Breakup of Finite-Size Colloidal Aggregates in Turbulent Flow Investigated by Three-Dimensional (3D) Particle Tracking Velocimetry.

Aggregates grown in mild shear flow are released, one at a time, into homogeneous isotropic turbulence, where their motion and intermittent breakup is recorded by three-dimensional particle tracking velocimetry (3D-PTV). The aggregates have an open structure with a fractal dimension of ∼2.2, and their size is 1.4 ± 0.4 mm, which is large, compared to the Kolmogorov length scale (η = 0.15 mm). 3D-PTV of flow tracers allows for the simultaneous measurement of aggregate trajectories and the full velocity gradient tensor along their pathlines, which enables us to access the Lagrangian stress history of individual breakup events. From this data, we found no consistent pattern that relates breakup to the local flow properties at the point of breakup. Also, the correlation between the aggregate size and both shear stress and normal stress at the location of breakage is found to be weaker, when compared with the correlation between size and drag stress. The analysis suggests that the aggregates are mostly broken due to the accumulation of the drag stress over a time lag on the order of the Kolmogorov time scale. This finding is explained by the fact that the aggregates are large, which gives their motion inertia and increases the time for stress propagation inside the aggregate. Furthermore, it is found that the scaling of the largest fragment and the accumulated stress at breakup follows an earlier established power law, i.e., dfrag ∼ σ(-0.6) obtained from laminar nozzle experiments. This indicates that, despite the large size and the different type of hydrodynamic stress, the microscopic mechanism causing breakup is consistent over a wide range of aggregate size and stress magnitude.

Experimental characterization of breakage rate of colloidal aggregates in axisymmetric extensional flow.

Aggregates prepared under fully destabilized conditions by the action of Brownian motion were exposed to an extensional flow generated at the entrance of a sudden contraction. Two noninvasive techniques were used to monitor their breakup process [i.e. light scattering and three-dimensional (3D) particle tracking velocimetry (3D-PTV)]. While the first one can be used to measure the size and the morphology of formed fragments after the breakage event, the latter is capable of resolving trajectories of individual aggregates up to the breakage point as well as the trajectories of formed fragments. Furthermore, measured velocity gradients were used to determine the local hydrodynamic conditions at the breakage point. All this information was combined to experimentally determine for the first time the breakage rate of individual aggregates, given in the form of a size reduction rate K(R), as a function of the applied strain rate, as well as the properties of the formed fragments (i.e., the number of formed fragments and the size ratio between the largest fragment and the original aggregate). It was found that K(R) scales with the applied strain rate according to a power law with the slope being dependent on the initial fractal dimension only, while the obtained data indicates a linear dependency of K(R) with the initial aggregate size. Furthermore, the probability distribution function (PDF) of the number of formed fragments and the PDF of the size ratio between the largest fragment and the original aggregate indicate that breakage will result with high probability (75%) in the formation of two to three fragments with a rather asymmetric ratio of sizes of about 0.8. The obtained results are well in agreement with the results from the numerical simulations published in the literature.

An in vitro investigation of the influence of stenosis severity on the flow in the ascending aorta.

Cardiovascular diseases can lead to abnormal blood flows, some of which are linked to hemolysis and thrombus formation. Abnormal turbulent flows of blood in the vessels with stenosis create strong shear stresses on blood elements and may cause blood cell destruction or platelet activation. We implemented a Lagrangian (following the fluid elements) measurement technique of three dimensional particle tracking velocimetry that provides insight on the evolution of viscous and turbulent stresses along blood element trajectories. We apply this method to study a pulsatile flow in a compliant phantom of an aorta and compare the results in three cases: the reference case (called "healthy" case), and two cases of abnormal flows due to mild and severe stenosis, respectively. The chosen conditions can mimic a clinical application of an abnormal flow due to a calcific valve. We estimate the effect of aortic stenosis on the kinetic energy of the mean flow and the turbulent kinetic energy, which increases about two orders of magnitude as compared with the healthy flow case. Measuring the total flow stress acting on a moving fluid element that incorporates viscous stresses and the apparent turbulent-induced stresses (the so-called Reynolds stresses) we find out similar increase of the stresses with the increased severity of the stenosis. Furthermore, these unique Lagrangian measurements provide full acceleration and, consequently, the forces acting on the blood elements that are estimated to reach the level that can considerably deform red blood cells. These forces are strong and abrupt due to the contribution of the turbulent fluctuations which is much stronger than the typically measured phase-averaged values.

Analysis of thoracic aorta hemodynamics using 3D particle tracking velocimetry and computational fluid dynamics.

Parallel to the massive use of image-based computational hemodynamics to study the complex flow establishing in the human aorta, the need for suitable experimental techniques and ad hoc cases for the validation and benchmarking of numerical codes has grown more and more. Here we present a study where the 3D pulsatile flow in an anatomically realistic phantom of human ascending aorta is investigated both experimentally and computationally. The experimental study uses 3D particle tracking velocimetry (PTV) to characterize the flow field in vitro, while finite volume method is applied to numerically solve the governing equations of motion in the same domain, under the same conditions. Our findings show that there is an excellent agreement between computational and measured flow fields during the forward flow phase, while the agreement is poorer during the reverse flow phase. In conclusion, here we demonstrate that 3D PTV is very suitable for a detailed study of complex unsteady flows as in aorta and for validating computational models of aortic hemodynamics. In a future step, it will be possible to take advantage from the ability of 3D PTV to evaluate velocity fluctuations and, for this reason, to gain further knowledge on the process of transition to turbulence occurring in the thoracic aorta.

Experimental investigation of the influence of the aortic stiffness on hemodynamics in the ascending aorta.

A three-dimensional (3-D) pulsatile aortic flow in a human ascending aorta is studied to investigate the effect of the aortic stiffness on the flow field and turbulent fluctuating velocities in the ascending aorta. A nonintrusive optical measurement technique, 3-D particle tracking velocimetry (3D-PTV), has been applied to anatomically accurate phantoms under clinically realistic conditions. A compliant silicon phantom was used to mimic the healthy aorta, and a rigid model was used to imitate the pathological case that appears in aortas for example as a result of aging. The realistic models are transparent which allows optical access to the investigation domain, and the index of refraction was matched to avoid optical distortions. Our results revealed that the aortic stiffness leads to an increase in systolic velocity and a decrease in the Windkessel effect, which is associated with the diastolic blood pressure. Furthermore, we found that the turbulent kinetic energy is about an order of magnitude higher for the rigid aorta, that is, an increase in aortic stiffness increases the magnitude of turbulent fluctuating velocities. The spatial distribution of the flow velocity showed that the flow is more organized and coherent spiraling patterns develop for the compliant aorta which helps to dampen the influence of disturbed flow. Finally, we observed higher Lagrangian acceleration and hence higher instantaneous forces acting on blood particles in the stiff case which implies that aging and hence arterial stiffening provokes distinctive alterations in blood flow, and these alterations may cause pathological symptoms in the cardiovascular system.

Mapping mean and fluctuating velocities by Bayesian multipoint MR velocity encoding-validation against 3D particle tracking velocimetry.

PURPOSE: To validate Bayesian multipoint MR velocity encoding against particle tracking velocimetry for measuring velocity vector fields and fluctuating velocities in a realistic aortic model. METHODS: An elastic cast of a human aortic arch equipped with an 80 or 64% stenotic section was driven by a pulsatile pump. Peak velocities and peak turbulent kinetic energies of more than 3 m/s and 1000 J/m(3) could be generated. Velocity vector fields and fluctuating velocities were assessed using Bayesian multipoint MR velocity encoding with varying numbers of velocity encoding points and particle tracking velocimetry in the ascending aorta. RESULTS: Velocities and turbulent kinetic energies measured with 5-fold k-t undersampled 10-point MR velocity encoding and particle tracking velocimetry were found to reveal good correlation with mean differences of -4.8 ± 13.3 cm/s and r(2) = 0.98 for velocities and -21.8 ± 53.9 J/m(3) and r(2) = 0.98 for turbulent kinetic energies, respectively. Three-dimensional velocity patterns of fast flow downstream of the stenoses and regions of elevated velocity fluctuations were found to agree well. CONCLUSION: Accelerated Bayesian multipoint MR velocity encoding has been demonstrated to be accurate for assessing mean and fluctuating velocities against the reference standard particle tracking velocimetry. The MR method holds considerable potential to map velocity vector fields and turbulent kinetic energies in clinically feasible exam times of <15 min.

Experimental investigation of Lagrangian structure functions in turbulence.

Lagrangian properties obtained from a particle tracking velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian structure functions and to measure intermittency at small temporal scales. The finiteness of the measurement volume can bias the results significantly. We present a robust way to overcome this obstacle. Despite no fully developed inertial range, we observe strong intermittency at the scale of dissipation. The multifractal model is only partially able to reproduce the results.

Backwards and forwards relative dispersion in turbulent flow: an experimental investigation.

From particle tracking velocimetry we present an experimental measure of the ratio between backwards and forwards relative dispersion in an intermediate Reynolds number turbulent flow. Lack of time-reversal symmetry implies that their ratio may be different from 1. From a stochastic model, this has recently been studied by Sawford et al [Phys. Fluids 17, 095109 (2005)] giving ratios between 5 and 20. We find a value of approximately 2 and discuss it in the context of the characteristics of the rate of strain tensor s(ij). An analysis of a direct numerical simulation by Biferale et al [Phys. Rev. Lett. 93, 064502 (2004) and Phys. Fluids 17, 021701 (2004)] gives the same result.

Stretching and tilting of material lines in turbulence: the effect of strain and vorticity.

The Lagrangian evolution of infinitesimal material lines is investigated experimentally through three dimensional particle tracking velocimetry (3D-PTV) in quasihomogeneous turbulence with the Taylor microscale Reynolds number Re(lambda)=50. Through 3D-PTV we access the full tensor of velocity derivatives du(i)/dx(j) along particle trajectories, which is necessary to monitor the Lagrangian evolution of infinitesimal material lines l. By integrating the effect on l of (i) the tensor du(i)/dx(j), (ii) its symmetric part s(ij), (iii) its antisymmetric part r(ij), along particle trajectories, we study the evolution of three sets of material lines driven by a genuine turbulent flow, by "strain only," or by "vorticity only," respectively. We observe that, statistically, vorticity reduces the stretching rate l(i)l(j)s(ij)/l2, altering (by tilting material lines) the preferential orientation between l and the first (stretching) eigenvector lambda1 of the rate of strain tensor. In contrast, s(ij), in "absence" of vorticity, significantly contributes to both tilting and stretching, resulting in an enhanced stretching rate compared to the case of material lines driven by the full tensor du(i)/dx(j). The same trend is observed for the deformation of material volumes.