Volume 26, Issue 11, November 2014
Index of content:
26(2014); http://dx.doi.org/10.1063/1.4901016View Description Hide Description
We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams. We present two algorithms: the first is mathematically equivalent to a standard “batch-processed” formulation; the second introduces a compression step that maintains computational efficiency, while enhancing the ability to isolate pertinent dynamical information from noisy measurements. Both algorithms reliably capture dominant fluid dynamic behaviors, as demonstrated on cylinder wake data collected from both direct numerical simulations and particle image velocimetry experiments.
26(2014); http://dx.doi.org/10.1063/1.4900848View Description Hide Description
We compare experiments and direct numerical simulations to evaluate the accuracy of the Stokes-drag model, which is used widely in studies of inertial particles in turbulence. We focus on statistics at the dissipation scale and on extreme values of relative particle velocities for moderately inertial particles (St < 1). The probability distributions of relative velocities in the simulations were qualitatively similar to those in the experiments. The agreement improved with increasing Stokes number and decreasing relative velocity. Simulations underestimated the probability of extreme events, which suggests that the Stokes drag model misses important dynamics. Nevertheless, the scaling behavior of the extreme events in both the experiments and the simulations can be captured by the same multi-fractal model.
26(2014); http://dx.doi.org/10.1063/1.4901958View Description Hide Description
The near-contact-line dynamics of evaporating sessile drops containing live E. coli cells is studied experimentally. The evaporation of the drop together with its pinned contact-line drives a radially outward fluid flow inside the drop concentrating the suspended cells near the contact-line. Our experiments reveal a collective behavior of the concentrated bacterial population near the contact-line appearing in the form of spatially periodic “bacterial jets” along the circumference of the drop. Based on a physical analysis of the continuum equations of bacterial suspensions, we hypothesize that the patterns result from a concentration instability driven by the active stress of swimming bacteria.
- Biofluid Mechanics
26(2014); http://dx.doi.org/10.1063/1.4900956View Description Hide Description
Phytoplankton patchiness, namely the heterogeneous distribution of microalgae over multiple spatial scales, dramatically impacts marine ecology. A spectacular example of such heterogeneity occurs in thin phytoplankton layers (TPLs), where large numbers of photosynthetic microorganisms are found within a small depth interval. Some species of motile phytoplankton can form TPLs by gyrotactic trapping due to the interplay of their particular swimming style (directed motion biased against gravity) and the transport by a flow with shear along the direction of gravity. Here we consider gyrotactic swimmers in numerical simulations of the Kolmogorov shear flow, both in laminar and turbulent regimes. In the laminar case, we show that the swimmer motion is integrable and the formation of TPLs can be fully characterized by means of dynamical systems tools. We then study the effects of rotational Brownian motion or turbulent fluctuations (appearing when the Reynolds number is large enough) on TPLs. In both cases, we show that TPLs become transient, and we characterize their persistence.
Dissipative particle dynamics simulations of deformation and aggregation of healthy and diseased red blood cells in a tube flow26(2014); http://dx.doi.org/10.1063/1.4900952View Description Hide Description
In this paper, we report simulation results assessing the deformation and aggregation of mixed healthy and malaria-infected red blood cells (RBCs) in a tube flow. A three dimensional particle model based on Dissipative Particle Dynamics (DPD) is developed to predict the tube flow containing interacting cells. The cells are also modelled by DPD, with a Morse potential to characterize the cell-cell interaction. As validation tests, a single RBC in a tube flow and two RBCs in a static flow are simulated to examine the cell deformation and intercellular interaction, respectively. The study of two cells, one healthy and the other malaria-infected RBCs in a tube flow demonstrates that the malaria-infected RBC (in the leading position along flow direction) has different effects on the healthy RBC (in the trailing position) at the different stage of parasite development or at the different capillary number. With parasitic development, the malaria-infected RBC gradually loses its deformability, and in turn the corresponding trailing healthy RBC also deforms less due to the intercellular interaction. With increasing capillary number, both the healthy and malaria-infected RBCs are likely to undergo an axisymmetric motion. The minimum intercellular distance becomes small enough so that rouleaux is easily formed, i.e., the healthy and malaria-infected RBCs are difficultly disaggregated.
- Micro- and Nanofluid Mechanics
Isothermal vortex flows in the vicinity of ferro- and diamagnetic condensation cores in magnetic fluids undergoing first-order phase transition26(2014); http://dx.doi.org/10.1063/1.4900841View Description Hide Description
The paper presents the system of analytical equations describing isothermal vortex flows induced in a plane magnetized ferrofluid layer by magnetophoresis of drop-like aggregates. Magnetophoresis of the aggregates is caused by configuration of a constant inhomogeneous magnetic field in the vicinity of a solid condensation core placed in the fluid. The vortex flow generated by inhomogeneous ponderomotive force drives the aggregates into the region of highest magnetic field intensity, which resembles condensation of drops at the surface of the core. The dynamic equations are written for the case of dilute magnetic fluids and take into account the dynamics of the drop-like aggregate growth. Numerical simulation based on the proposed system of equations is in qualitative agreement with the experimental data obtained in the Hele-Shaw cell.
26(2014); http://dx.doi.org/10.1063/1.4901330View Description Hide Description
Numerical simulation is used to calculate accurately the electrophoretic mobility of a charged spherical nanoparticle confined in a nanochannel, under a weakly applied electric field. Classic models for electrophoretic mobility are valid only in the linear regime of small particle zeta potential, and for an unbounded fluid domain. However, these models fail to predict the electrophoretic mobility measured experimentally in bounded nanochannels. We adopt asymptotically expanded formulations and solve the fully coupled equations on a 3D finite element domain. Factors affecting particle mobility include electrolyte concentration, channel size, and zeta potentials on both the particle surface and channel walls. Specifically, spherical particles are examined with diameters 2a = 10 and 50 nm, in a 100 nm high channel. The non-dimensional electric double layers were varied between 0.1 < κa < 100. The results indicate that the mobility of a particle located at the nanochannel centerline agrees to within 1% of the average mobility of a particle distributed transversely throughout the nanochannel. Furthermore, confinement by the nanochannel walls was found to affect greatly nanoparticle mobility. As a result, it is feasible to use nanochannels to separate two different size nanoparticles, even when the particles have equal zeta potentials. Finally, a new method is proposed to estimate accurately particle and wall zeta potentials by contrasting the observed differences in mobility between observed in two different height channels.
- Viscous and Non-Newtonian Flows
26(2014); http://dx.doi.org/10.1063/1.4900769View Description Hide Description
Interaction of a vortex ring impinging on multiple permeable screens orthogonal to the ring axis was studied to experimentally investigate the persistence and decay of vortical structures inside the screen array using digital particle image velocimetry in a refractive index matched environment. The permeable screens had porosities (open area ratios) of 83.8%, 69.0%, and 55.7% and were held by a transparent frame that allowed the screen spacing to be changed. Vortex rings were generated using a piston-cylinder mechanism at nominal jet Reynolds numbers of 1000, 2000, and 3000 with piston stroke length-to-diameter ratios of 2 and 3. The interaction of vortex rings with the porous medium showed a strong dependence of the overall flow evolution on the screen porosity, with a central flow being preserved and vortex ring-like structures (with smaller diameter than the primary vortex ring) being generated near the centerline. Due to the large rod size used in the screens, immediate reformation of the transmitted vortex ring with size comparable to the primary ring (as has been observed with thin screens) was not observed in most cases. Since the screens have lower complexity and high open area ratios, centerline vortex ring-like flow structures formed with comparable size to the screen pore size and penetrated through the screens. In the case of low porosity screens (55.7%) with large screen spacing, re-emergence of large scale (large separation), weak vortical structures/pairs (analogous to a transmitted vortex ring) was observed downstream of the first screen. Additional smaller scale vortical structures were generated by the interaction of the vortex ring with subsequent screens. The size distribution of the generated vortical structures were shown to be strongly affected by porosity, with smaller vortical structures playing a stronger role as porosity decreased. Finally, porosity significantly affected the decay of total energy, but the effect of screen spacing decreased as porosity decreased.
26(2014); http://dx.doi.org/10.1063/1.4900941View Description Hide Description
Filamentous networks and elastic polymers immersed in a viscous fluid are central to many processes in biology. Here, we present a model of a discrete viscoelastic network coupled to a Stokesian fluid. The network is built out of a collection of cross-linked nodes where each link is modeled by one or more simple viscoelastic elements. The method of regularized Stokeslets is used to couple network dynamics with a highly viscous fluid in three dimensions. We use computational rheometry tests to characterize the viscoelastic structures, such as computing their frequency-dependent loss and storage moduli. We find that when linkages between nodes are modeled by Maxwell elements, the qualitative behavior of these moduli reflects that of many biological viscoelastic structures.
Determination of dynamic surface tension and viscosity of non-Newtonian fluids from drop oscillations26(2014); http://dx.doi.org/10.1063/1.4901823View Description Hide Description
The oscillations of free-falling drops with size range from pl to μl have been used to measure the transient shear viscosity and the dynamic surface tension of shear-thinning fluids on the timescale of 10−5–10−2 s. The method is first validated with Newtonian fluids. For a given surface tension, the lower and upper limits for accurate measurement of the viscosity are determined as a function of drop size. The dynamic properties of two types of shear-thinning fluids with varying viscoelasticity are reported: aqueous suspensions of the antifungal drug griseofulvin and of the organic light-emitting diode material poly(3,4-ethylenedioxythiophene): polystyrene-sulphonate. In both cases, the free-falling drop retains the high-shear viscosity.
- Particulate, Multiphase, and Granular Flows
Application of Proper Orthogonal Decomposition to the morphological analysis of confined co-axial jets of immiscible liquids with comparable densities26(2014); http://dx.doi.org/10.1063/1.4900944View Description Hide Description
The development of a round liquid jet under the influence of a confined coaxial flow of an immiscible liquid of comparable density (central to annular flow density ratio of 8:10) was investigated in the vicinity of the nozzle exit. Two flow regimes were considered; one where the annular flow is faster than the central jet, so the central liquid jet is accelerated and one where the annular flow is slower, so the central liquid jet is decelerated. The central jet was visualised by high speed photography. Three modes of jet development were identified and classified in terms of the Reynolds number, Re, of the central jet which was in the range of 525 < Re < 2725, a modified definition of the Weber number, We, which allows the distinction between accelerating and deceleration flows and was in the range of −22 < We < 67 and the annular to central Momentum Ratio, MR, of the two streams which was in the range of 3.6 < MR < 91. By processing the time resolved jet images using Proper Orthogonal Decomposition (POD), it was possible to reduce the description of jet morphology to a small number of spatial modes, which isolated the most significant morphologies of the jet development. In this way, the temporal and spatial characteristics of the instabilities on the interface were clearly identified which highlights the advantages of POD over direct observation of the images. Relationships between the flow parameters and the interfacial waves were established. The wavelength of the interfacial instability was found to depend on the velocity of the fastest moving stream, which is contrary to findings for fluids with large density differences.
26(2014); http://dx.doi.org/10.1063/1.4900855View Description Hide Description
When a hole is created in a layer of a dense, vertically vibrated suspension, phenomena are known to occur that defy the natural tendency of gravity to close the hole. Here, an overview is presented of the different patterns that we observed in a variety of dense particulate suspensions. Subsequently, we relate the occurrence of these patterns to the system parameters, namely, the layer thickness, the particle concentration, and the shaking parameters. Special attention is given to the geometric properties of the particles in the various suspensions such as shape and particle size distribution. We observe these properties to be crucial for selecting the dynamics of the vibrated suspension.
Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows26(2014); http://dx.doi.org/10.1063/1.4901315View Description Hide Description
In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future developments can be safely built, which is also relevant for stochastic subgrid models for particle-laden flows in the context of Large Eddy Simulations.
- Laminar Flows
Lagrangian transport characteristics of a class of three-dimensional inline-mixing flows with fluid inertia26(2014); http://dx.doi.org/10.1063/1.4901822View Description Hide Description
Laminar mixing by the inline-mixing principle is a key to many industrial fluids-engineering systems of size extending from micrometers to meters. However, insight into fundamental transport phenomena particularly under the realistic conditions of three-dimensionality (3D) and fluid inertia remains limited. This study addresses these issues for inline mixers with cylindrical geometries and adopts the Rotated Arc Mixer (RAM) as a representative system. Transport is investigated from a Lagrangian perspective by identifying and examining coherent structures that form in the 3D streamline portrait. 3D effects and fluid inertia introduce three key features that are not found in simplified configurations: transition zones between consecutive mixing cells of the inline-mixing flow; local upstream flow (in certain parameter regimes); transition/inertia-induced breaking of symmetries in the Lagrangian equations of motion (causing topological changes in coherent structures). Topological considerations strongly suggest that there nonetheless always exists a net throughflow region between inlet and outlet of the inline-mixing flow that is strictly separated from possible internal regions. The Lagrangian dynamics in this region admits representation by a 2D time-periodic Hamiltonian system. This establishes one fundamental kinematic structure for the present class of inline-mixing flows and implies universal behavior in that all states follow from the Hamiltonian breakdown of one common integrable state. A so-called period-doubling bifurcation is the only way to eliminate transport barriers originating from this state and thus is a necessary (yet not sufficient) condition for global chaos. Important in a practical context is that a common simplification in literature, i.e., cell-wise fully-developed Stokes flow (“2.5D approach”), retains these fundamental kinematic properties and deviates from the generic 3D inertial case only in a quantitative sense. This substantiates its suitability for (at least first exploratory) studies on (qualitative) mixing properties.
- Instability and Transition
Stability of a film flowing down an inclined corrugated plate: The direct Navier-Stokes computations and Floquet theory26(2014); http://dx.doi.org/10.1063/1.4900857View Description Hide Description
The paper is devoted to a theoretical analysis of the linear stability of the viscous liquid film flowing down an inclined wavy surface. The study is based on the Navier-Stokes equations in their full statement. The developed numerical algorithm allows us to compute both the steady state solution of the nonlinear equations and the rates of growing or damping in time of the arbitrary two-dimensional disturbances of the solution which are bounded in space. The wall corrugations have a great influence on the disturbances behaviour. There is a critical Reynolds number Recr when the steady-state viscous flow over an undulated surface becomes unstable. It is found that the value of Recr depends essentially both on the topography parameters and the liquid's physical properties. In the case of the flat plate, the critical Reynolds number depends only on the value of the inclination angle. For different values of the Kapitza number, the inclination angle, and the Reynolds number we obtained the regions of the corrugation's parameters (amplitude and period) where all two-dimensional disturbances decay in time.
Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles26(2014); http://dx.doi.org/10.1063/1.4900859View Description Hide Description
To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other.
26(2014); http://dx.doi.org/10.1063/1.4900874View Description Hide Description
Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via the streamwise vorticity of an instantaneous and a time-averaged pattern are presented, as well as 2D visualizations of the average velocity field and the turbulent kinetic energy. Simulations for 2300 ⩾ Re b ⩾ 700 show the gradual development from uniform turbulence to a pattern with wavelength 20 half-gaps at Re b ≈ 1900, to a pattern with wavelength 40 at Re b ≈ 1300 and finally to laminar flow at Re b ≈ 800. These transitions are tracked quantitatively via diagnostics using the amplitude and phase of the Fourier transform and its probability distribution. The propagation velocity of the pattern is approximately that of the mean flux and is a decreasing function of Reynolds number. Examination of the time-averaged flow shows that a turbulent band is associated with two counter-rotating cells stacked in the cross-channel direction and that the turbulence is highly concentrated near the walls. Near the wall, the Reynolds stress force accelerates the fluid through a turbulent band while viscosity decelerates it; advection by the laminar profile acts in both directions. In the center, the Reynolds stress force decelerates the fluid through a turbulent band while advection by the laminar profile accelerates it. These characteristics are compared with those of turbulent-laminar banded patterns in plane Couette flow.
26(2014); http://dx.doi.org/10.1063/1.4901971View Description Hide Description
In previous works [R. González, G. Sarasua, and A. Costa, “Kelvin waves with helical Beltrami flow structure,” Phys. Fluids20, 024106 (2008) and R. González, A. Costa, and E. S. Santini, “On a variational principle for Beltrami flows,” Phys. Fluids22, 074102 (2010)], we analyzed the Beltrami flow structure of Kelvin waves in an ideal fluid. As a result, we were able to show an important feature of Beltrami flows: their stability for Beltrami perturbations with the same eigenvalue as the basic flow. Here, instead, we study the dynamics of Beltrami perturbations by performing a modal analysis. In the first place, we study the modes that are generated by perturbing a uniformly translating and solidly rotating basic flow. In order to simplify the analysis, we consider the non-inertial frame in which this basic flow is at rest. In the second place, we analyze a basic Beltrami flow that is stationary in the non-inertial frame considered and is perturbed with Beltrami modes. We find that the last case is only possible when the perturbation eigenvalue is the same as that of the basic Beltrami flow. This is what we have called dynamical property. In both cases, the dynamics are represented by progressive waves in the moving frame. We apply this analysis to a rotating flow in an infinite cylinder and to an axisymmetric rotating Beltrami flow in a semi-infinite cylinder. In both cases, the development of secondary Beltrami modes is possible due to the dynamical property.
- Turbulent Flows
26(2014); http://dx.doi.org/10.1063/1.4900876View Description Hide Description
A dynamic end cap methodology is proposed to account for spurious contributions to the far-field sound within the context of the Ffowcs–Williams and Hawkings (FW–H) acoustic analogy. The quadrupole source terms are correlated over multiple planes to obtain a convection velocity which is then used to determine a corrective convective flux at the FW–H porous surface. The proposed approach is first demonstrated for a convecting potential vortex. It is then evaluated by computing the sound emitted by flow over circular cylinders at Reynolds number of 150, 10 000, and 89 000, respectively. The low Re cylinder is used to validate against direct numerical simulation (DNS) and demonstrate insensitivity to end plane location and spacing, the effect of dynamic convection velocity and to compare to commonly used end cap corrections. The Re 100 00 cylinder is used to validate at turbulent Reynolds numbers against other simulations. Finally the Re 89 000 simulations are used to compare to experiment. The proposed approach demonstrates better performance than other commonly used approaches with the added benefit of computational efficiency and the ability to query independent volumes.
26(2014); http://dx.doi.org/10.1063/1.4901297View Description Hide Description
The strength of the nonlinearity is measured in decaying two-dimensional turbulence, by comparing its value to that found in a Gaussian field. It is shown how the nonlinearity drops following a two-step process. First a fast relaxation is observed on a timescale comparable to the time of formation of vortical structures, then at long times the nonlinearity relaxes further during the phase when the eddies merge to form the final dynamic state of decay. Both processes seem roughly independent of the value of the Reynolds number.