Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

Flow Visualization in Arteriovenous Fistula and Aneurysm Using Computational Fluid Dynamics

The arteriovenous fistula (AVF) is characterized by enhanced blood flow and is the most widely used vascular access for chronic haemodialysis (Sivanesan et al., 1998). A large proportion of the AVF late failures are related to local haemodynamics (Sivanesan et al., 1999a). As in AVF, blood flow dynamics plays an important role in growth, rupture, and surgical treatment of aneurysm. Several techniques have been used to study the flow patterns in simplified models of vascular anastomose and aneurysm. In the present investigation, Computational Fluid Dynamics (CFD) is used to analyze the flow patterns in AVF and aneurysm through the velocity waveform obtained from experimental surgeries in dogs (Galego et al., 2000), as well as intra-operative blood flow recordings of patients with radiocephalic AVF ( Sivanesan et al., 1999b) and physiological pulses (Aires, 1991), respectively. The flow patterns in AVF for dog and patient surgeries data are qualitatively similar. Perturbation, recirculation and separation zones appeared during cardiac cycle, and these were intensified in the diastole phase for the AVF and aneurysm models. The values of wall shear stress presented in this investigation of AVF and aneurysm models oscillated in the range that can both cause damage to endothelial cells and develop atherosclerosis.

Computational fluid dynamics investigation of a centrifugal blood pump

In the development of a ventricular assist device, computational fluid dynamics (CFD) analysis is an efficient tool to obtain the best design before making the final prototype. In this study, different designs of a centrifugal blood pump were developed to investigate flow characteristics and performance. This study assumed the blood flow as being an incompressible homogeneous Newtonian fluid. A constant velocity was applied at the inlet; no slip boundary conditions were applied at device wall; and pressure boundary conditions were applied at the outlet. The CFD code used in this work was based on the finite volume method. In the future, the results of CFD analysis can be compared with flow visualization and hemolysis tests.

Computational fluid dynamics of the right ventricular outflow tract and of the pulmonary artery: a bench model of flow dynamics.

OBJECTIVES: The reconstruction of the right ventricular outflow tract (RVOT) with valved conduits remains a challenge. The reoperation rate at 5 years can be as high as 25% and depends on age, type of conduit, conduit diameter and principal heart malformation. The aim of this study is to provide a bench model with computer fluid dynamics to analyse the haemodynamics of the RVOT, pulmonary artery, its bifurcation, and left and right pulmonary arteries that in the future may serve as a tool for analysis and prediction of outcome following RVOT reconstruction. METHODS: Pressure, flow and diameter at the RVOT, pulmonary artery, bifurcation of the pulmonary artery, and left and right pulmonary arteries were measured in five normal pigs with a mean weight of 24.6 ± 0.89 kg. Data obtained were used for a 3D computer fluid-dynamics simulation of flow conditions, focusing on the pressure, flow and shear stress profile of the pulmonary trunk to the level of the left and right pulmonary arteries. RESULTS: Three inlet steady flow profiles were obtained at 0.2, 0.29 and 0.36 m/s that correspond to the flow rates of 1.5, 2.0 and 2.5 l/min flow at the RVOT. The flow velocity profile was constant at the RVOT down to the bifurcation and decreased at the left and right pulmonary arteries. In all three inlet velocity profiles, low sheer stress and low-velocity areas were detected along the left wall of the pulmonary artery, at the pulmonary artery bifurcation and at the ostia of both pulmonary arteries. CONCLUSIONS: This computed fluid real-time model provides us with a realistic picture of fluid dynamics in the pulmonary tract area. Deep shear stress areas correspond to a turbulent flow profile that is a predictive factor for the development of vessel wall arteriosclerosis. We believe that this bench model may be a useful tool for further evaluation of RVOT pathology following surgical reconstructions.

Fluid dynamics simulation of right ventricular outflow tract oversizing.

OBJECTIVES: Repair of the right ventricular outflow tract (RVOT) in paediatric cardiac surgery remains challenging due to the high reoperation rate. Intimal hyperplasia and consequent arteriosclerosis is one of the most important limitation factors for graft durability. Since local shear stress and pressure are predictive elements for intimal hyperplasia and wall degeneration, we sought to determine in an oversized 12-mm RVOT model, with computed fluid dynamics simulation, the local haemodynamical factors that may explain intimal hyperplasia. This was done with the aim of identifying the optimal degree of oversizing for a 12-mm native RVOT. METHODS: Twenty domestic pigs, with a weight of 24.6 ± 0.89 kg and a native RVOT diameter of 12 ± 1.7 mm, had valve conduits of 12, 16, 18 and 20 mm implanted. Pressure and flow were measured at 75, 100 and 125% of normal flow at RVOT at the pulmonary artery, pulmonary artery bifurcation and at the left and right pulmonary arteries. Three-dimensional computed fluid dynamics (CFD) simulation in all four geometries in all flow modalities was performed. Local shear stress and pressure conditions were investigated. RESULTS: Corresponding to 75, 100 and 125% of steady-state flow, three inlet velocity profiles were obtained, 0.2, 0.29 and 0.36 m/s, respectively. At inflow velocity profiles, low shear stress areas, ranged from 0 to 2 Pa, combined with high-pressure areas ranging from 11.5 to 12.1 mmHg that were found at distal anastomosis, at bifurcation and at the ostia of the left and right pulmonary arteries in all geometries. CONCLUSIONS: In all three oversized geometries, the local reparation of shear stress and pressure in the 16-mm model showed a similar local profile as in the native 12 mm RVOT. According to these findings, we suggest oversizing the natural 12-mm RVOT by not more than 4 mm. The elements responsible for wall degeneration and intimal hyperplasia remain very similar to the conditions present in native RVOT.

Transient shear banding in time-dependent fluids

We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model is solved iteratively with the Navier-Stokes equation to obtain the time evolution of the local velocity and viscosity fields. It is found that the underlying reason for dynamic effects is the nonhomogeneous shear distribution, which is amplified due to a positive feedback between the flow field and the viscosity response of the shear thinning fluid. This offers a simple explanation for the recent observations of transient shear banding in time-dependent fluids. Extensions to more complicated rheological systems are considered.

Application of Computational Fluid Dynamics in Modeling Blood Flow in Human Thoracic Aorta

The aim of this study was to simulate blood flow in thoracic human aorta and understand the role of flow dynamics in the initialization and localization of atherosclerotic plaque in human thoracic aorta. The blood flow dynamics in idealized and realistic models of human thoracic aorta were numerically simulated in three idealized and two realistic thoracic aorta models. The idealized models of thoracic aorta were reconstructed with measurements available from literature, and the realistic models of thoracic aorta were constructed by image processing Computed Tomographic (CT) images. The CT images were made available by South Karelia Central Hospital in Lappeenranta. The reconstruction of thoracic aorta consisted of operations, such as contrast adjustment, image segmentations, and 3D surface rendering. Additional design operations were performed to make the aorta model compatible for the numerical method based computer code. The image processing and design operations were performed with specialized medical image processing software. Pulsatile pressure and velocity boundary conditions were deployed as inlet boundary conditions. The blood flow was assumed homogeneous and incompressible. The blood was assumed to be a Newtonian fluid. The simulations with idealized models of thoracic aorta were carried out with Finite Element Method based computer code, while the simulations with realistic models of thoracic aorta were carried out with Finite Volume Method based computer code. Simulations were carried out for four cardiac cycles. The distribution of flow, pressure and Wall Shear Stress (WSS) observed during the fourth cardiac cycle were extensively analyzed. The aim of carrying out the simulations with idealized model was to get an estimate of flow dynamics in a realistic aorta model. The motive behind the choice of three aorta models with distinct features was to understand the dependence of flow dynamics on aorta anatomy. Highly disturbed and nonuniform distribution of velocity and WSS was observed in aortic arch, near brachiocephalic, left common artery, and left subclavian artery. On the other hand, the WSS profiles at the roots of branches show significant differences with geometry variation of aorta and branches. The comparison of instantaneous WSS profiles revealed that the model with straight branching arteries had relatively lower WSS compared to that in the aorta model with curved branches. In addition to this, significant differences were observed in the spatial and temporal profiles of WSS, flow, and pressure. The study with idealized model was extended to study blood flow in thoracic aorta under the effects of hypertension and hypotension. One of the idealized aorta models was modified along with the boundary conditions to mimic the thoracic aorta under the effects of hypertension and hypotension. The results of simulations with realistic models extracted from CT scans demonstrated more realistic flow dynamics than that in the idealized models. During systole, the velocity in ascending aorta was skewed towards the outer wall of aortic arch. The flow develops secondary flow patterns as it moves downstream towards aortic arch. Unlike idealized models, the distribution of flow was nonplanar and heavily guided by the artery anatomy. Flow cavitation was observed in the aorta model which was imaged giving longer branches. This could not be properly observed in the model with imaging containing a shorter length for aortic branches. The flow circulation was also observed in the inner wall of the aortic arch. However, during the diastole, the flow profiles were almost flat and regular due the acceleration of flow at the inlet. The flow profiles were weakly turbulent during the flow reversal. The complex flow patterns caused a non-uniform distribution of WSS. High WSS was distributed at the junction of branches and aortic arch. Low WSS was distributed at the proximal part of the junction, while intermedium WSS was distributed in the distal part of the junction. The pulsatile nature of the inflow caused oscillating WSS at the branch entry region and inner curvature of aortic arch. Based on the WSS distribution in the realistic model, one of the aorta models was altered to induce artificial atherosclerotic plaque at the branch entry region and inner curvature of aortic arch. Atherosclerotic plaque causing 50% blockage of lumen was introduced in brachiocephalic artery, common carotid artery, left subclavian artery, and aortic arch. The aim of this part of the study was first to study the effect of stenosis on flow and WSS distribution, understand the effect of shape of atherosclerotic plaque on flow and WSS distribution, and finally to investigate the effect of lumen blockage severity on flow and WSS distributions. The results revealed that the distribution of WSS is significantly affected by plaque with mere 50% stenosis. The asymmetric shape of stenosis causes higher WSS in branching arteries than in the cases with symmetric plaque. The flow dynamics within thoracic aorta models has been extensively studied and reported here. The effects of pressure and arterial anatomy on the flow dynamic were investigated. The distribution of complex flow and WSS is correlated with the localization of atherosclerosis. With the available results we can conclude that the thoracic aorta, with complex anatomy is the most vulnerable artery for the localization and development of atherosclerosis. The flow dynamics and arterial anatomy play a role in the localization of atherosclerosis. The patient specific image based models can be used to diagnose the locations in the aorta vulnerable to the development of arterial diseases such as atherosclerosis.

Rheological and electrical properties of NaY zeolite electrorheological fluid

The relations between the rheological and electrical properties of NaY zeolite electrorheological fluid and its solid phase are studied. It is found that then exist complex relations between its electrical and theological properties. The temperature spectra of dielectric properties of the fluid under high AC electric field are strongly field strength dependent. The relation between the DC conductivity of the fluid and the exciting electric field is experimentally presented as log sigma =A+BE1/2, when A is a strong function, but B, a very weak function of temperature. The shear stress of the fluid under a fixed electric field and temperature decreases with shear rate. A relaxation time for the adsorbed charges is estimated to be about 0.3 to 6.6 s in the temperature range from 280 to 380 K. The relaxation time qualitatively corresponds to the shear rate at which the shear stress begins to drop. The time dependent leaking current of the ER fluids under DC electric field is also measured. The conductivity increase is mainly caused by the structure evolution of particles. The experimental results can he explained with the calculations of Davis (J. Appl. Phys. 81(1997) pp.1985-1991) and Martin (J. Chem. Phys. 110(1999) pp.4854-4866). It is predicted that the NaY zeolite ER fluid strength would get degraded slowly.

Influence of the size distribution of particles on the viscous property of an electrorheological fluid

The influence of the size distribution of particles on the viscous property of an electrorheological fluid has been investigated by the molecular dynamic simulation method. The shear stress of the fluid is found to decrease with the increase of the variance sigma(2) of the Gaussian distribution of the particle size, and then reach a steady value when sigma is larger than 0.5. This phenomenon is attributed to the influence of the particle size distribution on the dynamic structural evolution in the fluid as well as the strength of the different chain-like structures formed by the particles.

Dynamics, rheology and critical properties of colloidal fluid mixtures

Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.

Numerical modelling of fluid-structure interaction with application in hemodynamics

The thesis deals with numerical algorithms for fluid-structure interaction problems with application in blood flow modelling. It starts with a short introduction on the mathematical description of incompressible viscous flow with non-Newtonian viscosity and a moving linear viscoelastic structure. The mathematical model consists of the generalized Navier-Stokes equation used for the description of fluid flow and the generalized string model for structure movement. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. A part of the thesis is devoted to the discussion on the non-Newtonian behaviour of shear-thinning fluids, which is in our case blood, and derivation of two non-Newtonian models frequently used in the blood flow modelling. Further we give a brief overview on recent fluid-structure interaction schemes with discussion about the difficulties arising in numerical modelling of blood flow. Our main contribution lies in numerical and experimental study of a new loosely-coupled partitioned scheme called the kinematic splitting fluid-structure interaction algorithm. We present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Here, we assume both, the nonlinearity in convective as well is diffusive term. We analyse the convergence of proposed numerical scheme for a simplified fluid model of the Oseen type. Moreover, we present series of experiments including numerical error analysis, comparison of hemodynamic parameters for the Newtonian and non-Newtonian fluids and comparison of several physiologically relevant computational geometries in terms of wall displacement and wall shear stress. Numerical analysis and extensive experimental study for several standard geometries confirm reliability and accuracy of the proposed kinematic splitting scheme in order to approximate fluid-structure interaction problems.

Modifying peripheral IV catheters with side holes and side slits results in favorable changes in fluid dynamic properties during the injection of iodinated contrast material

OBJECTIVE: The purpose of this study was to compare a standard peripheral end-hole angiocatheter with those modified with side holes or side slits using experimental optical techniques to qualitatively compare the contrast material exit jets and using numeric techniques to provide flow visualization and quantitative comparisons. MATERIALS AND METHODS: A Schlieren imaging system was used to visualize the angiocatheter exit jet fluid dynamics at two different flow rates. Catheters were modified by drilling through-and-through side holes or by cutting slits into the catheters. A commercial computational fluid dynamics package was used to calculate numeric results for various vessel diameters and catheter orientations. RESULTS: Experimental images showed that modifying standard peripheral IV angiocatheters with side holes or side slits qualitatively changed the overall flow field and caused the exiting jet to become less well defined. Numeric calculations showed that the addition of side holes or slits resulted in a 9-30% reduction of the velocity of contrast material exiting the end hole of the angiocatheter. With the catheter tip directed obliquely to the wall, the maximum wall shear stress was always highest for the unmodified catheter and was always lowest for the four-side-slit catheter. CONCLUSION: Modified angiocatheters may have the potential to reduce extravasation events in patients by reducing vessel wall shear stress.

Comparison of morphological and rheological conditions between conventional and eversion carotid endarterectomy using computational fluid dynamics - a pilot study

PURPOSE To compare postoperative morphological and rheological conditions after eversion carotid endarterectomy versus conventional carotid endarterectomy using computational fluid dynamics. BASIC METHODS Hemodynamic metrics (velocity, wall shear stress, time-averaged wall shear stress and temporal gradient wall shear stress) in the carotid arteries were simulated in one patient after conventional carotid endarterectomy and one patient after eversion carotid endarterectomy by computational fluid dynamics analysis based on patient specific data. PRINCIPAL FINDINGS Systolic peak of the eversion carotid endarterectomy model showed a gradually decreased pressure along the stream path, the conventional carotid endarterectomy model revealed high pressure (about 180 Pa) at the carotid bulb. Regions of low wall shear stress in the conventional carotid endarterectomy model were much larger than that in the eversion carotid endarterectomy model and with lower time-averaged wall shear stress values (conventional carotid endarterectomy: 0.03-5.46 Pa vs. eversion carotid endarterectomy: 0.12-5.22 Pa). CONCLUSIONS Computational fluid dynamics after conventional carotid endarterectomy and eversion carotid endarterectomy disclosed differences in hemodynamic patterns. Larger studies are necessary to assess whether these differences are consistent and might explain different rates of restenosis in both techniques.

Computational fluid dynamics modelling in cardiovascular medicine.

This paper reviews the methods, benefits and challenges associated with the adoption and translation of computational fluid dynamics (CFD) modelling within cardiovascular medicine. CFD, a specialist area of mathematics and a branch of fluid mechanics, is used routinely in a diverse range of safety-critical engineering systems, which increasingly is being applied to the cardiovascular system. By facilitating rapid, economical, low-risk prototyping, CFD modelling has already revolutionised research and development of devices such as stents, valve prostheses, and ventricular assist devices. Combined with cardiovascular imaging, CFD simulation enables detailed characterisation of complex physiological pressure and flow fields and the computation of metrics which cannot be directly measured, for example, wall shear stress. CFD models are now being translated into clinical tools for physicians to use across the spectrum of coronary, valvular, congenital, myocardial and peripheral vascular diseases. CFD modelling is apposite for minimally-invasive patient assessment. Patient-specific (incorporating data unique to the individual) and multi-scale (combining models of different length- and time-scales) modelling enables individualised risk prediction and virtual treatment planning. This represents a significant departure from traditional dependence upon registry-based, population-averaged data. Model integration is progressively moving towards 'digital patient' or 'virtual physiological human' representations. When combined with population-scale numerical models, these models have the potential to reduce the cost, time and risk associated with clinical trials. The adoption of CFD modelling signals a new era in cardiovascular medicine. While potentially highly beneficial, a number of academic and commercial groups are addressing the associated methodological, regulatory, education- and service-related challenges.

Behavior of Granular Materials Under Triaxial Compression with Pulsating Deviator Stress, HR-131, Special Report

Behavior of granular material subjected to repeated load triaxial compression tests is characterized by a model based on rate process theory. Starting with the Arrhenius equation from chemical kinetics, the relationship of temperature, shear stress, normal stress and volume change to deformation rate is developed. The proposed model equation includes these factors as a product of exponential terms. An empirical relationship between deformation and the cube root of the number of stress applications at constant temperature and normal stress is combined with the rate equation to yield an integrated relationship of temperature, deviator stress, confining pressure and number of deviator stress applications to axial strain. The experimental program consists of 64 repeated load triaxial compression tests, 52 on untreated crushed stone and 12 on the same crushed stone material treated with 4% asphalt cement. Results were analyzed with multiple linear regression techniques and show substantial agreement with the model equations. Experimental results fit the rate equation somewhat better than the integrated equation when all variable quantities are considered. The coefficient of shear temperature gives the activation enthalpy, which is about 4.7 kilocalories/mole for untreated material and 39.4 kilocalories/mole for asphalt-treated material. This indicates the activation enthalpy is about that of the pore fluid. The proportionality coefficient of deviator stress may be used to measure flow unit volume. The volumes thus determined for untreated and asphalt-treated material are not substantially different. This may be coincidental since comparison with flow unit volumes reported by others indicates flow unit volume is related to gradation of untreated material. The flow unit volume of asphalt-treated material may relate to asphalt cement content. The proposed model equations provide a more rational basis for further studies of factors affecting deformation of granular materials under stress similar to that in pavement subjected to transient traffic loads.