On-line rheometer for the monitoring of polymer fermentations: Operating conditions

A turbine rheometer was developed and tested for on-line measurements of rheological properties of fermentation broths. The organism used in the test broth wasAureobasidium pullulans. Although the rheometer constants were found to be dependent on the nature of calibration fluids used, the variations in these constants had little effect on the measured rheological parameters of the power law equation. The rheological parameters did not vary with liquid flow rate through the on-line rheometer, and the repeatability of the measured rheological parameters were high. The broth showed some tendency to thixotropic (time-dependent) behaviour, but this was found to be negligible after 15 seconds of shear.     

Properties and principles of mycelial flow: experiments with a tube rheometer

The flow behavior of a penicillin mash has been investigated with a tube rheometer and compared with rotational viscometer observations. In the low-shear regions plug flow and breakdown of the plug have been studied. For turbulent flow turbulence damping was demonstrated. The Theological development during the fermentation was followed. At low deformation rates the pressure drop increased during the fermentation. In turbulent regions the opposite tendency was observed. The possible underlying flow mechanisms are discussed, and the influence of a number of physical parameters have been investigated.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.     

A new rheological method to measure fluidity change of blood during coagulation : application to in vitro evaluation of anticoagulability of artificial materials

In order to attempt in vitro evaluation of antithrombogenecity for materials of artificial blood vessel tube, a new type of rheometer was developed. The rheometer originally consists of a cylindrical tube suspended from a torsion wire and filled with blood. The tube is excited in torsional oscillation and subsequent damped oscillation is observed. The apparatus can sensitively follow the change of fluidity during coagulation of blood. The damped oscillation curves during coagulation for fibrinogen - thrombin solution and blood put in a cylindrical tube made of the artificial material were measured. For fibrinogen - thrombin solution with lower fibrinogen and thrombin concentrations, the values of logarithmic damping factor (LDF) during coagulation increased and then decreased through a maximum. For blood and fibrinogen-thrombin solution with the higher concentrations of fibrinogen and thrombin, LDF monotonously decreased with the progress of coagulation. With a glass tube, the decrease of LDF for whole blood taken without anticoagulant rapidly occurred within about 15 min after sampling, while, with expanded polytetrafluoroethylene (EPTFE; Goar tex) and polydimethylsiloxane (Silastic) tubes, the decrease of LDF proceeds over 40-60 min. The present method is probably available for in vitro evaluation of anticoagulability or antithrombogenecity of artificial materials.     

Microcontinuum model for pulsatile blood flow through a stenosed tube

The effects of polar nature of blood and pulsatility on flow through a stenosed tube have been analysed by assuming blood as a micropolar fluid. Linearized solutions of basic equations are obtained through consecutive applications of finite Hankel and Laplace transforms. The analytical expressions for axial and particle angular velocities, wall shear stress, resistance to flow and apparent viscosity have been obtained. The axial velocity profiles for Newtonian and micropolar fluids have been compared. The interesting observation of this analysis is velocity, in certain parts of cycle, for micropolar fluid is higher than Newtonain fluid. Variation of apparent viscosity eta a with tube radius shows both inverse Fahraeus-Lindqvist and Fahraeus-Lindqvist effects. Finally, the resistance to flow and wall shear stress for normal and diseased blood have been computed and compared.     

Two-layered blood flow in stenosed tubes for different diseases

A two-fluid model for blood flow through a stenosed tube has been developed. The model consists of a core (suspension of RBCs) and peripheral plasma layer. The core is assumed to be represented by a polar fluid and the plasma layer by a Newtonian fluid. The flow is assumed to be steady and laminar, and the fluids incompressible. The flow variables are computed for normal blood and for the cases of polycythemia, plasma cell dyscrasias and for Hb SS diseases. Resistance to flow has been computed for different stenosis length and for different stenosis height. Shear stress distribution along the axial distance has been computed for different stenosis height. The impact of size effects (particle size to tube diameter) on blood diseases is discussed.     

Flow in a two-dimensional collapsible channel with rigid inlet and outlet

This paper examines mainly oscillatory behavior of a fluid-conveying collapsible tube using a two-dimensional flexible channel made of a pair of membranes. The equation of equilibrium of the membrane in a large deflection theory is coupled with the equations of continuity and momentum of an incompressible flow in a one-dimensional flow theory accounting for flow separation. An explicit finite difference method was used to solve the governing equations numerically. According to numerical results, the fluids in the inlet and outlet rigid channels have strong effects on the oscillation of the system. Depending on initial values for the numerical integration, there may exist both a stable static equilibrium and an oscillatory solution for the same parameter values, but only if the external pressure is sufficiently large.     

Tissue collagenase: a simplified, semiquantitative enzyme assay

Tissue collagenase activity from the ulcerating rabbit cornea has been quantitated in a sensitive capillary tube assay system with an unlabeled, native collagen substrate. In this assay system, initial rates of gel lysis are proportional to enzyme concentration over a defined range of enzyme concentrations. Increased sensitivity to enzyme with an unlabeled substrate has been achieved by restricting diffusion of enzyme to one dimension, in a capillary gel. Corneal collagenase activity has been measured at concentrations down to 0.1 μg/μl. In addition to its high sensitivity to enzyme, the precision and simplicity of the assay and minimal equipment requirements all recommend its use for routine screening of biological fluids for collagenase activity and in the investigation of the effects of inhibitors and stimulators of collagenase activity.     

A rheological study of packed red blood cell suspensions with an oscillating ball microrheometer

Rheological properties of concentrated red blood cell suspensions are studied with a magneto acoustic microrheometer in which a ball is suspended in a vertically oriented cylindrical tube. The rheometer uses a conventional falling ball technique to measure steady state viscosity and a vertically oscillating, magnetically driven ball for viscoelastic measurements. The motion of the ball is tracked by ultrasound echo location in which sound waves are transmitted and received by an ultrasound transducer mounted at the base of the tube. The compact size of the rheometer allows rheological studies to be made with microliter quantities of opaque suspensions and permits sudden and accurate changes in temperature. Also, values for the adiabatic compressibility are evaluated from measurements of the speed of sound.     

Viscoelasticity of fibrinogen solution and of blood during coagulation studied by a new damped oscillation rheometer

The behavior of a newly developed damped oscillation type rheometer was analyzed for fibrinogen solution and blood during coagulation. This rheometer consists of a cylindrical tube suspended from a torsion wire, that is filled with liquid to be tested. The logarithmic damping factor (LDF) during coagulation for blood and fibrinogen solution was obtained by this rheometer, which was closely related to the changes of viscosity and/or viscoelasticity of the blood sample. The slight increase of LDF prior to the rapid decrease was observed for blood. The increase of LDF would be reflected in the formation of the aggregation structure of red blood cells (rouleaux network) prior to the formation of fibrin network. The value of LDF for fibrinogen solution sharply increased and then decreased through a maximum value with the progress of coagulation, although the change of LDF was remarkably dependent on the fibrinogen concentration. The initial increase in LDF for fibrinogen solution was considered to be due to the formation of small clots in the solution. The decrease in LDF after attaining a maximum value is ascribed to the formation of fully developed fibrin network. The maximum value of LDF during coagulation for fibrinogen solution is higher than that for blood. The behavior was compared with that for non-biological fluids such as viscosity standard liquids and polyvinyl alcohol solution. From those data, it was concluded that the higher value of LDF than that for Newtonian liquids was due to the formation of aggregation structure or inhomogeneous fine clots in the liquid, which was accompanied with the appearance of the elasticity.     

Studies of fluids simulating blood-like rheological properties and applications in models of arterial branches

We studied several non-Newtonian fluids to determine how closely they simulate the flow behavior of human blood. The viscous and viscoelastic properties of these fluids were compared with human blood samples in steady flow and transient flow Couette viscometers and in an oscillatory tube flow viscoelasticity analyzer. We examined: 1) A polyacrylamide suspension (Separan AP30 and AP45) to which we added 4% isopropanol and 0.01% magnesium chloride. 2) A suspension of 2% Dextran with 16% by weight biconcave disc-shaped particles simulating red blood cells. 3) 40% ghost cells prepared according to Dodge in Tri (hydroxymethyl) aminomethane. These ghost cells were used to simulate the two-phase flow behavior of blood. 4) A suspension of 5% Dextran (70,000) with 12% polystyrene particles (diameter of 1 micron) and 10 mMol calcium chloride. All these fluids closely approximate the flow behavior of blood and can be used in a variety of different experimental situations. To measure velocity distribution using a laser-Doppler-anemometer, we used fluids #1 and #3 in a rigid T-junction simulating the first septal branch of the left descending coronary artery. The measurements were done in steady and pulsatile flow experiments at different flow rate ratios. The fluids showed large differences in velocity profiles compared to Newtonian fluids.     

The flow of a viscous liquid in a converging tube

The problem of the viscous flow of an incompressible Newtonian liquid in a converging tapered tube has been solved in spherical polar coordinates. The method of the solution involves the Stokes' stream function and a technique introduced by Stokes in the study of a sphere oscillating in a fluid. The theory for the flow in a rigid tube includes: (1) the pulsatile flow with both radial and angular velocity components; (2) the steady state flow with both radial and angular velocity components and (3) the very slow steady state flow with only a radial velocity component present. For a tapered elastic tube, the velocity of the propagated pulse wave is determined. The solution given is in terms of the elastic constants of the system and the coordinates for this type of geometry. The pulse velocity is then related to the velocity in an elastic cylindrical tube with the necessary correction terms to account for the tapered tube. Supported in part by the American Heart Association (No. 62F4EG). This work was done during the tenure of an Established Investigatorship of the American Heart Association.     

Axial dispersion in packed bed reactors involving viscoinelastic and viscoelastic non-Newtonian fluids

Axial dispersion is an important parameter in the performance of packed bed reactors. A lot of fluids exhibit non-Newtonian behaviour but the effect of rheological parameters on axial dispersion is not available in literature. The effect of rheology on axial dispersion has been analysed for viscoinelastic and viscoelastic non-Newtonian fluids. Aqueous solutions of carboxymethyl cellulose and polyacrylamide have been chosen to represent viscoinelastic and viscoelastic liquid-phases. Axial dispersion has been measured in terms of Bo_L number. The single parameter axial dispersion model has been applied to analyse RTD response curve. The Bo_L numbers were observed to increase with increase in liquid flow rate and consistency index ‘K’ for viscoinelastic as well as viscoelastic fluids. Bodenstein correlation for Newtonian fluids proposed has been modified to account for the effect of fluid rheology. Further, Weissenberg number is introduced to quantify the effect of viscoelasticity.     

A perturbation model for the oscillatory flow of a Bingham plastic in rigid and periodically displaced tubes.

An approximate analytical model for the pulsatile flow of an ideal Bingham plastic fluid in both a rigid and a periodically displaced tube has been developed using regular perturbation methods. Relationships are derived for the velocity field and dimensionless flow rate. The solution compares adequately with available experimentally measured oscillatory non-Newtonian fluid flow data. These solutions provide useful analytical models supporting experimental and computation studies of arterial blood flow.     

Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow

The effects of non-Newtonian nature of blood and pulsatility on flow through a stenosed tube have been investigated. A perturbation method is used to analyse the flow. It is of interest to note that the thickness of the viscous flow region is non-uniform (changing with axial distance). An analytic relation between viscous flow region thickness and red cell concentration has been obtained. It is important to mention that some researchers have obtained an approximate solution for the flow rate-pressure gradient equation (assuming the ratio between the yield stress and the wall shear to be very small in comparison to unity); in the present analysis, we have obtained an exact solution for this non-linear equation without making that assumption. The approximate and exact solutions compare well with one of the exact solutions. Another important result is that the mean and steady flow rates decrease as the yield stress theta increases. For the low values of the yield stress, the mean flow rate is higher than the steady flow rate, but for high values of the yield stress, the mean flow rate behaviour is of opposite nature. The critical value of the yield stress at which the flow rate behaviour changes from one type to another has been determined. Further, it seems that there exists a value of the yield stress at which flow stops for both the flows (steady and pulsatile). It is observed that the flow stop yield value for pulsatile flow is lower than the steady flow. The most notable result of pulsatility is the phase lag between the pressure gradient and flow rate, which is further influenced by the yield stress and stenosis. Another important result of pulsatility is the mean resistance to flow is greater than its steady flow value, whereas the mean value of the wall shear for pulsatile flow is equal to steady wall shear. Many standard results regarding Casson and Newtonian fluids flow, uniform tube flow and steady flow can be obtained as the special cases of the present analysis. Finally, some applications of this theoretical analysis have been cited.     

Measurement of oscillatory flow pressure gradient in an elastic artery model

In vitro experiments were conducted to measure the oscillatory flow pressure gradient along an elastic tube in order to assess the recent nonlinear theory of Wang and Tarbell. According to this theory, in an elastic tube with oscillatory flow, the mean (time-averaged) pressure gradient cannot be calculated using Poiseuille's law. The effect of wall motion creates a nonlinear convective acceleration, and an induced mean pressure gradient is required to balance the convective acceleration. The induced mean pressure gradient depends on the diameter variation over a cycle, the pulsatility and unsteadiness of the flow, and the phase difference between the pressure wave form and the flow wave form. The amplitude of the pressure gradient also depends on these parameters and may deviate significantly from Womersley's rigid tube theory. A flow loop was constructed to produce oscillatory flow in an elastic tube. Flow wave forms were measured with an ultrasonic flow probe, and ultrasonic diameter crystals were used to measure wall movement. A special device for pressure drop measurement was constructed using Millar catheter tip transducers to obtain both forward and backward pressure drops that were then averaged. This averaging method eliminated the static error of the pressure transducers. The pressure-flow phase angle was varied by clamping a distal elastic section at various locations. Pressure gradients were obtained for a range of phase angles between −55 ° and +49 °. The mean and amplitude of the measured pressure gradient were compared to theoretical values. Both positive and negative induced mean pressure gradients were measured over the range of phase angles. The measured pressure gradient amplitudes were always lower than predicted by Womersley's rigid tube theory. The experimental means and amplitudes are in good agreement with the elastic tube theoretical values. Thus, the experiments verify the theory of Wang and Tarbell.     

Contributions to the mathematical biophysics of the cardiovascular system

The reflection of pressure waves in a fluid enclosed within a tube with an elastic wall is studied for the case of a localized change in diameter of the tube. The concept of impedance is introduced. The relation of the reflection characteristics of the parts of the tube at either side of the change is derived on the basis of the continuity of pressure and mass flow at the site of the change. This relations is used to derive the expression for the ratio of the pressure oscillations measured in front of, and behind, the constriction in terms of the constants of the system. As a result, a method is indicated to locate the coarctation from measurements of the pressures in front of, and behind it.     

One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.     

Influence of a downstream narrowing on the flow profile in a tube

The distance over which the upstream flow conditions in a tube are disturbed by a stenosis downstream, i.e. the outlet length, was investigated for Reynolds numbers in the range 210-2900. Two methods were used, the Navier-Stokes equations were solved with a computer and a physical model was constructed and maximal velocities were measured with an ultrasound Doppler system. The computer model showed that Re number does not influence the outlet length, varying the stenosis area from 25% to 90% has an effect. However, the outlet length remained small, below 70% of the diameter of the tube. The physical model confirmed for a 75% stenosis that the outlet length is small, this method set the limit at not more than 1.2 times the tube diameter.