Generalized dispersion in a synovial fluid of human joints

An unsteady convective diffusion in a synovial fluid of human joints modeled as a power-law fluid is studied using the generalized dispersion model of Gill and Sankara-subramanian [12]. The contributions of convection and diffusion, and pure convection on the dispersion of nutrient are investigated in detail. It is shown that the effect of decrease in non-Newtonian parameter is to decrease the dispersion coefficient. The mean concentration distribution appears to increase as the non-Newtonian parameter decreases upto a certain value of the axial distance. Beyond this point, however, the reverse pattern is observed.     

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.     

Evaluation of Taylor dispersion injections: determining kinetic/affinity interaction constants and diffusion coefficients in label-free biosensing

In label-free biomolecular interaction analysis, a standard injection provides an injection of uniform analyte concentration. An alternative approach exploiting Taylor dispersion produces a continuous analyte titration allowing a full analyte dose response to be recorded in a single injection. The enhanced biophysical characterization that is possible with this new technique is demonstrated using a commercially available surface plasmon resonance-based biosensor. A kinetic interaction model was fitted locally to Taylor dispersion curves for estimation of the analyte diffusion coefficient in addition to affinity/kinetic constants. Statistical confidence in the measured parameters from a single Taylor dispersion injection was comparable to that obtained for global analysis of multiple standard injections. The affinity constants for multisite interactions were resolved with acceptable confidence limits. Importantly, a single analyte injection could be treated as a high-resolution real-time affinity isotherm and was demonstrated using the complex two-site interaction of warfarin with human serum albumin. In all three model interactions tested, the kinetic/affinity constants compared favorably with those obtained from standard kinetic analysis and the estimates of analyte diffusion coefficients were in good agreement with the expected values.     

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.     

Analysis of Dispersion Mechanism in Gel Chromatography

The mechanism of dispersion of solute in gel chromatography using various Sephadex gels was quantitatively studied. In order to simplify the mathematical treatment, non-ad- sorptive low-molecular weight substances such as NaCl and glucose were chosen as samples. A pulse response experiment was carried out in a column. The longitudinal dispersion coefficient and the diffusion coefficient in gel phase were determined separately by applying the moment method to the elution curve. Then, their contribution to the column efficiency characterized by HETP was studied. Particularly, the effect of gel phase diffusion was examined in detail. The gel phase diffusion coefficient was apparently much smaller than the molecular diffusion coefficient. Consequently, it was revealed that gel phase diffusion played a much more important role in gel chromatography than what was expected by other investigators.     

Influence of electric field on the unsteady dispersion coefficient in couple-stress flow

The influence of electric field on unsteady convective diffusion in couple stress flow is studied using a time dependent dispersion model. The electric field, arising as a body couple in the governing equations, is shown to increase the axial dispersion coefficient. This is useful in the control of haemolysis caused by artificial organs implanted or extracorporeal. The contribution of pure convection in the dispersion of concentration is singled out and investigated in detail. The results obtained are compared with those in the absence of electric field and some important conclusions are drawn.     

Solute exclusion from cellulose in packed columns: process modeling and analysis

In this investigation, process modeling and analysis were used to explore the behavior of solute exclusion from cellulose in packed columns. The study focused on modeling the effects of dispersion, mass transport, and pore diffusion. Three mathematical models were used to predict the behavior of the columns: an equilibrium model, a mass transfer model, and a combined mass transfer and pore diffusion model. Computer implementations of these models were tested against experimental conditions where cellulose particle size and solution velocity were used to either amplify or minimize dispersion or skewness in the elution curves. For small cellulose particles (200-300 mesh), all three models accurately predicted the shape of the elution curve and the particle porosity. For larger particles (45-60 mesh), the mass transfer model and the combined mass and pore diffusion model best represented the behavior of the column. At high solution velocities (0.63 cm(3) min(-1)) and large particles, only the combined mass transfer and pore diffusion model accurately represent the column behavior. Sensitivity analysis revealed that the mass transfer coefficient had little effect on the elution curves for the range of values (10(-6)-10(-3) cm s(-1)) calculated from the experimental data. The combined mass transfer and pore diffusion model presented in this article can be used to design solute exclusion measurement experiments for the larger cellulose particles found in a commercial cellulose-to-ethanol plant.     

A modified model for predicting the performance of a compact artificial kidney.

A modified urea transfer model is presented in this work for predicting the urea removal in a compact artificial kidney. The modified model represents a departure from the previous one in two aspects. A simpler plug flow equation instead of a general dispersion one is employed for describing the urea transport in the blood flow. This is justified by the rather large Peclet number for the present system. Furthermore, the internal and external urea diffusion resistances in the microencapsulated urease particle are incorporated into the urea balance equations in this work. Results of numerical simulation indicate that the urea diffusion resistances play a dominating role in the determination of urea removal from the artificial kidney. Effects of other physical parameters, such as the urea concentration in microencapsule, the membrane thickness and the partition coefficient between the membrane and the urease solution, on the performance of the artificial kidney are found to be of less significance.     

Gas dispersion in volume-cycled tube flow. I. Theory.

A mathematical theory is derived for the dispersion of a contaminant bolus introduced into a fully developed volume-cycled oscillatory pipe flow. The convection-diffusion equation is solved for a tracer gas bolus by expressing the local concentration field as a series expansion of derivatives of the area-averaged concentration. The local, as well as the area-averaged, concentration is determined for a uniform initial slug or Gaussian bolus. The effect of various flow parameters such as Womersley parameter, Schmidt number, and tidal volume is investigated. The overall dispersion is characterized by a time-averaged effective diffusion coefficient, which for long duration coincides with previous dispersion theories based on a constant linear axial concentration profile. The effective diffusion coefficient can be determined from the local time history of concentration, independent of the spatial location or the initial tracer bolus. Furthermore the local peaks of the concentration-time curve follow a decaying curve dictated by the time-averaged effective diffusion coefficient. Thus the theory is directly applicable for dispersion measurements in oscillatory tube flows, a basis for the pulmonary airways application, as shown by Gaver et al. (J. Appl. Physiol. 72: 321-331, 1992).     

Apparent Diffusivity and Taylor Dispersion of Water and Solutes in Capillary Beds

A physical theory explaining the anisotropic dispersion of water and solutes in biological tissues is introduced based on the phenomena of Taylor dispersion, in which highly diffusive solutes cycle between flowing and stagnant regions in the tissue, enhancing dispersion in the direction of microvascular flow. An effective diffusion equation is derived, for which the coefficient of dispersion in the axial direction (direction of capillary orientation) depends on the molecular diffusion coefficient, tissue perfusion, and vessel density. This analysis provides a homogenization that represents three-dimensional transport in capillary beds as an effectively one-dimensional phenomenon. The derived dispersion equation may be used to simulate the transport of solutes in tissues, such as in pharmacokinetic modeling. In addition, the analysis provides a physically based hypothesis for explaining dispersion anisotropy observed in diffusion-weighted imaging (DWI) and diffusion-tensor magnetic resonance imaging (DTMRI) and suggests the means of obtaining quantitative functional information on capillary vessel density from measurements of dispersion coefficients. It is shown that a failure to account for flow-mediated dispersion in vascular tissues may lead to misinterpretations of imaging data and significant overestimates of directional bias in molecular diffusivity in biological tissues. Measurement of the ratio of axial to transverse diffusivity may be combined with an independent measurement of perfusion to provide an estimate of capillary vessel density in the tissue.     

An axisymmetric single-path model for gas transport in the conducting airways

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.     

Diffusion Coefficient of Paramecium as a Function of Temperature1

The motion of Paramecium caudatum has been investigated at various temperatures by measuring the transient behavior of spatial distribution in the diffusion process of organisms that, by electric stimulus, are initially gathered at a single place in the glass culture cell. The spatial distribution through the course of diffusion has a nearly Gaussian profile. Dispersion was obtained at 1 sec intervals and increased linearly with time. The time dependence of the dispersion gave a diffusion coefficient for the random motion of the organisms. The results show that the diffusion coefficient has a maximum at the temperature at which the paramecia were cultivated.     

Analysis of acetylene reduction rates of soybean nodules at low acetylene concentrations

It has been previously proposed that acetylene reduction data at subsaturating acetylene concentrations could be interpreted by use of the Michaelis-Menten equation, based on the acetylene concentration external to the nodules. One difficulty of this view is that the assumption that the system is not diffusion limited is violated when studying intact nodules. The presence of a gas diffusion barrier in the nodule cortex leads to an alternate expression for the gas exchange rates at subsaturating gas concentrations. A theoretical comparison of the `apparent' Michaelis-Menten model and diffusion model illustrated the difficulties observed in the former model of overestimating the Michaelis-Menten coefficient and yielding a correlation between the Michaelis-Menten coefficient and the maximum rate. On the other hand, use of a diffusion model resulted in (a) estimates of the Michaelis-Menten coefficient consistent with enzyme studies, (b) stability of the estimates of the Michaelis-Menten coefficient independent of treatment, and (c) a sensitivity of the diffusion barrier conductance to plant drought stress. It was concluded that all studies of nodule gas exchange need to consider possible effects caused by the presence of a diffusion barrier.     

Linear and non-linear diffusion models applied to the behavior of a population of an intertidal snail

The flux and continuity equations are presented for a non-linear diffusion of populations. The generalized diffusion-reaction equations are presented for both random and biased diffusion, where a bias is introduced toward the existing gradient of the population density. An ecological field experiment is presented and analyzed in light of the non-linear diffusion models. The dispersion of the population of intertidal snails near the Red Sea has been measured over a period of 20 months. The dispersion can be described by a one-dimensional random motion and the obtained diffusion coefficient 0·1 m² day^?1 is in good agreement with velocity and free path measurements of individual snails.     

Improved Model of Fluorescence Recovery Expands the Application of Multiphoton Fluorescence Recovery after Photobleaching in Vivo

Multiphoton fluorescence recovery after photobleaching is a well-established microscopy technique used to measure the diffusion of macromolecules in biological systems. We have developed an improved model of the fluorescence recovery that includes the effects of convective flows within a system. We demonstrate the validity of this two-component diffusion-convection model through in vitro experimentation in systems with known diffusion coefficients and known flow speeds, and show that the diffusion-convection model broadens the applicability of the multiphoton fluorescence recovery after photobleaching technique by enabling accurate determination of the diffusion coefficient, even when significant flows are present. Additionally, we find that this model allows for simultaneous measurement of the flow speed in certain regimes. Finally, we demonstrate the effectiveness of the diffusion-convection model in vivo by measuring the diffusion coefficient and flow speed within tumor vessels of 4T1 murine mammary adenocarcinomas implanted in the dorsal skinfold chamber.     

Modeling Taylor dispersion injections: determination of kinetic/affinity interaction constants and diffusion coefficients in label-free biosensing

A new method based on Taylor dispersion has been developed that enables an analyte gradient to be titrated over a ligand-coated surface for kinetic/affinity analysis of interactions from a minimal number of injections. Taylor dispersion injections generate concentration ranges in excess of four orders of magnitude and enable the analyte diffusion coefficient to be reliably estimated as a fitted parameter when fitting binding interaction models. A numerical model based on finite element analysis, Monte Carlo simulations, and statistical profiling were used to compare the Taylor dispersion method with standard fixed concentration injections in terms of parameter correlation, linearity of parameter error space, and global versus local model fitting. A dramatic decrease in parameter correlations was observed for TDi curves relative to curves from standard fixed concentration injections when surface saturation was achieved. In FCI the binding progress is recorded with respect to injection time, whereas in TDi the second time dependency encoded in the analyte gradient increases resolving power. This greatly lowers the dependence of all parameters on each other and on experimental interferences. When model parameters were fitted locally, the performance of TDis remained comparable to global model fitting, whereas fixed concentration binding response curves yielded unreliable parameter estimates.     

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.     

Diffusion in immobilized-cell gels

Summary The relationship between the diffusion coefficient, the effective diffusion coefficient and the partition coefficient for a solute in a cell-containing gel is discussed. The use of correlation equations that are based on some kind of physical model is recommended when the effect of cell concentration on diffusion is interpreted.