Gaussian thermostat applied to the wall particles. This method is effective for studying diffusivities in a slit pore as well as more natural, complex wall geometries. The dependence of the diffusive flux on the external field sheds light on the transport diffusivities and allows a direct calculation of effective diffusivities. Both pore and fluid particle interactions are represented by coarse-grained molecular models in order to present a proof-of-concept and to retain computational efficiency in the simulations. The application of the method is demonstrated in two different scenarios, namely the effective mass transport through a slit pore and the calculation of the effective self-diffusion through this system. The method allows for a distinction between diffusive and convective contributions of the mass transport.     

Micromotion-induced peri-prosthetic fluid flow around a cementless femoral stem

Micromotion-induced interstitial fluid flow at the bone-implant interface has been proposed to play an important role in aseptic loosening of cementless implants. High fluid velocities are thought to promote aseptic loosening through activation of osteoclasts, shear stress induced control of mesenchymal stem cells differentiation, or transport of molecules. In this study, our objectives were to characterize and quantify micromotion-induced fluid flow around a cementless femoral stem using finite element modeling. With a 2D model of the bone-implant interface and full-factorial design, we first evaluated the relative influence of material properties, and bone-implant micromotion and gap on fluid velocity. Transverse sections around a femoral stem were built from computed tomography images, while boundary conditions were obtained from experimental measurements on the same femur. In a second step, a 3D model was built from the same data-set to estimate the shear stress experienced by cells hosted in the peri-implant tissues. The full-factorial design analysis showed that local micromotion had the most influence on peak fluid velocity at the interface. Remarkable variations in fluid velocity were observed in the macrostructures at the surface of the implant in the 2D transverse sections of the stem. The 3D model predicted peak fluid velocities extending up to 2.2 mm/s in the granulation tissue and to 3.9 mm/s in the trabecular bone. Peak shear stresses on the cells hosted in these tissues ranged from 0.1 to 12.5 Pa. These results offer insight into mechanical stimuli encountered at the bone-implant interface.     

Evidence for increased de novo synthesis of NAD in immune-activated RAW264.7 macrophages: a self-protective mechanism?

Chondrogenesis in cartilage development and repair and cartilage degeneration in arthritis can be regulated by mechanical-load-induced physical factors such as tissue deformation, interstitial fluid flow and pressure, and electrical fields or streaming potentials. Previous animal and tissue explant studies have shown that time-varying dynamic tissue loading can increase the synthesis and deposition of matrix molecules in an amplitude-, frequency-, and spatially dependent manner. To provide information on the cell-level physical factors which may stimulate chondrocytes to increase production and export of aggrecan, the main proteoglycan component of the cartilage matrix, we characterized local changes in aggrecan synthesis within cyclically loaded tissue explant disks and compared those changes to values of predicted local physical factors. Aggrecan synthesis following a 23-h compression/radiolabel protocol was measured with a spatial resolution of approximately 0.1 mm across the 1.5-mm radius of explanted disks using a quantitative autoradiography method. A uniform stimulation of aggrecan synthesis was observed at an intermediate frequency of 0.01 Hz, while, at a higher frequency of 0.1 Hz, stimulation was only seen at peripheral radial positions. Profiles of radial solid matrix deformation and interstitial fluid pressure and velocity predicted to be occurring across the radius of the disk during sinusoidal loading were estimated using a composite poroelastic model. Tissue regions experiencing high interstitial fluid velocities corresponded to those displaying increased aggrecan synthesis. These results reinforce the role of load-induced flow of interstitial fluid in the stimulation of aggrecan production during dynamic loading of cartilage.     

Exposure of biofilms to slow flow fields: the convective contribution to growth and disinfection

A previously introduced degenerate diffusion-reaction model of biofilm growth and disinfection is extended to account for convective transport of oxygen and disinfectants in an aqueous environment. To achieve this in a computationally efficient manner we employ a thin-film approximation to the (Navier)-Stokes equations that can be solved analytically. In numerical experiments, we investigate how the convective transport of nutrients and disinfectants due to bulk flow hydrodynamics affects the balance between growth and disinfection processes. It is found that the development of biofilms can be significantly affected by the flow field even at extremely low Reynolds numbers. While it is natural to expect that increased bulk flow velocities imply increased mass transfer of both, nutrients and disinfectants, and hence an acceleration of both, growth and decay of biomass, it is found, furthermore, that in many instances the actual flow conditions, determine the success or failure of disinfection, i.e. persistence or extinction of a biofilm community.     

Skeletal adaptation to intramedullary pressure-induced interstitial fluid flow is enhanced in mice subjected to targeted osteocyte ablation

Interstitial fluid flow (IFF) is a potent regulatory signal in bone. During mechanical loading, IFF is generated through two distinct mechanisms that result in spatially distinct flow profiles: poroelastic interactions within the lacunar-canalicular system, and intramedullary pressurization. While the former generates IFF primarily within the lacunar-canalicular network, the latter generates significant flow at the endosteal surface as well as within the tissue. This gives rise to the intriguing possibility that loading-induced IFF may differentially activate osteocytes or surface-residing cells depending on the generating mechanism, and that sensation of IFF generated via intramedullary pressurization may be mediated by a non-osteocytic bone cell population. To begin to explore this possibility, we used the Dmp1-HBEGF inducible osteocyte ablation mouse model and a microfluidic system for modulating intramedullary pressure (ImP) to assess whether structural adaptation to ImP-driven IFF is altered by partial osteocyte depletion. Canalicular convective velocities during pressurization were estimated through the use of fluorescence recovery after photobleaching and computational modeling. Following osteocyte ablation, transgenic mice exhibited severe losses in bone structure and altered responses to hindlimb suspension in a compartment-specific manner. In pressure-loaded limbs, transgenic mice displayed similar or significantly enhanced structural adaptation to Imp-driven IFF, particularly in the trabecular compartment, despite up to ～50% of trabecular lacunae being uninhabited following ablation. Interestingly, regression analysis revealed relative gains in bone structure in pressure-loaded limbs were correlated with reductions in bone structure in unpressurized control limbs, suggesting that adaptation to ImP-driven IFF was potentiated by increases in osteoclastic activity and/or reductions in osteoblastic activity incurred independently of pressure loading. Collectively, these studies indicate that structural adaptation to ImP-driven IFF can proceed unimpeded following a significant depletion in osteocytes, consistent with the potential existence of a non-osteocytic bone cell population that senses ImP-driven IFF independently and potentially parallel to osteocytic sensation of poroelasticity-derived IFF.     

A new fluid distribution system for scale-flexible expanded bed adsorption

A new fluid distribution system designed for expanded bed adsorption was introduced and studied in a 150-cm diameter column. Based on fluid application through a rotating distributor, it eradicates the need for perforated plates, meshes, or local mixers. The effect of rotation rate on column performance was examined by fluidizing a 30-cm high bed of supports with tap water and introducing pulses of dye or acetone tracer. Linear bed expansion was seen as the superficial fluid velocity was raised from 170 x h(-1) to 450 cm x h(-1) (3000 L x h(-1) to 8000 L x h(-1)), and there was little change in expansion characteristics as distributor rotation rate was increased from 2.5 to 10 rpm. The distributor was observed to generate a flow pattern suitable for expanded bed adsorption when the supports were fluidized at a superficial fluid velocity of 283 cm center dot h(-1) and dye pulses introduced. At a rotation rate of 2.5 rpm, no significant dead zones were observed, and a discrete band was formed that moved up through the bed. Furthermore, the pattern of dye movement could be used to calculate interstitial linear fluid velocities of 460 cm x h(-1) and 572 cm x h(-1) at the column wall and center, respectively, indicating a parabolic flow profile. The distributor rotation rate giving the best operating conditions was found to be 2.5 rpm when the bed was fluidized at a flow velocity of 283 cm x h(-1) and the residence time distribution of acetone tracer examined. Under these conditions, the coefficient of axial dispersion was 6.1 x 10(-6) m(2) x s(-1) and 29 theoretical plates were measured. When the rotation rate was raised to 10 rpm, the coefficient of axial dispersion increased to 8.08 x 10(-6) m(2) x s(-1) and the number of theoretical plates decreased to 22.     

Direct measurement of intraparticle fluid velocity in superporous agarose beads

Superporous agarose beads contain both normal diffusion pores and special, very wide superpores through which part of the chromatographic flow is transported, a situation that may greatly improve the chromatographic performance. For the first time such pore flow was measured directly by following the movement of microparticles (dyed yeast cells) through superporous beads packed in a chromatographic bed. The passage of the microparticles through the superpores and through the interstitial pores was recorded by a microscope/video camera. The video recordings were subsequently used to determine flow paths as well as the convective fluid velocities in both the superpores and the interstitial pores. The superpore fluid velocity was found to be proportional to the ratio between the squares of the respective pore diameters, which is in agreement with the Kozeny-Carman equation. Values for two-dimensional and three-dimensional tortuosity of the flow paths were measured and calculated respectively.