Physics of Fluids

Published by American Institute of Physics
Online ISSN: 1089-7666
Publications
Article
Abdominal aortic aneurysm (AAA) is characterized by disturbed blood flow patterns that are hypothesized to contribute to disease progression. The transport topology in six patient-specific abdominal aortic aneurysms was studied. Velocity data were obtained by image-based computational fluid dynamics modeling, with magnetic resonance imaging providing the necessary simulation parameters. Finite-time Lyapunov exponent (FTLE) fields were computed from the velocity data, and used to identify Lagrangian coherent structures (LCS). The combination of FTLE fields and LCS was used to characterize topological flow features such as separation zones, vortex transport, mixing regions, and flow impingement. These measures offer a novel perspective into AAA flow. It was observed that all aneurysms exhibited coherent vortex formation at the proximal segment of the aneurysm. The evolution of the systolic vortex strongly influences the flow topology in the aneurysm. It was difficult to predict the vortex dynamics from the aneurysm morphology, motivating the application of image-based flow modeling.
 
Article
The video showcases how C. elegans worms respond to DC and AC electrical stimulations. Gabel et al (2007) demonstrated that in the presence of DC and low frequency AC fields, worms of stage L2 and larger propel themselves towards the cathode. Rezai et al (2010) have demonstrated that this phenomenon, dubbed electrotaxis, can be used to control the motion of worms. In the video, we reproduce Rezai's experimental results. Furthermore, we show, for the first time, that worms can be trapped with high frequency, nonuniform electric fields. We studied the effect of the electric field on the nematode as a function of field intensity and frequency and identified a range of electric field intensities and frequencies that trap worms without apparent adverse effect on their viability. Worms tethered by dielectrophoresis (DEP) avoid blue light, indicating that at least some of the nervous system functions remain unimpaired in the presence of the electric field. DEP is useful to dynamically confine nematodes for observations, sort them according to size, and separate dead worms from live ones. Comment: Two videos are included. The videos have been uploaded on eCommons@Cornell. The link address is as follow: http://ecommons.library.cornell.edu/handle/1813/14100
 
Article
Study of mixing is important in understanding transport of submicron sized particles in the acinar region of the lung. In this article, we investigate transport in view of advective mixing utilizing Lagrangian particle tracking techniques: tracer advection, stretch rate and dispersion analysis. The phenomenon of steady streaming in an oscillatory flow is found to hold the key to the origin of kinematic mixing in the alveolus, the alveolar mouth and the alveolated duct. This mechanism provides the common route to folding of material lines and surfaces in any region of the acinar flow, and has no bearing on whether the geometry is expanding or if flow separates within the cavity or not. All analyses consistently indicate a significant decrease in mixing with decreasing Reynolds number (Re). For a given Re, dispersion is found to increase with degree of alveolation, indicating that geometry effects are important. These effects of Re and geometry can also be explained by the streaming mechanism. Based on flow conditions and resultant convective mixing measures, we conclude that significant convective mixing in the duct and within an alveolus could originate only in the first few generations of the acinar tree as a result of nonzero inertia, flow asymmetry, and large Keulegan-Carpenter (K(C)) number.
 
Article
The effects of intra- and intersubject variabilities in airway geometry on airflow in the human lungs are investigated by large eddy simulation. The airway models of two human subjects consisting of extra- and intrathoracic airways are reconstructed from CT images. For intrasubject study, airflows at two inspiratory flow rates are simulated on the airway geometries of the same subject with four different levels of truncation. These airway models are the original complete geometry and three geometries obtained by truncating the original one at the subglottis, the supraglottis, and the laryngopharynx, respectively. A comparison of the airflows in the complete geometry model shows that the characteristics of the turbulent laryngeal jet in the trachea are similar regardless of Reynolds number in terms of mean velocities, turbulence statistics, coherent structures, and pressure distribution. The truncated airway models, however, do not produce the similar flow structures observed in the complete geometry. An improved inlet boundary condition is then proposed for the airway model truncated at the laryngopharynx to improve the accuracy of solution. The new boundary condition significantly improves the mean flow. The spectral analysis shows that turbulent characteristics are captured downstream away from the glottis. For intersubject study, although the overall flow characteristics are similar, two morphological factors are found to significantly affect the flows between subjects. These are the constriction ratio of the glottis with respect to the trachea and the curvature and shape of the airways.
 
Results from normal mode analysis using the Jeffreys model with ␮ s = 0.5 showing how the growth rate g varies with wave number k for different values of We . 
The effect of the solvent viscosity ␮ s = ␮ 2 / We on the growth rate using the Jeffreys model, with We = 15. Note that in the limit as ␮ s → 0 
Article
The lungs consist of a network of bifurcating airways that are lined with a thin liquid film. This film is a bilayer consisting of a mucus layer on top of a periciliary fluid layer. Mucus is a non-Newtonian fluid possessing viscoelastic characteristics. Surface tension induces flows within the layer, which may cause the lung's airways to close due to liquid plug formation if the liquid film is sufficiently thick. The stability of the liquid layer is also influenced by the viscoelastic nature of the liquid, which is modeled using the Oldroyd-B constitutive equation or as a Jeffreys fluid. To examine the role of mucus alone, a single layer of a viscoelastic fluid is considered. A system of nonlinear evolution equations is derived using lubrication theory for the film thickness and the film flow rate. A uniform film is initially perturbed and a normal mode analysis is carried out that shows that the growth rate g for a viscoelastic layer is larger than for a Newtonian fluid with the same viscosity. Closure occurs if the minimum core radius, R(min)(t), reaches zero within one breath. Solutions of the nonlinear evolution equations reveal that R(min) normally decreases to zero faster with increasing relaxation time parameter, the Weissenberg number We. For small values of the dimensionless film thickness parameter epsilon, the closure time, t(c), increases slightly with We, while for moderate values of epsilon, ranging from 14% to 18% of the tube radius, t(c) decreases rapidly with We provided the solvent viscosity is sufficiently small. Viscoelasticity was found to have little effect for epsilon>0.18, indicating the strong influence of surface tension. The film thickness parameter epsilon and the Weissenberg number We also have a significant effect on the maximum shear stress on tube wall, max(tau(w)), and thus, potentially, an impact on cell damage. Max(tau(w)) increases with epsilon for fixed We, and it decreases with increasing We for small We provided the solvent viscosity parameter is sufficiently small. For large epsilon approximately 0.2, there is no significant difference between the Newtonian flow case and the large We cases.
 
Article
In the present study, we investigate the effect of wall flexibility on the plug propagation and the resulting wall stresses in small airway models with experimental measurements and numerical simulations. Experimentally, a flexible microchannel was fabricated to mimic the flexible small airways using soft lithography. Liquid plugs were generated and propagated through the microchannels. The local wall deformation is observed instantaneously during plug propagation with the maximum increasing with plug speed. The pressure drop across the plug is measured and observed to increase with plug speed, and is slightly smaller in a flexible channel compared to that in a rigid channel. A computational model is then presented to model the steady plug propagation through a flexible channel corresponding to the middle plane in the experimental device. The results show qualitative agreements with experiments on wall shapes and pressure drops and the discrepancies bring up interesting questions on current field of modeling. The flexible wall deforms inward near the plug core region, the deformation and pressure drop across the plug increase with the plug speed. The wall deformation and resulting stresses vary with different longitudinal tensions, i.e., for large wall longitudinal tension, the wall deforms slightly, which causes decreased fluid stress and stress gradients on the flexible wall comparing to that on rigid walls; however, the wall stress gradients are found to be much larger on highly deformable walls with small longitudinal tensions. Therefore, in diseases such as emphysema, with more deformable airways, there is a high possibility of induced injuries on lining cells along the airways because of larger wall stresses and stress gradients.
 
Definition sketch of the vaginal canal. The introitus is to the right. See also anatomical figures in Ref. 42.
Article
ELASTOHYDRODYNAMIC LUBRICATION OVER SOFT SUBSTRATES IS OF IMPORTANCE IN A NUMBER OF BIOMEDICAL PROBLEMS: From lubrication of the eye surface by the tear film, to lubrication of joints by synovial fluid, to lubrication between the pleural surfaces that protect the lungs and other organs. Such flows are also important for the drug delivery functions of vehicles for anti-HIV topical microbicides. These are intended to inhibit transmission into vulnerable mucosa, e.g., in the vagina. First generation prototype microbicides have gel vehicles, which spread after insertion and coat luminal surfaces. Effectiveness derives from potency of the active ingredients and completeness and durability of coating. Delivery vehicle rheology, luminal biomechanical properties, and the force due to gravity influence the coating mechanics. We develop a framework for understanding the relative importance of boundary squeezing and body forces on the extent and speed of the coating that results. A single dimensionless number, independent of viscosity, characterizes the relative influences of squeezing and gravitational acceleration on the shape of spreading in the Newtonian case. A second scale, involving viscosity, determines the spreading rate. In the case of a shear-thinning fluid, the Carreau number also plays a role. Numerical solutions were developed for a range of the dimensionless parameter and compared well with asymptotic theory in the limited case where such results can be obtained. Results were interpreted with respect to trade-offs between wall elasticity, longitudinal forces, bolus viscosity, and bolus volume. These provide initial insights of practical value for formulators of gel delivery vehicles for anti-HIV microbicidal formulations.
 
Definition sketch of the vaginal canal. Epithelium surface is only shown below the film. The introitus is to the right. The transverse direction has an “H” shaped cross section; see text. 
Velocity (circles) at the open end (z = L) obtained by Eq. (8) for several L and C film values.
Tenefovir absorption at 2 h for a range of Fk a and k el .
Article
There is a widespread agreement that more effective drug delivery vehicles with more alternatives, as well as better active pharmaceutical ingredients (APIs), must be developed to improve the efficacy of microbicide products. For instance, in tropical regions, films are more appropriate than gels due to better stability of drugs at extremes of moisture and temperature. Here, we apply fundamental fluid mechanical and physicochemical transport theory to help better understand how successful microbicide API delivery depends upon properties of a film and the human reproductive tract environment. Several critical components of successful drug delivery are addressed. Among these are: elastohydrodynamic flow of a dissolved non-Newtonian film; mass transfer due to inhomogeneous dilution of the film by vaginal fluid contacting it along a moving boundary (the locally deforming vaginal epithelial surface); and drug absorption by the epithelium. Local rheological properties of the film are dependent on local volume fraction of the vaginal fluid. We evaluated this experimentally, delineating the way that constitutive parameters of a shear-thinning dissolved film are modified by dilution. To develop the mathematical model, we integrate the Reynolds lubrication equation with a mass conservation equation to model diluting fluid movement across the moving vaginal epithelial surface and into the film. This is a complex physicochemical phenomenon that is not well understood. We explore time- and space-varying boundary flux model based upon osmotic gradients. Results show that the model produces fluxes that are comparable to experimental data. Further experimental characterization of the vaginal wall is required for a more precise set of parameters and a more sophisticated theoretical treatment of epithelium.
 
Article
A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when topically applied, significantly inhibits sexual HIV transmission to women [Karim et al., Science 329, 1168 (2010)]. However, the gel for this drug and anti-HIV microbicide gels in general have not been designed using an understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model spreading of microbicide gels [Szeri et al., Phys. Fluids 20, 083101 (2008)]. This should incorporate the full rheological behavior of a gel, including how rheological properties change due to contact with, and dilution by, ambient vaginal fluids. Here, we extend our initial analysis, incorporating the effects of gel dilution due to contact with vaginal fluid produced at the gel-tissue interface. Our original model is supplemented with a convective-diffusive transport equation to characterize water transport into the gel and, thus, local gel dilution. The problem is solved using a multi-step scheme in a moving domain. The association between local dilution of gel and rheological properties is obtained experimentally, delineating the way constitutive parameters of a shear-thinning gel are modified by dilution. Results show that dilution accelerates the coating flow by creating a slippery region near the vaginal wall akin to a dilution boundary layer, especially if the boundary flux exceeds a certain value. On the other hand, if the diffusion coefficient of boundary fluid is increased, the slippery region diminishes in extent and the overall rate of gel spreading decreases.
 
Comparison of the theoretically derived coefficient γ () (solid lines), the experimentally inferred coefficient C = 8.16 (dashed lines), and the experimental record (crosses) for pore dynamics. 3 (a) For the simulation, we used μ 0 = 32 cP, R = 19.7, μ l = 1 P, T = 12.5 pN, and S = 0.045 kT nm −2 , the values reported for the experimental records. 1, 26 (b)
Cut-away portion of a rotationally symmetric open surface Σ t  representing a spherical liposome of radius R with a pore of radius c(t) lying between the azimuthal angles 0 < ϕ < π. A viscous ambient fluid occupies the region bathing the surface. The pore contracts (expands) by decreasing (increasing) c(t).
Article
A problem for fluid flow around an axisymmetric spherical surface with a hole is presented to characterize pore dynamics in liposomes. A rotational stream function for the contraction of a punctured plane region is obtained and is used in the perturbation expansion for a stream function in the case of a spherical surface with a hole of small radius compared to the spherical radius. The Rayleigh dissipation function is calculated and used to infer the aqueous friction induced by the contraction of the hole. The theoretical aqueous friction coefficient is compared with one derived from experimental data, and they are in agreement.
 
Article
A method to characterize shock wave lithotripters by examining the potential for cavitation associated with the lithotripter shock wave (LSW) has been developed. The method uses the maximum radius achieved by a bubble subjected to a LSW as a representation of the cavitation potential for that region in the lithotripter. It is found that the maximum radius is determined by the work done on a bubble by the LSW. The method is used to characterize two reflectors: an ellipsoidal reflector and an ellipsoidal reflector with an insert. The results show that the use of an insert reduced the -6 dB volume (with respect to peak positive pressure) from 1.6 to 0.4 cm(3), the -6 dB volume (with respect to peak negative pressure) from 14.5 to 8.3 cm(3), and reduced the volume characterized by high cavitation potential (i.e., regions characterized by bubbles with radii larger than 429 µm) from 103 to 26 cm(3). Thus, the insert is an effective way to localize the potentially damaging effects of shock wave lithotripsy, and suggests an approach to optimize the shape of the reflector.
 
Article
Distinct regimes of droplet charging, determined by the dominant charge transport process, are identified for an ultrasonic droplet ejector using electrohydrodynamic computational simulations, a fundamental scale analysis, and experimental measurements. The regimes of droplet charging are determined by the relative magnitudes of the dimensionless Strouhal and electric Reynolds numbers, which are a function of the process (pressure forcing), advection, and charge relaxation time scales for charge transport. Optimal (net maximum) droplet charging has been identified to exist for conditions in which the electric Reynolds number is of the order of the inverse Strouhal number, i.e., the charge relaxation time is on the order of the pressure forcing (droplet formation) time scale. The conditions necessary for optimal droplet charging have been identified as a function of the dimensionless Debye number (i.e., liquid conductivity), external electric field (magnitude and duration), and atomization drive signal (frequency and amplitude). The specific regime of droplet charging also determines the functional relationship between droplet charge and charging electric field strength. The commonly expected linear relationship between droplet charge and external electric field strength is only found when either the inverse of the Strouhal number is less than the electric Reynolds number, i.e., the charge relaxation is slower than both the advection and external pressure forcing, or in the electrostatic limit, i.e., when charge relaxation is much faster than all other processes. The analysis provides a basic understanding of the dominant physics of droplet charging with implications to many important applications, such as electrospray mass spectrometry, ink jet printing, and drop-on-demand manufacturing.
 
Article
Motivated by a developmental gas embolotherapy technique for selective occlusion of blood flow to tumors, we examined the transport of a pressure-driven semi-infinite bubble through a liquid-filled bifurcating channel. Homogeneity of bubble splitting as the bubble passes through a vessel bifurcation affects the degree to which the vascular network near the tumor can be uniformly occluded. The homogeneity of bubble splitting was found to increase with bubble driving pressure and to decrease with increased bifurcation angle. Viscous losses at the bifurcation were observed to affect the bubble speed significantly. The potential for oscillating bubble interfaces to induce flow recirculation and impart high stresses on the vessel endothelium was also observed.
 
Article
We experimentally investigated molecular effects of the slip/no-slip boundary condition of Newtonian liquids in micro-and nanochannels as small as 350 nm. The slip was measurable for channels smaller than approximately 2 mu m. The amount of slip is found to be independent of the channel size, but is a function of the shear rate, the type of liquid (polar or nonpolar molecular structure), and the morphology of the solid surface (molecular-level smoothness). (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3006031]
 
Article
We consider the Brownian motion of a nanoparticle in an incompressible Newtonian fluid medium (quiescent or fully developed Poiseuille flow) with the fluctuating hydrodynamics approach. The formalism considers situations where both the Brownian motion and the hydrodynamic interactions are important. The flow results have been modified to account for compressibility effects. Different nanoparticle sizes and nearly neutrally buoyant particle densities are also considered. Tracked particles are initially located at various distances from the bounding wall to delineate wall effects. The results for thermal equilibrium are validated by comparing the predictions for the temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical and experimental results where available. The equipartition theorem for a Brownian particle in Poiseuille flow is verified for a range of low Reynolds numbers. Numerical predictions of wall interactions with the particle in terms of particle diffusivities are consistent with results, where available.
 
Equilibrium PDF, fr, for various values of and with C p = −0.84Ca, for linear inviscid bubbles.
Article
The problem of predicting the moments of the distribution of bubble radius in bubbly flows is considered. The particular case where bubble oscillations occur due to a rapid (impulsive or step change) change in pressure is analyzed, and it is mathematically shown that in this case, inviscid bubble oscillations reach a stationary statistical equilibrium, whereby phase cancellations among bubbles with different sizes lead to time-invariant values of the statistics. It is also shown that at statistical equilibrium, moments of the bubble radius may be computed using the period-averaged bubble radius in place of the instantaneous one. For sufficiently broad distributions of bubble equilibrium (or initial) radius, it is demonstrated that bubble statistics reach equilibrium on a time scale that is fast compared to physical damping of bubble oscillations due to viscosity, heat transfer, and liquid compressibility. The period-averaged bubble radius may then be used to predict the slow changes in the moments caused by the damping. A benefit is that period averaging gives a much smoother integrand, and accurate statistics can be obtained by tracking as few as five bubbles from the broad distribution. The period-averaged formula may therefore prove useful in reducing computational effort in models of dilute bubbly flow wherein bubbles are forced by shock waves or other rapid pressure changes, for which, at present, the strong effects caused by a distribution in bubble size can only be accurately predicted by tracking thousands of bubbles. Some challenges associated with extending the results to more general (nonimpulsive) forcing and strong two-way coupled bubbly flows are briefly discussed.
 
Color The streamlines for flow through the isotropic fiber network 4.
True vs apparent fiber volume fraction for the networks used in this study.
(a) Permeability calculations for flow parallel to the preferred fiber direction of the moderately oriented networks. (b) Permeability calculations for flow transverse to the preferred fiber direction of the moderately oriented networks. The permeability calculated using Eqs. (11) and (12) is the average over the five moderately aligned networks.
(a) Permeability calculations for flow parallel to the preferred fiber direction of the strongly oriented networks. The permeability calculated using Eqs. (11) and (12) is the average over the five highly aligned networks. (b) Permeability calculations for flow transverse to the preferred fiber direction of the strongly oriented networks. The permeability calculated using Eqs. (11) and (12) is the average over the five highly aligned networks.
The four steps for the generation of the FE mesh from the fiber networks. (a) The initial network generated with the method described in Sec. II A. (b) The parasolid model of the fibers. (c) The parasolid model of the surrounding fluid. (d) The final FE mesh.
Article
Hydraulic permeabilities of fiber networks are of interest for many applications and have been studied extensively. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with today's high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius, and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flows parallel and perpendicular to a single fiber or an array thereof, using a volume-averaging theory, were compared to the detailed analysis. The detailed model agreed well with existing analytical solutions for square arrays of fibers up to fiber volume fractions of 46% for parallel flow and 33% for transverse flow. Permeability calculations were then performed for isotropic and oriented fiber networks within the fiber volume fraction range of 0.3%-15%. When drag coefficients for spatially periodic arrays were used, the results of the volume-averaging method agreed well with the direct finite element calculations. On the contrary, the use of drag coefficients for isolated fibers overpredicted the permeability for the volume fraction range that was employed. We concluded that a weighted combination of drag coefficients for spatially periodic arrays of fibers could be used as a good approximation for fiber networks, which further implies that the effect of the fiber volume fraction and orientation on the permeability of fiber networks are more important than the effect of local network structure.
 
Article
A low-dimensional parametric deformation model of a cancer cell under shear flow is developed. The model is built around an experiment in which MDA-MB-231 adherent cells are subjected to flow with increasing shear. The cell surface deformation is imaged using differential interference contrast microscopy imaging techniques until the cell releases into the flow. We post-process the time sequence of images using an active shape model from which we obtain the principal components of deformation. These principal components are then used to obtain the parameters in an empirical constitutive equation determining the cell deformations as a function of the fluid normal and shear forces imparted. The cell surface is modeled as a 2D Gaussian interface which can be deformed with three active parameters: H (height), σ(x) (x-width), and σ(y) (y-width). Fluid forces are calculated on the cell surface by discretizing the surface with regularized Stokeslets, and the flow is driven by a stochastically fluctuating pressure gradient. The Stokeslet strengths are obtained so that viscous boundary conditions are enforced on the surface of the cell and the surrounding plate. We show that the low-dimensional model is able to capture the principal deformations of the cell reasonably well and argue that active shape models can be exploited further as a useful tool to bridge the gap between experiments, models, and numerical simulations in this biological setting.
 
Pre- and post thrombosis CT imaging in patient B (left) and simulation results showing correlation between WSS predictions in simulation and locations of thrombosis.
Typical boundary condition specification for a patient specific model of the Fontan surgery. (a) Open loop boundary conditions with prescribed inflow and RCR Windkessel outflow conditions. (b) Multiscale closed loop boundary conditions using a lumped parameter network. Blocks representing different portions of the anatomy (heart, lungs, etc.) are shown.
Steps in the process of patient specific modeling, from left to right for a patient with coronary aneurysms caused by Kawasaki disease: (1) volume rendered CT image data, (2) patient specific model with aorta and coronary arteries, (3) adapted mesh, (4) contours of wall shear stress from simulation results.
(a) Post-operative image data for three patients who received a Y-graft and their corresponding patient specific models. (b) Comparison between early post-operative simulation-derived hepatic flow distribution and clinical lung perfusion scan results for three Fontan Y-graft patients. Pulmonary flow split (PFS) is provided for each patient. Hepatic flow distribution is measured by distribution of flow from the inferior vena cava (IVC) going to the right pulmonary artery (blue) or left pulmonary artery (red).
Article
Hemodynamics plays an essential role in the progression and treatment of cardiovascular disease. However, while medical imaging provides increasingly detailed anatomical information, clinicians often have limited access to hemodynamic data that may be crucial to patient risk assessment and treatment planning. Computational simulations can now provide detailed hemodynamic data to augment clinical knowledge in both adult and pediatric applications. There is a particular need for simulation tools in pediatric cardiology, due to the wide variation in anatomy and physiology in congenital heart disease patients, necessitating individualized treatment plans. Despite great strides in medical imaging, enabling extraction of flow information from magnetic resonance and ultrasound imaging, simulations offer predictive capabilities that imaging alone cannot provide. Patient specific simulations can be used for in silico testing of new surgical designs, treatment planning, device testing, and patient risk stratification. Furthermore, simulations can be performed at no direct risk to the patient. In this paper, we outline the current state of the art in methods for cardiovascular blood flow simulation and virtual surgery. We then step through pressing challenges in the field, including multiscale modeling, boundary condition selection, optimization, and uncertainty quantification. Finally, we summarize simulation results of two representative examples from pediatric cardiology: single ventricle physiology, and coronary aneurysms caused by Kawasaki disease. These examples illustrate the potential impact of computational modeling tools in the clinical setting.
 
Article
Numerical simulations of the unsteady, two-dimensional, incompressible Navier-Stokes equations are performed for a Newtonian fluid in a channel having a symmetric constriction modeled by a two-parameter Gaussian distribution on both channel walls. The Reynolds number based on inlet half-channel height and mean inlet velocity ranges from 1 to 3000. Constriction ratios based on the half-channel height of 0.25, 0.5, and 0.75 are considered. The results show that both the Reynolds number and constriction geometry have a significant effect on the behavior of the post-constriction flow field. The Navier-Stokes solutions are observed to experience a number of bifurcations: steady attached flow, steady separated flow (symmetric and asymmetric), and unsteady vortex shedding downstream of the constriction depending on the Reynolds number and constriction ratio. A sequence of events is described showing how a sustained spatially growing flow instability, reminiscent of a convective instability, leads to the vortex shedding phenomenon via a proposed streamwise pressure-gradient mechanism.
 
Article
The impact and spreading of a compound viscous droplet on a flat surface are studied computationally using a front-tracking method as a model for the single cell epitaxy. This is a technology developed to create two-dimensional and three-dimensional tissue constructs cell by cell by printing cell-encapsulating droplets precisely on a substrate using an existing ink-jet printing method. The success of cell printing mainly depends on the cell viability during the printing process, which requires a deeper understanding of the impact dynamics of encapsulated cells onto a solid surface. The present study is a first step in developing a model for deposition of cell-encapsulating droplets. The inner droplet representing the cell, the encapsulating droplet, and the ambient fluid are all assumed to be Newtonian. Simulations are performed for a range of dimensionless parameters to probe the deformation and rate of deformation of the encapsulated cell, which are both hypothesized to be related to cell damage. The deformation of the inner droplet consistently increases: as the Reynolds number increases; as the diameter ratio of the encapsulating droplet to the cell decreases; as the ratio of surface tensions of the air-solution interface to the solution-cell interface increases; as the viscosity ratio of the cell to encapsulating droplet decreases; or as the equilibrium contact angle decreases. It is observed that maximum deformation for a range of Weber numbers has (at least) one local minimum at We=2. Thereafter, the effects of cell deformation on viability are estimated by employing a correlation based on the experimental data of compression of cells between parallel plates. These results provide insight into achieving optimal parameter ranges for maximal cell viability during cell printing.
 
Article
Cardiovascular simulations provide a promising means to predict risk of thrombosis in grafts, devices, and surgical anatomies in adult and pediatric patients. Although the pathways for platelet activation and clot formation are not yet fully understood, recent findings suggest that thrombosis risk is increased in regions of flow recirculation and high residence time (RT). Current approaches for calculating RT are typically based on releasing a finite number of Lagrangian particles into the flow field and calculating RT by tracking their positions. However, special care must be taken to achieve temporal and spatial convergence, often requiring repeated simulations. In this work, we introduce a non-discrete method in which RT is calculated in an Eulerian framework using the advection-diffusion equation. We first present the formulation for calculating residence time in a given region of interest using two alternate definitions. The physical significance and sensitivity of the two measures of RT are discussed and their mathematical relation is established. An extension to a point-wise value is also presented. The methods presented here are then applied in a 2D cavity and two representative clinical scenarios, involving shunt placement for single ventricle heart defects and Kawasaki disease. In the second case study, we explored the relationship between RT and wall shear stress, a parameter of particular importance in cardiovascular disease.
 
Article
In the present work, we revisit the temporal and the spatio-temporal stability of confined plane wakes under the perspective of the counterpropagating Rossby waves (CRWs). Within the context of broken line velocity profiles, each vorticity discontinuity can be associated to a counterpropagating Rossby wave. In the case of a wake modeled by a broken line profile, the interaction of two CRWs is shown to originate in a shear instability. Following this description, we first recover the stability results obtained by Juniper [J. Fluid Mech. 590, 163-185 (2007)]10.1017/S0022112007007975 and Biancofiore and Gallaire [Phys. Fluids 23, 034103 (2011)]10.1063/1.3554764 by means of the classical normal mode analysis. In this manner, we propose an explanation of the stabilizing influence of the confinement on the temporal stability properties. The CRW description further allows us to propose a new interpretation of the counterintuitive spatio-temporal destabilization in wake flows at moderate confinement noticed by Juniper [J. Fluid Mech. 565, 171-195 (2006)]10.1017/S0022112006001558: it is well predicted by the mean group velocity of the uncoupled CRWs.
 
Article
The hydrodynamic forces and torques on a rotating cylinder in a narrow channel are investigated in this paper using lubrication analysis and scaling analysis. To explore the effect of the shape of the gap, three different geometries are considered. The force and torque expressions from lubrication analysis agree well with numerical solutions when the gap between cylinder and wall is small. The solutions from scaling analysis can be applied over a broader range, but only if the scaling coefficients are properly deduced from numerical solution or lubrication analysis. Self-similarity in the solutions is discussed as well.
 
Article
A fundamental study to characterize the flow around an oscillating cylinder in a pulsatile flow environment is investigated. This work is motivated by a new proposed design of the total artificial lung (TAL), which is envisioned to provide better gas exchange. The Navier-Stokes computations in a moving frame of reference were performed to compute the dynamic flow field surrounding the cylinder. Cylinder oscillations and pulsatile free-stream velocity were represented by two sinusoidal waves with amplitudes A and B and frequencies ω(c) and ω, respectively. The Keulegan-Carpenter number (K(c)=U(o)∕Dω(c)) was used to describe the frequency of the oscillating cylinder while the pulsatile free-stream velocity was fixed by imposing ω∕K(c)=1 for all cases investigated. The parameters of interest and their values were amplitude (0.5D<A<D), the Keulegan-Carpenter number (0.33<K(c)<1), and the Reynolds number (5<Re<20) corresponding to operating conditions of the TAL. It was observed that an increase in amplitude and a decrease in K(c) are associated with an increase in vorticity (up to 246%) for every Re suggesting that mixing could be enhanced by the proposed TAL design. The drag coefficient was found to decrease for higher amplitudes and lower K(c) for all cases investigated. In some cases the drag coefficient values were found to be lower than the stationary cylinder values (A=0.5, K(c)=0.3, and Re=10 and 20). A lock-in phenomenon (cylinder oscillating frequency matched the vortex shedding frequency) was found when K(c)=1 for all cases. This lock-in condition was attributed to be the cause of the rise in drag observed in that operating regime. For optimal performance of the modified TAL design it is recommended to operate the device at higher fiber oscillation amplitudes and lower K(c) (avoiding the lock-in regime).
 
Particle tracking microrheology with    100  nm    diameter fluorescent polymer spheres embedded within NIH3T3 fibroblast cells. (a)    20  s    trajectories of typical transport in NIH3T3 cells. The approximate speeds of particles (2) and (3), calculated by end-to-end displacement, are 18 and    12  nm ∕ s   , respectively. Particle 1 shows a partial trajectory that continues past the top of the figure. (b) Time-dependent mean-square displacements (MSDs) of the particles in (a). All the particles exhibit directional motion correlated to cell crawling (arrow).
Average probe transport characteristics as a function of incubation time,    t wait   , in nocodazole, averaged over trajectories of particles in 15 cells. (a) Percent of the number of particles exhibiting locally trapped to subdiffusive motion in nocodazole, averaged over hundreds of particles. (b) Probed microdomain diameter in which particles become trapped, assuming a spherical cage, averaged over tens of particles.
Article
Quantification of cellular responses to stimuli is challenging. Cells respond to changing external conditions through internal structural and compositional and functional modifications, thereby altering their transport and mechanical properties. By properly interpreting particle-tracking microrheology, we evaluate the response of live cells to cytoskeletal disruption mediated by the drug nocodazole. Prior to administering the drug, the particles exhibit an apparently diffusive behavior that is actually a combination of temporally heterogeneous ballistic and caged motion. Selectively depolymerizing microtubules with the drug causes actively crawling cells to halt, providing a means for assessing drug efficacy, and making the caged motion of the probes readily apparent.
 
Article
Wall induced lateral migration of a viscoelastic (FENE-MCR) drop in a Newtonian fluid is investigated. Just like a Newtonian drop, a viscoelastic drop reaches a quasi-steady state where the lateral velocity only depends on the instantaneous distance from the wall. The drop migration velocity and the deformation scale inversely with the square and the cube of the distance from the wall, respectively. The migration velocity varies non-monotonically with increasing viscoelasticity (increasing Deborah number); initially increasing and then decreasing. An analytical explanation has been given of the effects by computing the migration velocity as arising from an image stresslet field due to the drop. The semi-analytical expression matches well with the simulated migration velocity away from the wall. It contains a viscoelastic stresslet component apart from those arising from interfacial tension and viscosity ratio. The migration dynamics is a result of the competition between the viscous (interfacial tension and viscosity ratio) and the viscoelastic effects. The viscoelastic stresslet contribution towards the migration velocity steadily increases. But the interfacial stresslet-arising purely from the drop shape-first increases and then decreases with rising Deborah number causing the migration velocity to be non-monotonic. The geometric effect of the interfacial stresslet is caused by a corresponding nonmonotonic variation of the drop inclination. High viscosity ratio is briefly considered to show that the drop viscoelasticity could stabilize a drop against breakup, and the increase in migration velocity due to viscoelasticity is larger compared to the viscosity-matched case.
 
Article
This report details a comprehensive study of inertial focusing dynamics and particle behavior in low aspect ratio (h/w ∼ 1/1 to 1/8) spiral microchannels. A continuum of particle streak behavior is shown with longitudinal, cross-sectional, and velocity resolution, yielding a large analyzed parameter space. The dataset is then summarized and compared to prior results from both straight microchannels and other low aspect ratio spiral microchannel designs. Breakdown of focusing into a primary and secondary fluorescent streak is observed in the lowest aspect ratio channels at high average downstream velocities. Streak movement away from the theoretically predicted near inner wall equilibrium position towards the center of the channel at high average downstream velocities is also detailed as a precursor to breakdown. State diagrams detail the overall performance of each device including values of the required channel lengths and the range of velocities over which quality focusing can be achieved.
 
A dielectric wedge, of angle 2α, with local cylindrical coordinates (s, θ).
Article
Electrically generated flows around a thin dielectric plate pierced by a cylindrical hole are computed numerically. The geometry represents that of a single nanopore in a membrane. When the membrane is uncharged, flow is due solely to induced charge electroosmosis, and eddies are generated by the high fields at the corners of the nanopore. These eddies meet at stagnation points. If the geometry is chosen correctly, the stagnation points merge to form a single stagnation point at which four streamlines cross at a point and eight eddies meet.
 
Instantaneous contours of polymer extension in an x − y plane showing streamwise sheet-like regions. Re = 1000, W i = 100 (a); Re = 6000, W i = 100 (b) and Re = 6000, W i = 700 for hibernating (c) and active (d) state. The continuous and dashed lines superimposed to the contours of polymer stretch represent isosurfaces of Qa: black, negative; white, positive.
Profiles of the production of turbulent kinetic energy, P k (lines), the negative contribution of dissipation rate of TKE, ε(closed symbols) and transfer of energy between elastic energy and TKE, Πe (open symbols). The sum of the volumetric integral of these term results in the energy balance found in Eq. (6). Re = 1000, W i = 100: , • , • ; Re = 6000, W i = 100: , , ; Re = 6000, W i = 700: , , .
Article
Elasto-inertial turbulence (EIT) is a new state of turbulence found in inertial flows with polymer additives. The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The flow topology of EIT is found to differ significantly from Newtonian wall-turbulence. Structures identified by positive (rotational flow topology) and negative (extensional/compressional flow topology) second invariant Q a isosurfaces of the velocity gradient are cylindrical and aligned in the spanwise direction. Polymers are significantly stretched in sheet-like regions that extend in the streamwise direction with a small upward tilt. The Q a cylindrical structures emerge from the sheets of high polymer extension, in a mechanism of energy transfer from the fluctuations of the polymer stress work to the turbulent kinetic energy. At subcritical Reynolds numbers, EIT is observed at modest Weissenberg number (Wi, ratio polymer relaxation time to viscous time scale). For supercritical Reynolds numbers, flows approach EIT at large Wi. EIT provides new insights on the nature of the asymptotic state of polymer drag reduction (maximum drag reduction), and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows observed in some polymeric flows.
 
Article
In recent years, a wide variety of applications have been found for the use of pulsed jets in the area of flow control. The goal of the current study was to identify the flow field and mixing characteristics associated with an incompressible elongated jet emitted from a flexible nozzle. The shape of the nozzle was that of a high aspect ratio jet deforming from a fully opened to a completely closed configuration. The jet was characterized by a pulsatile flow that was self-excited by the motion of the flexible tube. The frequency of excitation was found to be between 150 and 175 Hz and the Strouhal number (nondimensional frequency) varied from 0.17 to 0.45. The jet flow was dominated by vortices that were shed from the nozzle with an axis parallel to the major axis. The vortices in the near field were quasi-two-dimensional so that measurements performed at the center plane represented the dynamics of the entire vortex. The nozzle excited two different modes depending on the tension applied to the flexible nozzle and the volumetric flow through it. The first was a flapping mode, which was associated with alternate shedding of vortices. This caused strong steering of the jet to one side or the other. The second mode was a symmetric mode that was associated with the formation of counter-rotating vortex pairs. Turbulence and jet spread in the measured planes were much larger in the first mode than the second one.
 
A cross section of the infinite filament, showing the undeformed dashed line and current configuration solid line, and the relation between b and the convective coordinate .
Article
Many micro-organisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on micro-organisms which use flagella for propulsion. We address how swimming velocities are affected in nonlinearly viscoelastic fluids by examining the problem of an infinitely long cylinder with arbitrary beating motion in the Oldroyd-B fluid. We solve for the swimming velocity in the limit in which deflections of the cylinder from its straight configuration are small relative to the radius of the cylinder and the wavelength of the deflections; furthermore, the radius of the cylinder is small compared to the wavelength of deflections. We find that swimming velocities are diminished by nonlinear viscoelastic effects. We apply these results to examine what types of swimming motions can produce net translation in a nonlinear fluid, comparing to the Newtonian case, for which Purcell's "scallop" theorem describes how time-reversibility constrains which swimming motions are effective. We find that a leading order violation of the scallop theorem occurs for reciprocal motions in which the backward and forward strokes occur at different rates.
 
Article
This article covers several aspects of respiratory fluid mechanics that have been actively investigated by our group over the years. For the most part, the topics involve two-phase flows in the respiratory system with applications to normal and diseased lungs, as well as therapeutic interventions. Specifically, the topics include liquid plug flow in airways and at airway bifurcations as it relates to surfactant, drug, gene, or stem cell delivery into the lung; liquid plug rupture and its damaging effects on underlying airway epithelial cells as well as a source of crackling sounds in the lung; airway closure from "capillary-elastic instabilities," as well as nonlinear stabilization from oscillatory core flow which we call the "oscillating butter knife;" liquid film, and surfactant dynamics in an oscillating alveolus and the steady streaming, and surfactant spreading on thin viscous films including our discovery of the Grotberg-Borgas-Gaver shock.
 
Flow and pressure field for h 2 = 0.05. P =1, L P0 =1, = 1000. a t = 50; L P = 0.97; Ca= 0.021, z P = 0.70. b t = 200; L P = 0.55, Ca= 0.036, z P = 5.18, and c t = 300; L P = 0.15, Ca= 0.043, and z P = 9.06.
Flow and pressure field for h 2 = 0.03 when L P = 0.3. t = 232, h 2 = 0.03, P =1, L P0 =1, = 1000, and Ca= 0.034. a The relative flow streamline and pressure field. b The velocity profiles and pressure field in the precursor film near the front meniscus.
Flow and pressure field for h 2 = 0.01 when L P = 0.3. t = 245, h 2 = 0.01, P =1, L P0 =1, = 1000, and Ca= 0.026. a The relative flow streamlines and pressure field. b The velocity profiles and pressure field in the precursor film near the front meniscus.
Article
This paper considers the propagation of a liquid plug driven by a constant pressure within a rigid axisymmetric tube whose inner surface is coated by a thin liquid film. The Navier-Stokes equations are solved using the finite-volume method and the SIMPLEST algorithm. The effects of precursor film thickness, initial plug length, pressure drop across the plug, and constant surface tension on the plug behavior and tube wall mechanical stresses are investigated. As a plug propagates through a liquid-lined tube, the plug gains liquid from the leading front film, and it deposits liquid into the trailing film. If the trailing film is thicker (thinner) than the precursor film, the plug volume decreases (increases) as it propagates. For a decreasing volume, eventually the plug ruptures. Under a specific set of conditions, the trailing film thickness equals the precursor film thickness, which leads to steady state results. The plug speed decreases as the precursor film thins because the resistance to the moving front meniscus increases. As the pressure drop across the plug decreases, the plug speed decreases resulting in thinning of the trailing film. As the plug length becomes longer, the viscous resistance in the plug core region increases, which slows the plug and causes the trailing film to become even thinner. The magnitude of the pressure and shear stress at the tube inner wall is maximum in the front meniscus region, and it increases with a thinner precursor film. As the surface tension increases, the plug propagation speed decreases, the strength of the wall pressure in the front meniscus region increases, and the pressure gradient around the peak pressure becomes steeper.
 
Conference Paper
An acoustic field is used to increase the critical heat flux (CHF) of a flat-boiling-heat-transfer surface. The increase is a result of the acoustic effects on the vapor bubbles. Experiments are performed to explore the effects of an acoustic field on vapor bubbles in the vicinity of a rigid-heated wall. Work includes the construction of a novel heater used to produce a single vapor bubble of a prescribed size and at a prescribed location on a flat-boiling surface for better study of an individual vapor bubble's reaction to the acoustic field. Work also includes application of the results from the single-bubble heater to a calibrated-copper heater used for quantifying the improvements in CHF.
 
Trajectories of flames propagating in various methane-air mixtures. The marks on the 9.5% curve are the basis points used to construct an approximating polynomial (Sec. III B 1). Source: Fig. 1 of Ref. [4]-Reproduced by permission of The Royal Society of Chemistry.
Flame acceleration as a function of time in the 6.2% methane mixture. Shown is the second derivative of the approximating polynomial from Table  I  (solid curve), and a number of solutions to Eqs.  (3)–(5) and (20)  [the circles and squares represent type I and type II solutions, respectively].
Schematics of a flame accelerating in horizontal channel. The y-coordinate is measured in the natural units (Sec.  II B ). The two vertical broken lines bound the transition domain y ∈ (0, U) (Sec.  II C ). The pair of neighboring streamlines and the transversal line elements are used in writing Eqs.  (7)–(15) .
Article
The problem of spontaneous acceleration of premixed flames propagating in open horizontal tubes with smooth walls is revisited. It is proved that in long tubes, this process can be considered quasi-steady, and an equation for the flame front position is derived using the on-shell description. Numerical solutions of this equation are found which show that as in the case of uniform flame movement, there are two essentially different regimes of flame propagation. In the type I regime, the flame speed and its acceleration are comparatively low, whereas the type II regime is characterized by significant flame acceleration that rapidly increases as the flame travels along the tube. A detailed comparison of the obtained results with the experimental data on flame acceleration in methane-air mixtures is given. In particular, it is confirmed that flames propagating in near-stoichiometric mixtures and mixtures near the limits of inflammability belong to the types II and I, respectively, whereas flames in transient mixtures undergo transitions between the two regimes during their travel.
 
Article
We comment on the paper by Van Gorder ["Motion of a helical vortex filament in superfluid ${}^4$He under the extrinsic form of the local induction approximation", Phys. Fluids 25, 085101 (2013)]. We point out that the flow of the normal fluid component parallel to the vortex will often lead into the Donnelly-Glaberson instability, which will cause the amplification of the Kelvin wave. We explain why the comparison to local nonlinear equation is unreasonable, and remark that neglecting the motion in the $x$-direction is not reasonable for a Kelvin wave with an arbitrary wave length and amplitude. The correct equations in the general case are also derived.
 
Article
A change of solute dispersion regime with the flow velocity has been studied both at the macroscopic and pore scales in a transparent array of capillary channels using an optical technique allowing for simultaneous local and global concentration mappings. Two solutions of different polymer concentrations (500 and 1000 ppm) have been used at different P\'eclet numbers. At the macroscopic scale, the displacement front displays a diffusive spreading: for $Pe \leq 10$, the dispersivity $l\_d$ is constant with $Pe$ and increases with the polymer concentration; for $Pe > 10$, $l\_d$ increases as $Pe^{1.35}$ and is similar for the two concentrations. At the local scale, a time lag between the saturations of channels parallel and perpendicular to the mean flow has been observed and studied as a function of the flow rate. These local measurements suggest that the change of dispersion regime is related to variations of the degree of mixing at the junctions. For $Pe \leq 10$, complete mixing leads to pure geometrical dispersion enhanced for shear thinning fluids; for $Pe >10$ weaker mixing results in higher correlation lengths along flow paths parallel to the mean flow and in a combination of geometrical and Taylor dispersion.
 
Energy spectra E(k) in cm 3 /s 2 measured at the centerline. The upper curve () is the enstrophy cascade and the lower curve () is the energy cascade data. While they are only guides to the eye, the straight lines are the expected slopes for the energy and enstrophy cascades (Kr67 or dimensional reasoning). The spectra are normalized such that ∞ 0 dkE(k) = 1 2 u 2 .
The third order structure function S 3(r) vs. r for several R λ. The sign of S 3(r) is positive for r in the inertial range of each case. This indicates that energy is being transferred to large scales, in agreement with the prediction for the inverse energy cascade of 2D turbulence.
Flatness F(r) of P(δu(r)) depending on the scale r (normalized by channel width w). The two upper curves are for energy cascade data (◯: R λ = 60, □: R λ = 90) and the two bottom curves are for enstrophy cascade data (△: R λ = 490, ⋄: R λ = 690). The arrows denote the beginning and end of the inertial range for each curve, as determined by the power law region of the structure functions. All of the curves start out above the gaussian value of 3, but the energy cascade data remain above and seem to asymptote to 3 as r increases. The enstrophy cascade curves cross guassianity in the inertial range and then asymptote to a value smaller than 3.
Flatness of the velocity derivative F η vs. R λ with ∂ x  u estimated using the central difference method. The energy cascade data (□) and the enstrophy cascade data (△) fall into two sections with distinct R λ. A curved dashed line is shown (f(R λ) = 8(log R λ)−1/2) which suggests a (sub-) logarithmic approach to zero.
Article
The Reynolds number dependency of intermittency for 2D turbulence is studied in a flowing soap film. The Reynolds number used here is the Taylor microscale Reynolds number R_{\lambda}, which ranges from 20 to 800. Strong intermittency is found for both the inverse energy and direct enstrophy cascades as measured by (a) the pdf of velocity differences P(\delta u(r)) at inertial scales r, (b) the kurtosis of P(\partial_x u), and (c) the scaling of the so-called intermittency exponent \mu, which is zero if intermittency is absent. Measures (b) and (c) are quantitative, while (a) is qualitative. These measurements are in disagreement with some previous results but not all. The velocity derivatives are nongaussian at all R_{\lambda} but show signs of becoming gaussian as R_{\lambda} increases beyond the largest values that could be reached. The kurtosis of P(\delta u(r)) at various r indicates that the intermittency is scale dependent. The structure function scaling exponents also deviate strongly from the Kraichnan prediction. For the enstrophy cascade, the intermittancy decreases as a power law in R_{\lambda}. This study suggests the need for a new look at the statistics of 2D turbulence.
 
Article
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.
 
Article
This paper describes the creation, by temporal direct numerical simulation and the analysis based on the Reynolds stress transport equations, of a high-quality data set that represents the laminar-turbulent transition of a high-speed boundary-layer flow. Following Pruett and Zang (1992), and with the help of algorithmic refinements, the evolution of an axial, Mach 4.5 boundary-layer flow along a hollow cylinder is simulated numerically. Favre-averaged Reynolds stress transport equations are derived in generalized curvilinear coordinates and are then specialized to the cylindrical geometry at hand. Reynolds stresses and various turbulence quantities, such as turbulent kinetic energy and turbulent Mach number, are calculated from the numerical data at various stages of the transition process. The kinetic energy 'budgets' are constructed from the transport equations. Various contributing terms for the evolution of kinetic energy, like the rates of production and dissipation, transport, and diffusion, are presented. The compressible dissipation rate is small in comparison with the solenoidal dissipation rate for all times. The pressure-dilatation term is of the same order of magnitude as the compressible dissipation rate.
 
Article
The ABC flow is a prototype for fast dynamo action, essential to the origin of magnetic field in large astrophysical objects. Probably the most studied configuration is the classical 1:1:1 flow. We investigate its dynamo properties varying the magnetic Reynolds number Rm. We identify two kinks in the growth rate, which correspond respectively to an eigenvalue crossing and to an eigenvalue coalescence. The dominant eigenvalue becomes purely real for a finite value of the control parameter. Finally we show that even for Rm = 25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its still varies very significantly with the controlling parameter. Even at these very large values of Rm the fast dynamo property of this flow cannot yet be established.
 
Integration contour in the complex plane.
Plot of the scaling function ω(τ )
Probability density function of the first passage times. The statistics for different initial conditions, indicated in the legend, is collected from 5 · 10 6 realization of the Langevin equation corresponding to eq. (4). A t −5/2 power law is also shown for reference.
Article
We consider the recently addressed problem of a passive particle (a predator), being the center of a ``sphere of interception'' of radius $R$ and able to absorb other passive particles (the preys) entering into the sphere. Assuming that all the particles are advected by a turbulent flow and that, in particular, the Richardson equation properly describes the relative dispersion, we calculate an analytical expression for the flux into the sphere as a function of time, assuming an initial constant density of preys outside the sphere. In the same framework, we show that the distribution of times of first passage into the sphere has a $t^{-5/2}$ power law tail, seen in contrast to the $t^{-3/2}$ appearing in standard 3D diffusion. We also discuss the correction due to the integral length scale on the results in the stationary case.
 
Article
Viscous flow past a finite flat plate accelerating in the direction normal to itself is studied numerically. The plate moves with nondimensional speed tp , where p = 0, 1/2, 1, 2. The work focuses on resolving the flow at early to moderately large times and determining the dependence on the acceleration parameter p. Three stages in the vortex evolution are identified and quantified. The first stage, referred to as the Rayleigh stage [Luchini and Tognaccini, “The start-up vortex issuing from a semi-infinite flat plate,” J. Fluid Mech. 455, 175–193 (2002)], consists of a vortical boundary layer of roughly uniform thickness surrounding the plate and its tip, without any separating streamlines. This stage is present only for p > 0, for a time-interval that scales like p 3, as p → 0. The second stage is one of self-similar growth. The vortex trajectory and circulation satisfy inviscid scaling laws, the boundary layer thickness satisfies viscous laws. The self-similar trajectory starts immediately after the Rayleigh stage ends and lasts until the plate has moved a distance d = 0.5 to 1 times its length. Finally, in the third stage, the image vorticity due to the finite plate length becomes relevant and the flow departs from self-similar growth. The onset of an instability in the outer spiral vortex turns is also observed, however, at least for the zero-thickness plate considered here, it is shown to be easily triggered numerically by underresolution. The present numerical results are compared with experimental results of Pullin and Perry [“Some flow visualization experiments on the starting vortex,” J. Fluid Mech. 97, 239–255 (1980)], and numerical results of Koumoutsakos and Shiels [“Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate,” J. Fluid Mech. 328, 177–227 (1996)].
 
Article
We experimentally study the detachment of drops of granular suspensions using a density matched model suspension with varying volume fraction ({\phi} = 15% to 55%) and grain diameter (d = 20 {\mu}m to 140 {\mu}m). We show that at the beginning of the detachment process, the suspensions behave as an effective fluid. The detachment dynamics in this regime can be entirely described by the shear viscosity of the suspension. At later stages of the detachment the dynamics become independent of the volume fraction and are found to be identical to the dynamics of the interstitial fluid. Surprisingly, visual observation reveals that at this stage particles are still present in the neck. We suspect rearrangements of particles to locally free the neck of grains, causing the observed dynamics. Close to the final pinch off, the detachment of the suspensions is further accelerated, compared to the dynamics of pure interstitial fluid. This acceleration might be due to the fact that the neck diameter gets of the order of magnitude of the size of the grains and a continuous thinning of the liquid thread is not possible any more. The crossover between the different detachment regimes is function of the grain size and the initial volume fraction. We characterize the overall acceleration as a function of the grain size and volume fraction.
 
Article
Spontaneous flame acceleration leading to explosion triggering in open tubes/channels due to wall friction was analytically and computationally studied. It was first demonstrated that the acceleration is effected when the thermal expansion across the flame exceeds a critical value depending on the combustion configuration. For the axisymmetric flame propagation in cylindrical tubes with both ends open, a theory of the initial (exponential) stage of flame acceleration in the quasi-isobaric limit was developed and substantiated by extensive numerical simulation of the hydrodynamics and combustion with an Arrhenius reaction. The dynamics of the flame shape, velocity, and acceleration rate, as well as the velocity profile ahead and behind the flame, have been determined.
 
Article
(Abridged) A series of three-dimensional numerical simulations is used to study the intrinsic stability of high-speed turbulent flames. Calculations model the interaction of a fully-resolved premixed flame with a highly subsonic, statistically steady, homogeneous, isotropic turbulence. We consider a wide range of turbulent intensities and system sizes, corresponding to the Damk\"ohler numbers Da = 0.1-6.0. These calculations show that turbulent flames in the regimes considered are intrinsically unstable. In particular, we find three effects. 1) Turbulent flame speed develops pulsations with the observed peak-to-peak amplitude > 10 and a characteristic time scale close to a large-scale eddy turnover time. Such variability is caused by the interplay between turbulence, which continuously creates the flame surface, and highly intermittent flame collisions, which consume the flame surface. 2) Unstable burning results in the periodic pressure build-up and the formation of pressure waves or shocks, when the flame speed approaches or exceeds the speed of a Chapman-Jouguet deflagration. 3) Coupling of pressure gradients formed during pulsations with density gradients across the flame leads to the anisotropic amplification of turbulence inside the flame volume and flame acceleration. Such process, which is driven by the baroclinic term in the vorticity transport equation, is a reacting-flow analog of the mechanism underlying the Richtmyer-Meshkov instability. With the increase in turbulent intensity, the limit-cycle instability discussed here transitions to the regime described in our previous work, in which the growth of the flame speed becomes unbounded and produces a detonation.
 
Same as Figure 6 but for time t = 200.
The perturbed surface density (in arbitrary units) as a function of r (solid line). The unperturbed surface density Σ0(r) is shown by the dotted line
Article
Thin viscous Keplerian accretion disks are considered asymptotically stable, even though they can show significant dynamic activity on short timescales. In this paper the dynamics of non-axisymmetric hydrodynamical disturbances of disks are investigated analytically building upon the steady state three-dimensional structure and evolution of axisymmetric perturbations explored in previous work. Assuming a polytropic equation of state solutions are found by means of an asymptotic expansion in the small parameter measuring the ratio of the disk thickness to characteristic radius. In-depth analysis shows that every perturbation that disturbs the radial velocity induces significant transient growth in the (acoustic) energy of the evolving disturbance. This effect is most evident in the density and vertical velocity. The transient growth observed is tied to the non-separable nature of the solutions where, in particular, pattern evolution is controlled by a similarity variable composed of the radial coordinate and time. This leads to growing winding perturbations that display successive radial peaks and troughs. We argue that these transient non-axisymmetric structures may precipitate secondary instabilities which, consequently, may be a critical element for a new alternative picture of turbulence arousal in non-magnetized astrophysical disks. Comment: Accepted in Physics of Fluids
 
Particle position X (0) as a function of T for a standing wave in the Basset limit of Regime II obtained by solving (56) analytically (solid line, see Appendix A) and numerically (dashed line).
Contour for the inverse Laplace transform in  (A3) . The countour encloses two poles denoted by 1 and 2, and two sides of the branch cut (−∞, 0] associated with s 1/2.
Parameters controlling the motion of a spherical particle in an acoustic field.
Article
A rigid spherical particle in an acoustic wave field oscillates at the wave period but has also a mean motion on a longer time scale. The dynamics of this mean motion is crucial for numerous applications of acoustic microfluidics, including particle manipulation and flow visualisation. It is controlled by four physical effects: acoustic (radiation) pressure, streaming, inertia and viscous drag. In this paper, we carry out a systematic multiscale analysis of the problem in order to assess the relative importance of these effects depending on the parameters of the system that include wave amplitude, wavelength, sound speed, sphere radius, and viscosity. We identify two distinguished regimes characterised by a balance among three of the four effects, and we derive the equations that govern the mean particle motion in each regime. This recovers and organises classical results by King, Gor'kov and Doinikov, clarifies the range of validity of these results, and reveals a new nonlinear dynamical regime. In this regime, the mean motion of the particle remains intimately coupled to that of the surrounding fluid, and while viscosity affects the fluid motion, it plays no part in the acoustic pressure. Simplified equations, valid when only two physical effects control the particle motion, are also derived. They are used to obtain sufficient conditions for the particle to behave as a passive tracer of the Lagrangian-mean fluid motion.
 
Top-cited authors
J. Blair Perot
  • University of Massachusetts Amherst
Jonathan Rothstein
  • University of Massachusetts Amherst
Jeffrey F Morris
  • City College of New York
Olivier Simonin
  • Institut de Mécanique des Fluides de Toulouse
Elie Bou-Zeid
  • Princeton University