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.     

A numerical study of flow in curved tubes simulating coronary arteries

Numerical simulations of pulsatile flow in coronary arteries which take into account the curvature associated with the bending of arteries over the surface of the heart are presented for resting, excited and drug induced states. The study was motivated by reported observations of atherosclerotic plaque localization on the inner curvature of coronary arteries. The simulated flow field appears quasi-steady under resting conditions with wall shear stress always highest on the outside wall and only a single secondary flow vortex in the half tube. However, reversal of wall shear stress direction at the inside wall does occur under resting flow conditions and this is not a quasi-steady characteristic. The flow field is markedly unsteady under excited conditions with wall shear stress sometimes peaking on the inside wall and an increase in the magnitude of wall shear stress reversal on the inside wall. However, only a single secondary flow vortex in the half tube is observed. Implications of the simulations for the role of fluid mechanics in coronary artery atherosclerosis are also discussed.     

Blood flow in tapered tubes with biorheological applications

A steady laminar flow of blood in a uniform tapered tube has been examined. Blood rheology is assumed to be described by a polar fluid. The analytical expressions for velocities (both axial and radial), total angular velocity, wall shear and pressure drop have been obtained. In literature, the parameters N (coupling number) and L (length ratio) have been chosen independently. But, in the present analysis, it is found that they are interrelated. Variation of the flow variables with suspension concentration and tapered angle have been investigated. Some of the theoretical models for the flow through tapered tubes have been critically examined. The pressure-flow relationship has been studied numerically over the flow rate range 0.01-0.1 cc/sec and compared with experimental results. It has been shown that the existing experimental results are for the tapered tubes of larger diameter which correspond to the flow under Newtonian conditions. Finally, some biological implications and future developments of this theory have been indicated.     

Effects of curved inlet tubes on air flow and particle deposition in bifurcating lung models

In vivo bifurcating airways are complex and the airway segments leading to the bifurcations are not always straight, but curved to various degrees. How do such curved inlet tubes influence the motion as well as local deposition and hence the biological responses of inhaled particulate matter in lung airways? In this paper steady laminar dilute suspension flows of micron-particles are simulated in realistic double bifurcations with curved inlet tubes, i.e., 0 degrees < or =theta< or =90 degrees, using a commercial finite-volume code with user-enhanced programs. The resulting air-flow patterns as well as particle transport and wall depositions were analyzed for different flow inlet conditions, i.e., uniform and parabolic velocity profiles, and geometric configurations. The curved inlet segments have quite pronounced effects on air-flow, particle motion and wall deposition in the downstream bifurcating airways. In contrast to straight double bifurcations, those with bent parent tubes also exhibit irregular variations in particle deposition efficiencies as a function of Stokes number and Reynolds number. There are fewer particles deposited at mildly curved inlet segments, but the particle deposition efficiencies at the downstream sequential bifurcations vary much when compared to those with straight inlets. Under certain flow conditions in sharply curved lung airways, relatively high, localized particle depositions may take place. The findings provide necessary information for toxicologic or therapeutic impact assessments and for global lung dosimetry models of inhaled particulate matter.     

Effect of nonaxisymmetric hematocrit distribution on non-Newtonian blood flow in small tubes

Hematocrit distribution and red blood cell aggregation are the major determinants of blood flow in narrow tubes at low flow rates. It has been observed experimentally that in microcirculation the hematocrit distribution is not uniform. This nonuniformity may result from plasma skimming and cell screening effects and also from red cell sedimentation. The goal of the present study is to understand the effect of nonaxisymmetric hematocrit distribution on the flow of human and cat blood in small blood vessels of the microcirculation. Blood vessels are modeled as circular cylindrical tubes. Human blood is described by Quemada's rheological model, in which local viscosity is a function of both the local hematocrit and a structural parameter that is related to the size of red blood cell aggregates. Cat blood is described by Casson's model. Eccentric hematocrit distribution is considered such that the axis of the cylindrical core region of red cell suspension is parallel to the axis of the blood vessel but not coincident. The problem is solved numerically by using finite element method. The calculations predict nonaxisymmetric distribution of velocity and shear stress in the blood vessel and the increase of apparent viscosity with increasing eccentricity of the core.     

Peristaltic flow in tubes

The study is concerned with the analysis of two flow domains of peristaltic motion in tubes. In the first analysis the wall disturbance wavelength is much larger than the average tube radius. There is a simple algebraic relation between the average flow rate and pressure differential across a wavelength. In the second analysis the disturbance wavelength may be as small as the average radius. A numerical technique may be used to determine the relation between average flow rate and pressure differential across a wavelength.     

Effects of sedimentation of small red blood cell aggregates on blood flow in narrow horizontal tubes

The flow properties of aggregating red cell suspensions flowing at low flow rates through horizontal tubes are analyzed using a theoretical model. The effects of sedimentation of small aggregates, which will be formed at comparatively high flow rates, on the relative apparent viscosity are considered. In the case in which a large number of small aggregates are formed in a suspension flowing through a horizontal tube, it seems that red cells are transported as a concentrated suspension through the bottom part of the tube because of sedimentation of aggregates. A two-layer flow model is used for the distribution of red cells. It consists of plasma in the upper part and a concentrated red cell suspension in the bottom part of the tube divided by a smooth and horizontal interface. It is assumed that the suspension is a Newtonian fluid whose viscosity increases exponentially with hematocrit. The velocity distribution, the relative apparent viscosity and the flux of red cells are calculated as functions of width of plasma layer for a different discharge hematocrit. The theoretical results are compared with the results obtained from experimental data. The relative apparent viscosity increases rapidly with an increasing degree of sedimentation over a wide range of plasma layer widths.     

Blood viscosity and optimal hematocrit in narrow tubes

Blood viscosity in normal adults was measured in glass tubes with diameters of 50, 100 and 500 microns for a wide range of adjusted feed hematocrits (15-70%). Blood viscosity decreased at each of the adjusted feed hematocrits when going from a 500-micron tube to a 50-micron tube. The viscosity reduction increased with increasing hematocrit. The steepness in the hematocrit-viscosity curves decreased with decreasing tube diameter. Erythrocyte transport efficiency (hematocrit/blood viscosity) was calculated to estimate the optimal hematocrit for oxygen transport. Optimal hematocrit averaged 38% in 500-micron tubes, 44% in 100-micron tubes and 51% in 50-micron tubes. Our results suggest that the strong F?hraeus-Lindqvist effect at high hematocrits may help to maintain oxygen transport in polycythemic patients as long as the driving pressure is sufficient.