Gas dispersion in volume-cycled tube flow. II. Tracer bolus experiments.

We present a new method for rapid measurement of local gas dispersion in volume-cycled tube flow. After a small bolus of tracer gas (argon) was injected into the oscillating flow, the time-averaged effective diffusion coefficient (mean value of Deff/D) for axial transport of a tracer gas is evaluated from local argon concentration measurements taken by a mass spectrometer. Two methods are presented for the evaluation of mean value of Deff/D from the concentration measurements: one uses all the sampled data, and the other uses only the local peaks of the concentration. Experiments were conducted in two tubes (radius = 0.85 or 1.0 cm) over a range of frequencies (0.42 less than or equal to f less than or equal to 8.5 Hz) and tidal volumes (7 less than or equal to VT less than or equal to 48 ml). The experimental results show very good agreement with the theoretical predictions of Elad et al. (J. Appl. Physiol. 72: 312-320, 1992). In the absence of oscillations (static fluid), the resulting mean value of Deff/D converges to that of molecular diffusion. We also show that concentration data may be acquired at any radial or axial position, not necessarily at the tracer gas injection point, and the resulting mean value of Deff/D is independent of the spatial position of the sampling catheter. This method is of similar accuracy and is substantially faster than previous methods for measuring gas dispersion in oscillatory flows. The rapidity of these measurements may permit this method to be used for the in vivo assessment of gas transport properties within the pulmonary system.     

Bolus contaminant dispersion in oscillating flow in curved tubes.

The investigation of longitudinal dispersion of tracer substances in unsteady flows has biomechanical application in the study of heat and mass transport within the bronchial airways during normal, abnormal, and artificial pulmonary ventilation. To model the effects of airway curvature on intrapulmonary gas transport, we have measured local gas dispersion in axially uniform helical tubes of slight pitch during volume-cycled oscillatory flow. Following a small argon bolus injection into the flow field, the time-averaged effective diffusion coefficient (Deff/Dmol) for axial transport of the contaminant was evaluated from the time-dependent local argon concentration measured with a mass spectrometer. The value of (Deff/Dmol) is extracted from the curve of concentration versus time by two techniques yielding identical results. Experiments were conducted in two helical coiled tubes (delta = 0.031, lambda = 0.022 or delta = 0.085, lambda = 0.060) over a range of 2 < alpha < 15, 3 < A < 15, where delta is the ratio of tube radius to radius of curvature, lambda is the ratio of pitch height to radius of curvature, alpha is the Womersley parameter or dimensionless frequency, and A is the stroke amplitude or dimensionless tidal volume. Experimental results show that, when compared to transport in straight tubes, the effective diffusivity markedly increases in the presence of axial curvature. Results also compare favorably to mathematical predictions of bolus dispersion in a curved tube over the ranges of frequency and tidal volume studied.     

Effect of anatomical fine structure on the dispersion of solutes in the spinal subarachnoid space

The dispersion of a solute bolus is calculated for cerebrospinal fluid undergoing oscillatory flow in the subarachnoid space of the spine. The fine structure of the subarachnoid space (nerves and trabeculae) enhances both longitudinal and transverse dispersions five to ten times over a simple model with an open annular space. Overall, dispersion is >10(3) times simple molecular diffusion. The result of enhanced dispersion is rapid spread and dilution of the bolus, effectively stirred by fluid movement around the fine structure.     

Kinematically irreversible acinar flow: a departure from classical dispersive aerosol transport theories.

Current theories describe aerosol transport in the lung as a dispersive (diffusion-like) process, characterized by an effective diffusion coefficient in the context of reversible alveolar flow. Our recent experimental data, however, question the validity of these basic assumptions. In this study, we describe the behavior of fluid particles (or bolus) in a realistic, numerical, alveolated duct model with rhythmically expanding walls. We found acinar flow exhibiting multiple saddle points, characteristic of chaotic flow, resulting in substantial flow irreversibility. Computations of axial variance of bolus spreading indicate that the growth of the variance with respect to time is faster than linear, a finding inconsistent with dispersion theory. Lateral behavior of the bolus shows fine-scale, stretch-and-fold striations, exhibiting fractal-like patterns with a fractal dimension of 1.2, which compares well with the fractal dimension of 1.1 observed in our experimental studies performed with rat lungs. We conclude that kinematic irreversibility of acinar flow due to chaotic flow may be the dominant mechanism of aerosol transport deep in the lungs.     

A Multiple-Relaxation-Time Lattice-Boltzmann Model for Bacterial Chemotaxis: Effects of Initial Concentration,Diffusion, and Hydrodynamic Dispersion on Traveling Bacterial Bands

Bacterial chemotaxis can enhance the bioremediation of contaminants in aqueous and subsurface environments if the contaminant is a chemoattractant that the bacteria degrade. The process can be promoted by traveling bands of chemotactic bacteria that form due to metabolism-generated gradients in chemoattractant concentration. We developed a multiple-relaxation-time (MRT) lattice-Boltzmann method (LBM) to model chemotaxis, because LBMs are well suited to model reactive transport in the complex geometries that are typical for subsurface porous media. This MRT-LBM can attain a better numerical stability than its corresponding single-relaxation-time LBM. We performed simulations to investigate the effects of substrate diffusion, initial bacterial concentration, and hydrodynamic dispersion on the formation, shape, and propagation of bacterial bands. Band formation requires a sufficiently high initial number of bacteria and a small substrate diffusion coefficient. Uniform flow does not affect the bands while shear flow does. Bacterial bands can move both upstream and downstream when the flow velocity is small. However, the bands disappear once the velocity becomes too large due to hydrodynamic dispersion. Generally bands can only be observed if the dimensionless ratio between the chemotactic sensitivity coefficient and the effective diffusion coefficient of the bacteria exceeds a critical value, that is, when the biased movement due to chemotaxis overcomes the diffusion-like movement due to the random motility and hydrodynamic dispersion.     

Augmentation of axial dispersion by intermittent oscillatory flow.

The efficiency of axial gas dispersion during ventilation with high-frequency oscillation (HFO) is improved by manipulating the oscillatory flow waveform such that intermittent oscillatory flow occurs. We therefore measured the velocity profiles and effective axial gas diffusivity during intermittent oscillatory flow in a straight tube to verify the intermittency augmentation effect on axial gas transfer. The effective diffusivity was dependent on the flow patterns and significantly increased with an increase in the duration of the stationary phase. It was also found that the ratio of effective diffusivity to molecular diffusivity is two times greater than that in sinusoidal oscillatory flow. Moreover, turbulence during deceleration or at the beginning of the stationary phase further augments axial dispersion, with the effective diffusivity being over three times as large, thereby proving that the use of intermittent oscillatory flow effectively augments axial dispersion for ventilation with HFO.     

A mechanical approach to the longitudinal dispersion of gas flowing in human airways

The aim of this work is to contribute to elucidating the mechanism underlying gas mixing in the human pulmonary airways. For this purpose, a particular attempt is made to analyse the fluid mechanical aspects of gaseous dispersion using bolus response methods. The experiments were performed on five normal subjects by injection of 10 cm3 bolus of He, Ar and SF6 into the latter part of the inspired airstream, in such a way that the whole bolus entered the inspiratory flow and was recovered during the following expiration. The results, presented in a logarithmic plot of dimensionless variance (dispersion of the output bolus) against the Peclet number, show that gaseous dispersion is only slightly dependent on the nature of the tracer gas but is strongly related to flow velocity. This is in agreement with the theory of turbulent or disturbed dispersion; however, it seems that Taylor laminar dispersion does not play a significant role in the airways.     

Lateral diffusion and aggregation. A Monte Carlo study.

Aggregation in a lipid bilayer is modeled as cluster-cluster aggregation on a square lattice. In the model, clusters carry out a random walk on the lattice, with a diffusion coefficient inversely proportional to mass. On contact, they adhere with a prescribed probability, rigidly and irreversibly. Monte Carlo calculations show that, as expected, rotational diffusion of the aggregating species is highly sensitive to the initial stages of aggregation. Lateral diffusion of an inert tracer obstructed by the aggregate is a sensitive probe of the later stages of aggregation. Cluster-cluster aggregates are much more effective barriers to lateral diffusion of an inert tracer than the same area fraction of random point obstacles is, but random point obstacles are more effective barriers than the same area fraction of compact obstacles. The effectiveness of aggregates as obstacles is discussed in terms of particle-particle correlation functions and fractal dimensions. Results are applicable to aggregation of membrane proteins, and at least qualitatively to aggregation of gel-phase lipid during lateral phase separation.     

Fluid particle diffusion through high-hematocrit blood flow within a capillary tube

Fluid particle diffusion through blood flow within a capillary tube is an important phenomenon to understand, especially for studies in mass transport in the microcirculation as well as in solving technical issues involved in mixing in biomedical microdevices. In this paper, the spreading of tracer particles through up to 20% hematocrit blood, flowing in a capillary tube, was studied using a confocal micro-PTV system. We tracked hundreds of particles in high-hematocrit blood and measured the radial dispersion coefficient. Results yielded significant enhancement of the particle diffusion, due to a micron-scale flow-field generated by red blood cell motions. By increasing the flow rate, the particle dispersion increased almost linearly under constant hematocrit levels. The particle dispersion also showed near linear dependency on hematocrit up to 20%. A scaling analysis of the results, on the assumption that the tracer trajectories were unbiased random walks, was shown to capture the main features of the results. The dispersion of tracer particles was about 0.7 times that of RBCs. These findings provide good insight into transport phenomena in the microcirculation and in biomedical microdevices.     

Determination of pulmonary mean transit time and cardiac output using a one-dimensional model

In this work, we show that a one-dimensional model of the blood flow across the lungs can reproduce the evolution of a bolus versus the time. Solving the differential equation governing the bolus concentration in the framework of this model, we determine the solution which fulfills Gaussian initial boundary conditions. An effective parameter related to the ratio of a diffusion coefficient to the square of the mean speed of the flow is defined. The determination of its numerical values following a semi-empirical approach enables us to know accurately the mean transit time and the cardiac output. The results have been compared to other methods, and were found in good agreement. Such an approach could be of interest in all studies where the knowledge of flow—including micro-circulation—is needed.     

Residence time distribution of diazepam in the isolated perfused rat liver. Analysis with the axial dispersion model.

The application of the axial dispersion model to diazepam hepatic elimination was evaluated using data obtained for impulse-response experiments with diazepam in the single-pass isolated perfused rat liver preparation. The transient form of the two-compartment dispersion model was applied to the output concentration versus time profile of diazepam after bolus input of a radiolabelled tracer into the hepatic portal vein (n = 4), providing DN and CLint estimates of 0.251 +/- 0.093 and 135 +/- 59 ml min-1, respectively. In contrast, the one-compartment form of the axial dispersion model, which assumes instantaneous transversal distribution of substance to the accessible spaces within the liver, could not adequately describe the residence time distribution (RTD) of diazepam. Furthermore, the magnitude of DN, a stochastic parameter which characterizes the axial spreading of solutes during transit through the liver, is similar to that determined for non-eliminated substances such as erythrocytes, albumin, sucrose and water. These findings suggest that the dispersion of diazepam in the perfused rat liver is determined primarily by the architecture of the hepatic microvasculature.     

Mass transport parameters of aspen wood chip beds via stimulus-response tracer techniques

A stimulus-response tracer technique has been used to characterize packed beds of untreated, as well as acid prehydrolyzed, and enzymatically hydrolyzed aspen wood chips. Glucose was used as the tracer. Bulk liquid phase dispersion, interphase mass transfer, and intraparticle diffusion coefficients were determined for these materials as well as effective porosities and tortuosities. The untreated and prehydrolyzed aspen wood chips were found to have effective coid fractions of ca. 0.8, while the enzymatically hydrolyzed wood chips exhibited a void fraction of 0.37. Intraparticle diffusion was approximately twice as rapid in the prehydrolyzed and enzymatically hydrolyzed wood chips as in the untreated wood chips. Also, under the current experimental conditions, intraparticle diffusional transport resistance accounted for roughly half of the total tracer pulse dispersion. It is demonstrated that stimulus-response tracer techniques can be useful and convenient probes for beds of lignocellulosic, or other conversion and/or treatment. (c) 1993 John Wiley & Sons, Inc.     

Lateral diffusion of membrane proteins in protein-rich membranes. A simple hard particle model for concentration dependence of the two-dimensional diffusion coefficient.

A model for the effect of protein concentration on the rate of lateral diffusion of integral membrane proteins is presented, in which the proteins are represented by equivalent hard circular particles on a surface. As the density of particles increases, the probability of finding a vacancy immediately adjacent to a tracer particle into which it may diffuse decreases, resulting in a concomitant reduction of the tracer diffusion coefficient. Using scaled particle theory to calculate the concentration-dependent probabilities, a simple approximate result is obtained in closed form, that is compared with the results of previously published Monte Carlo lattice simulations and experimental observations.     

Effect of couple stresses on the unsteady convective diffusion in fluid flow through a channel

A generalized dispersion model is used to obtain exact solution for unsteady convective diffusion in the presence of couple stresses. The effect of the couple stress parameter 'a' on the most dominant dispersion coefficient is clearly depicted. The dimensionless mean concentration distribution is obtained as a function of dimensionless axial distance, time and 'a'. The results for 'pure convection' are also reported. It is shown that the effect of couple stress is predominant only for small values of 'a' and when a----infinity the flow characteristics tend to their equivalents in Newtonian theory. The results of Taylor's dispersion model are recovered as a particular case in the limit tau----infinity.     

Tracer diffusion coefficients of proteins by means of holographic relaxation spectroscopy: application to bovine serum albumin

Holographic relaxation spectroscopy has been used to measure tracer diffusion coefficients for photochromically labeled bovine serum albumin in solutions having total bovine serum albumin concentrations in the range 3.25 to 257 g/liter. In the limit of zero concentration, the diffusion coefficient (20 degrees C, 0.1 M NaCl, 0.05 M Tris, pH 8.0) was found to be (5.9 +/- 0.1) X 10(-7) cm2/s and the initial slope was zero. The concentration dependence of the diffusion coefficient was not significantly affected by the fraction of protein molecules which were labeled. Holographic relaxation spectroscopy permits rapid, accurate determination of tracer diffusion coefficients for proteins in mixtures.     

Gas transport during oscillatory flow in a network of branching tubes

A transport coefficient was measured for a range of oscillatory flow conditions in a branching network of tubes. Measurements were made both across the first generation of a three-generation network and the second generation of a four-generation network. The results for these two series of tests were similar, indicating that there was no significant effect due to the system boundaries. The results are cast in terms of an effective axial diffusion coefficient of the form (Formula: see text) where kappa is the molecular diffusivity, Vt is the local stroke volume (cc); and f is the oscillation frequency (Hz). These results are compared to those obtained by other investigators in branching systems of similar geometry. At low frequency, this result is found to be in approximate agreement with the steady flow result of Scherer, et al. [15]. This expression differs from the oscillatory flow results of Tarbell, et al. [19] for liquids, primarily in terms of the effects of oscillation frequency.     

Intraparticle diffusion alters the dynamic response of immobilized cell/enzyme columns

The effect of intra-particle tracer diffusion on the transient response of a fixed-bed column containing porous Ca-alginate beads is investigated experimentally. Dynamic response experiments are carried out using acetone solutions as tracer, whose concentration in the effluent stream is monitored on-line using a UV analyzer. Comparison of the response of such columns for two particle sizes (radii of 2 and 1?mm) to that of otherwise identical beds filled with solid glass particles of equal size reveals a substantial difference, mainly characterized by a trailing of the effluent concentration-vs-time curves at longer times. This cannot be explained by assuming a change in the effective porosity of the system, nor a change in the hydrodynamic dispersion. Following independent experimental determination of the pertinent physical parameters, a model based on the tanks-in-series concept [1,?2] is implemented on a personal computer and its predictions are compared to the experimental data. The essential assumption of the model is that tracer convection in the bulk liquid is substantially faster than intra-particle diffusion and, as a result, a bead is always surrounded by fluid of uniform (albeit time-dependent) concentration. In the absence of external mass transfer resistances and assuming that the porous nature of the Ca-alginate beads does not substantially alter the hydrodynamic dispersion in the column, the agreement between model and experiment is remarkably good. This leads to the suggestion that the observed response can be explained as the combined result of (fast) tracer convection in the bulk liquid and (slower) tracer diffusion from the bulk liquid to the beads.     

Simulation of particle-hemodynamics in a partially occluded artery segment with implications to the initiation of microemboli and secondary stenoses.

Computational results of laminar incompressible blood-particle flow analyses in an axisymmetric artery segment with a smooth local area constriction of 75 percent have been presented. The flow input waveform was sinusoidal with a nonzero average. The non-Newtonian behavior of blood was simulated with a modified Quemada model, platelet concentrations were calculated with a drift-flux model, and monocyte trajectories were described and compared for both Newtonian and Quemada rheologies. Indicators of "disturbed flow" included the time-averaged wall shear stress (WSS), the oscillatory shear index (OSI), and the wall shear stress gradient (WSSG). Implications of the vortical flow patterns behind the primary stenosis to the formation of microemboli and downstream stenoses are as follows. Elevated platelet concentrations due to accumulation in recirculation zones mixed with thrombin and ADP complexes assumed to be released upstream in high wall shear stress regions, could form microemboli, which are convected downstream. Distinct near-wall vortices causing a local increase in the WSSG and OSI as well as blood-particle entrainment with possible wall deposition, indicate sites susceptible to the onset of an additional stenosis proximal to the initial geometric disturbance.     

On the Distribution of a Permeable Solute during Poiseuille Flow in Capillary Tubes

Equations are derived describing the dispersion of a permeable solute during Poiseuille flow in a capillary model. It is shown that for the normal range of physiological parameters such as capillary radius, capillary length, blood flow, permeability coefficients, and diffusion constants, the center of mass of a bolus of solute moves at a speed very close to the mean speed of flow and that the solute leaves the capillary with an exponential time course depending on the permeability but not on the diffusion constant. There is no appreciable difference in the dispersion of the solute or in its rate of permeation from the capillary whether one considers piston flow or Poiseuille flow. A bolus of arbitrary radial shape tends to become radially uniform very close to the arterial end of the capillary.