Minimum Shear Rate Research Articles

Magnetic nanoparticle interaction with a hydrogel in an oscillating magnetic field

A study was conducted of the effect of superparamagnetic nanoparticles on a hydrogel in the presence of an oscillating magnetic field directed tangent to the hydrogel surface. The oscillating magnetic field causes the particles to oscillate laterally in the hydrogel, with some of the particles adhering to the hydrogel matrix and other particles moving freely through the hydrogel pore spaces. The analysis was performed for a three-phase matrix-water-particles model, in which the solvent (water) and hydrogel matrix are interacting continua and the particles are a discrete phase. The study examined the effect of fluid elasticity on wave propagation due to the no-slip boundary condition acting under the transversely oscillating magnetic field. A memory effect within the fluid results in a deviation of the minimum and maximum shear rates observed in one half of the oscillation period from those observed in the other half of the oscillation period. The behavior of the hydrogel with different values of the governing dimensionless parameters was assessed. The matrix Reynolds number, the Deborah number, and the ratio of matrix relaxation to retardation times were all observed to have significant influence on the hydrogel viscoelastic response and on the wave propagation within the hydrogel. The phase difference between the water and matrix oscillations is strongly influenced by the phase interaction force coefficient, the Deborah number, and the ratio of free to captured particles. The system is found to approach an asymptotic state at a high Deborah number, which is independent of the value of the Deborah number.

DIRECTED REGULATION OF THE STRUCTURAL AND RHEOLOGICAL PROPERTIES OF HEAT-INSULATING ACRYLIC AQUEOUS DISPERSIONS USING THE COMBINED USE OF HYDROPHILIC AND HYDROPHOBIC SILICATE FILLERS

The formation technology and performance characteristics of coatings based on aqueous dispersions are largely determined by the properties of the initial film-forming materials, which should ensure uniform thin-layer distribution on the substrate surface and the formation of coatings with the required technological complex of properties. Among them, due to their functional properties and relatively low cost, the most widespread are water-dispersion polymer coatings based on acrylic film-formers. In this paper, mathematical models of the structural and rheological dependences of heat-insulating acrylic aqueous dispersions are considered depending on the combined content of hydrophilic-hydrophobic fillers. To describe these dependencies, it is advisable to use equations of the second degree. According to the mathematical theory of experiment, the second-order orthogonal central compositional design makes it possible to predict the behavior of the response function. Carrying out an experiment in accordance with this plan makes it possible to establish the analytical dependence of the response function on the corresponding factors in the form of a polynomial equation of the second degree. The main response functions were: conditionally static yield stress, viscosity at the minimum rate of onset of fracture (initial effective viscosity), viscosity of the “destroyed” structure according to the Newtonian nature of the flow, activation energy of viscous flow at minimum, average and maximum shear rates. On the basis of the established dependences, the optimal ratios of hydrophobized aerosil and aluminosilicate microspheres were selected, the combined use of which makes it possible to reduce shear stresses to create a homogeneous aqueous acrylic dispersion, to predict the activation energy at various technological stages of preparation and application of heat-insulating coatings. The established results made it possible to create a hydrophilic-hydrophobic aqueous acrylic dispersion, which, without the use of surfactants, makes it possible to simplify the production technology of heat-insulating water-dispersion coatings, namely, to exclude the stage of pretreatment of fillers, to reduce the rotation speed of the frame mixer, and also to increase the kinetic stability of the finished dispersion.

CFD modelling of oscillatory flow in columns having different types of internals

Single-phase oscillatory, turbulent flow in cylindrical columns having different types of internals is simulated using Computational Fluid Dynamics (CFD). Standard k-ε model is used to model turbulence. CFD model is validated by using experimentally obtained residence time distribution (RTD) curves. The validated CFD model is used to understand the effect of the design of internals on fluid dynamics prevalent inside the column. Five different types of internals - disc and doughnut, slanted disc and doughnut, concave disc and doughnut, convex disc and doughnut, and inflexed disc and doughnut – are evaluated. The internals are compared on the basis of key hydrodynamic parameters such as Peclet number, shear rate, turbulent energy dissipation rate and pressure drop per unit length for the same oscillation velocity. For the same oscillation velocity, convex disc and doughnut internal is found to have minimum axial mixing with minimum shear rate and minimum turbulent energy dissipation rate which makes it ideal for intensification of applications such as homogeneous reactions of positive order. Inflexed disc and doughnut internal is found to have high shear rate, high turbulent energy dissipation rate with moderate axial mixing which makes it suitable for intensification of two-phase applications such as solvent extraction, and absorption.

Investigation of the Effect of Filler Concentration on the Flow Characteristics of Filled Polyethylene Melts

Abstract All polymeric slurries that have a high concentration of filler are shear thinning. Shear thinning is an important characteristic of polymers, filled and unfilled, because it enables an increase in the throughput, shear rate in a die or an injection molding system without having to use substantially more power to increase the flow rate. Newtonian fluid-based slurries show an increase in shear thinning as the concentration of “filler” increases above the percolation threshold. As particle maximum packing concentration is approached the slurries begin to approach a perfect pseudoplastic fluid. In some cases, the shear thinning characteristics of a filled polymer do not increase substantially as the filler loading is increased. This is a quite different response than in Newtonian fluid-based slurry. Therefore, it is important to understand the materials engineering interactions that control shear thinning so that process flow models can better predict the performance of filled polymer systems. Highly filled polymers can have processing issues, including high screw shaft torque, energy consumption, die pressure and melt temperature rise. Previous theoretical developments and experimental evaluations of highly filled polymer melts showed that the rheology can be effectively described with a percolation model. In this work, capillary rheometer measurements using several low-density polyethylene resins, calcium carbonate and titanium dioxide fillers are reported using percolation theory concepts. The theoretical treatment of the rheology as a particulate percolating system with power-law behavior is used to analyze capillary rheometer data. The observed effects of resin molecular weight, filler type and size on rheology are described. Engineers that design and debottleneck polymer processes need to utilize the polymer viscosity at the minimum process shear rate to determine the smallest motor that will allow the process to run; in addition, the shear thinning characteristics of the polymer are used to indicate how much increased production may be possible with a given motor size. Thus, some examples of expected effects on melt processing are also presented.

Exfoliation of 2D materials by high shear mixing

While it has been demonstrated that large scale liquid exfoliation of graphene is possible using high-shear exfoliation, it has not yet been shown to be applicable to a broader range of layered materials. In addition, it would be useful to determine whether the mechanisms reported for shear exfoliation of graphene also apply to other 2D materials. In this work we show that previous models describing high-shear exfoliation of graphene apply to MoS2 and WS2. However, we find the minimum shear rate required to exfoliate MoS2 and WS2 to be ~3 × 104 s−1, somewhat higher than the value for graphene. We also demonstrate the scalability of shear exfoliation of WS2. By measuring and then optimising the scaling parameters, shear exfoliation of WS2 is shown to be capable of reaching concentrations of 1.82 g l−1 in 6 h and demonstrating a maximum production rate of 0.95 g h−1.

Experimental observations of bands of suspended colloidal particles subject to shear flow and steady electric field

Manipulating suspended colloidal particles flowing through a microchannel is of interest in microfluidics and nanotechnology. However, the flow itself can affect the dynamics of these suspended particles via wall-normal “lift” forces. The near-wall dynamics of particles suspended in shear flow and subject to a dc electric field was quantified in combined Poiseuille and EO flow through a ~ 30 μm deep channel. When the two flows are in opposite directions, the particles are attracted to the wall. They then assemble into very high aspect ratio structures, or concentrated streamwise “bands,” above a minimum electric field magnitude, and, it appears, a minimum near-wall shear rate. These bands only exist over the few micrometers next to the wall and are roughly periodic in the cross-stream direction, although there are no external forces along this direction. Experimental observations and dimensional analysis of the time for the first band to form and the number of bands over a field of view of ~ 200 μm are presented for dilute suspensions of polystyrene particles over a range of particle radii, concentrations, and zeta potentials. To our knowledge, there is no theoretical explanation for band assembly, but the results presented here demonstrate that it occurs over a wide range of different particle and flow parameters.

Efficacy of magnetically driven temperature-dependent plastic flows in exciting the magnetosphere of CXOU J164710.2-455216

Using verified transition state theory and quantum plasticity theory we calculate the temperature-dependent shear (strain) rates as well as temperature-dependent (shear) viscosity considering magnetically driven plastic flows in the neutron star (like CXOU J164710.2-455216) crust. Our numerical results which are based on previous works like the critical shear stress as well as the minimum shear (strain) rate of crust (around $1~\mbox{rad}/\mbox{year}$ ) demonstrate that a plastic deformation of the neutron star crust could induced a very slight twist (or shear) in the external magnetic field. We then extend Lander’s calculation of magnetospheric twist to slip-flow cases that will generated currents in the magnetosphere of the magnetar, say, CXOU J164710.2-455216 in Westerlund 1. The latter is believed to be the direct cause of the observed X-ray outburst by Muno et al. once we examine the associated energy scales for corresponding magnetic fields considering the age or history of CXOUJ164710.2-455216 which can be estimated from available measurements or observations. Our results and analysis of relevant energy scales confirm the onset of the soft gamma repeater outburst is controlled by magnetospheric dissipation induced by the plastic motions of the crust.

Gate shape optimization using design of experiment to reduce the shear rate around the gate

Numerical analysis is used to optimize the gate shape of the mold part in the molding process. The objective of this research was to develop a procedure that will optimize the gate shape of the mold part by using Design of Experiments approach. The computer-aided engineering software Moldflow was used to simulate the plastic injection molding process and the Minitab software was used to analyze the computational results from Moldflow. The Bulk Molding Compounds (BMC) UNI-203S thermoset material was chosen as the molding material. Four different types of gate shapes were analyzed to find the gate shape to be used in the optimization. The Type 3 gate shape was selected as basis for the gate optimization because this shape yielded the minimum shear rate around the gate among all. The thickness, width, length and angle of the gate were selected as the design variables. Erosion around a gate due to repetitive shear flow during molding process was considered as an important issue to extend the service life of the expensive mold. It is normally very difficult to prevent erosion due to high injection pressure and repetitive use of the mold, especially in certain molding parts as BMC reflector in automotive parts, so it has become the subject of researches. The effectiveness of design variables was evaluated by observing shear rate around the gate. The objective of the optimization was to minimize the average shear rate around the gate. Response Surface Method was applied to identify the optimum values of the design variables. The computed optimum values were validated numerically. The optimized gate shape showed the reduced shear rate by about 11%.

Fluorine-containing arborescent polystyrene-graft-polyisoprene copolymers as polymer processing additives

Linear low density polyethylene (LLDPE) can suffer from melt extrusion defects including sharkskin, cyclic melt fracture, and gross melt fracture during processing. Arborescent polymers are dendritic macromolecules with characteristics, such as a compact structure and a rigid spherical topology, making them potentially useful as polymer processing additives (PPA) to alleviate melt extrusion defects. Arborescent polystyrene-graft-polyisoprene copolymer samples were synthesized from polystyrene substrates of linear and branched architectures functionalized with acetyl groups, and coupled with polyisoprene macroanions. A linear polyisoprene sample was also investigated for comparison. The polymers were hydrosilylated with (tridecafluoro-1,1,2,2-tetrahydrooctyl)dimethylsilane on 17–52% of the isoprene units and blended with LLDPE at 0.1 and 0.5% w/w to evaluate their performance as PPA by extrusion at different shear rates. All the samples led to some degree of improvement in the extrusion of LLDPE, albeit the performance of the branched additives was inferior to a commercial fluoroelastomer PPA. The lower molecular weight and more compact (G0 or comb-branched) PPA generally performed better than those with a high molecular weight. Several PPA samples induced the early onset of cyclic melt fracture but glossy, defect-free surfaces were obtained at higher shear rates. This suggests that a minimum shear rate is required for these additives to coat the extrusion die under the experimental conditions used.

Mixing of isotopic heterogeneities in the Mauna Kea plume conduit

We have measured high-precision Hf, Nd, and Pb isotope compositions for 40 samples from the final leg of the Hawaii Scientific Drilling Project (HSDP) core using solution chemistry and MC-ICP-MS. The new isotope data are indistinguishable from those higher up in the Mauna Kea part of the core. The Pb isotope data define three linear trends with a common intersection. Principal component analysis recognizes no more than three geochemical end-members among these trends. When all the Pb isotope data acquired so far for the HSDP core are pooled, two contrasting groups stand out. A first coherent, prevalent group represents the Kea main eruptive sequence. This group combines the Kea-mid8 and Kea-lo8 subgroups of Eisele et al. (Eisele, J., Abouchami, W., Galer, S.J.G., Hofmann, A.W., 2003. The 320 kyr Pb isotope evolution of Mauna Kea lavas recorded in the HSDP-2 drill core. Geochem. Geophys. Geosyst. 4, doi: 10.1029/2002GC000339): although defining two separate trends in Pb–Pb isotope space, they follow each other smoothly in time. A second group of 14 flows below 2000 mbsl is characterized by distinctly higher source Th/U and high 3He/ 4He. These samples belong to the Kea-hi8 group and are about 0.4 (Hf) and 0.5 (Nd) ε units below the main sequence Kea values. The toggle between these two groups is so sharp and repetitive and the gap between the values so conspicuous that the alternation must reflect eruptions from distinct volcanic centers, those of Mauna Kea and an unknown volcano, the latter of which bears isotopic resemblance to Kilauea for Nd and Hf and to Loihi for He. This ‘lost’ volcano stopped erupting about 550 ka ago, i.e., 200 ka before the oldest known ages for Kilauea, and is presently buried under 2000–3000 m of Kea flows. Periodograms show no wavelengths exceeding the 95% significance level (white spectrum). Except for a few minor wiggles in Hf at shallow depth, the isotopic signals display overall smooth up-core variations with little short-distance variability. Analysis of the flow regime within the plume conduit shows that temperature dependence of viscosity makes the conduit narrow and sharply bound. The hot core is highly mobile with minimum shear rates and a regime of pipe (Poiseuille) flow. The core is rimmed by a sheath of colder, strongly stretched material (filaments). A broadly concentric zoning of the plume is expected. The white spectra suggest, however, that, at any given depth within the plume conduit, lateral mixing results from the rheological variability across the plume conduit.

Miniaturizing the Fermentation Assay: Effects of Fermentor Size and Fermentation Kinetics on Detection of Premature Yeast Flocculation

This article reports on fermentation assays used to test the fermentability of malt, especially malt implicated in premature yeast flocculation (PYF). No standard small-scale method currently exists. The current study involved 12°C fermentations with three vessel configurations: a 4.4-cm high spectrophotometer cuvette, a 12.5-cm high test tube, and a 122-cm high “tall” tube fermentor. Worts tested were made from control and PYF malts. We included in our experiments the method of Jibiki and associates, using wort supplemented with 4% glucose and fermented at 21°C. The decline in Plato values (or real extract) was fit with a sigmoidal model. The model parameters and fermentor height were used to estimate CO2 evolution and average shear rates. It was confirmed that both fermentor height and fermentation speed are the major independent variables determining CO2 evolution and agitation within the fermenting wort. In examining the fermentation data, it is evident that the yeast did not stay equally suspended in all three fermentation vessels. When fermented at 12°C, yeast fell out of suspension rapidly in both the cuvette and test tube fermentors. In the tall tubes, the yeast remained in suspension as expected. The 21°C test tube fermentations supplemented with glucose had fermentation profiles similar to the tall tube fermentations but were complete in less than 72 hr. It is notable that these profiles could be used to distinguish between PYF and control malts. The minimum average shear rate required to keep yeast suspended was determined to be between 4 and 7.5 sec−1. Thus, when downscaling a fermentation assay by reducing the fermentor height, the rate of fermentation must be increased to maintain adequate shear rates. We confirmed that the PYF fermentation assay could be reduced to 15 mL, resulting in reduced labor, time, and material costs.

Flow visualization in a centrifugal blood pump with an eccentric inlet port.

Flow visualization analysis was applied to the Baylor/Miwatec centrifugal artificial heart to evaluate its fluid dynamic characteristics regarding antithrombogenicity. An eccentric vortex was found both in the upper and the lower gaps of the impeller, which is supposed to be caused by the eccentric inlet port. Therefore, one-way flow toward the outlet is formed and washes the pivot. The combination of an eccentric vortex and a pivot bearing that is washed is unique to the Baylor/Miwatec pump. For the male pivots exposed to periodic wash, the minimum shear rate around the bottom pivot was estimated to be 650/s, which is higher than the threshold for thrombus formation shown by other studies. The wall shear rate at the impeller bottom surface was found to be larger in the top contact mode than in the bottom contact mode.

Negative thixotropy of polymer solutions. 1. A model explaining time-dependent viscosity

Negative thixotropy, also called antithixotropy, is the effect of a flow-induced increase in viscosity that has been observed for many polymer solutions. Here, a simple quantitative model describing the time dependence of the shear stress or viscosity is presented. The model assumes a dynamic gel or network in the polymer solution, whose cross-links are dynamically formed and broken. The cross-links exist with or without deformation or flow of the solution. A second property of the model network is that it cannot be deformed infinitely, which is also true for any real network. The dynamic network solution is characterized by four parameters: its elastic shear modulus, its maximum degree of deformation, the rate with which the dynamic cross-links form and break and the viscous contribution of the polymer solution. The first two parameters can be related to each other, so only three independent parameters enter the model. An analytical solution is obtained which describes the flow-induced increase in viscosity, the minimum shear rate required for negative thixotropy and the dependence of the induction time on the shear rate. The results are shown to be in agreement with reported experimental results.

Dispersion of Carbon-Nanotubes in a Polymer Matrix by a Visualization Analysis of Shear Flow

The filler size in polymer composites has experienced a tremendous reduction, especially in nano-composite formulations. The physical properties of polymer composites are also strongly dominated by the dispersion conditions of the filler. In the case of nano-composites, break up of the agglomerated filler is an important factor for improvement of the properties.In our previous report, the dispersion conditions were explained by using total shear strain [γ·t] as the dominant dispersion parameter, and the optimum mixing conditions for the blending of polycarbonate (PC) and carbon-nanotubes(CNT) were determined.In this study, break up of agglomerated CNT (analysis of dispersion process) was observed by a visualization analysis of shear flow. CNT was used as the filler in a PC matrix as we reported previously. The minimum shear rate required to break up the agglomerated CNT was defined as “critical shear rate” [γ c]. “Critical shear rate” was observed in two steps of the break up of agglomerated CNT. Dispersion conditions by a visualization analysis of shear flow were explained in terms of total shear strain as performed in the previous report. At the same total shear strains, the shear rate [γ] had a greater effect on the dispersion conditions than the shear rate history time [t] in the PC/CNT material combination.

Investigation of the band texture occurring in acetoxypropylcellulose thermotropic liquid crystalline polymer using rheo-optical, rheological and light scattering techniques

The optical evolution of the band texture occurring in acetoxypropylcellulose thermotropic polymer has been investigated as a function of temperature and primary shear rate. Two distinct kinds of band texture were observed which are referred to here as the `fast' and `slow' band textures with regard to their rate of evolution. The fast band texture appears very quickly following the cessation of shear and then disappears. The slow band texture is much finer than the fast band texture and appears to exist both during and after the appearance of the fast band texture. The evolution behaviour of the fast band texture is interpreted in terms of the shifting of a three-region evolution curve. Particular attention has been paid to investigating the influence of temperature on the formation of the fast band texture. Rheo-optical experiments show that the minimum shear rate required to form the fast band texture increases as a power-law function of the temperature. By subsequently performing steady flow measurements over a range of temperatures, the minimum shear stress required to form the fast band texture has been found to be independent of temperature and to increase linearly with the molecular weight of the sample. Results obtained from dynamic tests are compared with similar tests conducted previously on a lyotropic hydroxypropylcellulose water solution (Harrison and Navard 1999). The results of the comparison provide evidence in support of a connection between the behaviour of the dynamic functions and the optical evolution of the slow band texture. These results suggest that nematic and cholesteric fluids can relax through several different possible mechanisms, each of which results in a periodic band texture following the cessation of shear.

Pointwise observations for rheological characterization using nuclear magnetic resonance imaging

This study focuses on development of a nuclear magnetic resonance (NMR) imaging based viscometric technique using pulsed gradient NMR for characterizing fluid materials under steady tube flow conditions. By simultaneously measuring velocity profiles and pressure gradients it is possible to characterize complex fluids locally. Shear viscosity–shear rate data, ranging from one to over two decades of shear rate from one combined velocity profile/pressure drop per unit tube length measurement, are provided for five fluids that exhibit both Newtonian and shear thinning characteristics. The resolution of the velocity data controls the accuracy of the measured shear viscosity whereas the radial resolution prescribes the number of shear viscosity–shear rate data points and the minimum shear rate. Velocity profile measurements with a velocity resolution of 1 mm/s and radial resolutions which provided from 22 to 110 spatially resolved velocity data points accurately characterized fluids for shear rates greater than...

Compliance and diameter mismatch affect the wall shear rate distribution near an end-to-end anastomosis

The development of intimal hyperplasia near the anastomosis of a vascular graft to an artery may be related to changes in the wall shear rate distribution. Mismatches in compliance and diameter at the end-to-end anastomosis of a compliant artery and a rigid graft cause shear rate disturbances that may induce intimal hyperplasia and ultimately graft failure. The goal of this study is to determine how compliance mismatch, diameter mismatch, and impedance phase angle affect the wall shear rate distribution in end-to-end anastomosis models under sinusoidal flow conditions. Wall shear rates are obtained through flow visualization using a photochromic dye. In a model with a well-matched graft diameter (6% undersized), the compliance mismatch causes low mean wall shear rates near the distal anastomosis. Considering diameter mismatch, the wall shear rate distributions in 6% undersized, 16% undersized, and 13% oversized graft models are markedly different at similar phase angles. In the two undersized graft models, the minimum mean shear rate occurs near the distal anastomosis, and this minimum is lower in the model with greater diameter mismatch. The oversized graft model has a minimum mean shear rate near the proximal anastomosis. Thus in all three models, the minimum mean wall shear rate is observed at the site of the divergent geometry. The impedance phase angle, which can be altered by disease states and vasoactive drugs, has a minor effect on the wall shear rate amplitude far from the anastomosis but a more pronounced effect closer to the anastomosis. Mean wall shear rates under sinusoidal flow conditions are significantly lower than under steady flow conditions at the same mean flow rate, but they are fairly insensitive to phase angle changes. In order to avoid the divergent geometry that may cause lower wall shear rates, we recommend that compliance mismatch be minimized whenever possible and that graft diameter be chosen to match the arterial diameter at the relevant physiologic pressure, not at the reduced pressure present when the graft is implanted.

Intramural mechanics in hypertrophic cardiomyopathy: functional mapping with strain-rate MR imaging.

To characterize systolic and diastolic intramural mechanics in hypertrophic cardiomyopathy (HCM) with a new metric of contractile activity. Eleven healthy subjects and eight patients with HCM underwent velocity-encoded echo-planar magnetic resonance (MR) imaging (6-8-frame gated breath-hold movies, 3 x 3-mm resolution). A scalar strain rate (SR) parameter was compared with wall thickness and symptoms. The normal pattern of SR included regional uniformity, a monotonically increasing subepicardial to subendocardial gradient, and minimum transmural shear rate. In HCM, heterogeneity of SRs increased in diastole. Regional diastolic SR correlated with regional wall thickness (r = .785, P = .0001). Interobserver global SR assignment agreed in seven of eight patients. All four patients with New York Heart Association class 1 disease had a low global SR deficit score, whereas three of four patients with class 2 or 3 disease had a high SR deficit score (Spearman r = .775, P = .187). SR characterization may provide an objective measure of disease course in HCM.

Clot growth under periodically fluctuating shear rate.

To control the morphology of a clot formed on an artificial flow path in pulsatile blood flow, the hydrodynamic effect of periodically fluctuating shear rate on clot growth has been quantitatively investigated in vitro. Uniform shear rates were applied to a sample of beagle blood in the concave-convex cones system. These shear rates were sinusoidally fluctuated between a maximum and a minimum in one direction at frequencies between 0.1 and 0.6 Hz. Evaluation of clot growth was derived from a clot ratio, which was experimentally determined from the rate of increase of frictional torque between the two cones. The results show that clot growth is controlled so as not to occupy a large space when the minimum shear rate is higher than 100 s-1, or when the time of application of lower (< 100 s-1) shear rates is modified by the intermittent application of higher (> 500 s-1) shear rates as long as the frequency is less than 0.6 Hz.

Preliminary analysis of the effects of blood vessel movement on blood flow patterns in the coronary arteries.

Blood flow patterns are believed to be involved in the formation and progression of arterial diseases. It is possible that the normal physiologic movement of blood vessels during the cardiac cycle affects blood flow patterns significantly. For example, the contraction of the heart in systole and subsequent relaxation in diastole create movements of the coronary arteries, as evidenced in real-time angiography. The effects of this movement on coronary artery flow patterns have never been previously analyzed. This work was undertaken to provide a preliminary estimate of the importance of the effects of such physiologic movements on blood flow patterns in the coronary arteries. A Womersley-type solution was used to determine the effect of axial movement on the wall shear rate in a simplified model of the coronary arteries. The pulsatile pressure gradient was derived from previously published coronary artery flow waveforms. The axial movement function was obtained from a three-dimensional reconstruction of a biplanar coronary angiogram. Significant changes in wall shear rate were noted when the movement was taken into account. The maximum and minimum wall shear rates were 10 percent smaller and 107 percent larger in magnitude respectively, and the Oscillatory Shear Index (OSI) was doubled. Most of the changes in wall shear rate were observed in systole, when the pressure gradient is minimal and the movement is strongest. The results indicate that blood vessel movement during the cardiac cycle has a significant effect on hemodynamic phenomena which have been associated with the development of atherosclerosis.