Volume 24, Issue 8, August 2012
Index of content:

Simulations of converging spherical shock waves propagating through a region of compressible isotropic turbulence are carried out. Both converging and reflected phases of the shock are studied. Effect of the reflected phase of the shock is found to be quite different from the expanding shock in the Taylor blast waveturbulence interaction problem. Vorticity and turbulent kinetic energy are amplified due to passage of the shock. Similar to the latter problem, the vorticitydilatation term is primarily responsible for the observed behavior. This is confirmed through Eulerian and Lagrangian statistics. Transverse vorticity amplification is compared with linear planar shockturbulence theory. The smallest eddies, represented by the Kolmogorov scale, decrease in size after passing through the converging shock and this is shown to be related to a decrease in kinematic viscosity and increase in dissipation behind the converging shock. Distortion of the shock due to turbulence is also investigated and quantified. Turbulence also affects maximum compression achieved at the point of shock reflection, when the shock radius is at a minimum. This decrease in compression is quantified by comparing with pure shock simulations.
 ANNOUNCEMENTS


Announcement: Free access to Letters published in Physics of Fluids
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 LETTERS


Pulsatility role in cylinder flow dynamics at low Reynolds number
View Description Hide DescriptionWe present dynamics of pulsatile flow past a stationary cylinder characterized by three nondimensional parameters: the Reynolds number (Re), nondimensional amplitude (A) of the pulsatile flow velocity, and KeuleganCarpenter number (KC = U_{o}/Dω _{c}). This work is motivated by the development of total artificial lungs (TAL) device, which is envisioned to provide ambulatory support to patients. Results are presented for 0.2 ≤ A ≤ 0.6 and 0.57 ≤ KC ≤ 2 at Re = 5 and 10, which correspond to the operating range of TAL. Two distinct fluid regimes are identified. In both regimes, the size of the separated zone is much greater than the uniform flow case, the onset of separation is function of KC, and the separation vortex collapses rapidly during the last fraction of the pulsatile cycle. The vortex size is independent of KC, but with an exponential dependency on A. In regime I, the separation point remains attached to the cylinder surface. In regime II, the separation point migrates upstream of the cylinder. Two distinct vortex collapse mechanisms are observed. For A < 0.4 and all KC and Re values, collapse occurs on the cylinder surface, whereas for A > 0.4 the separation vortex detaches from the cylinder surface and collapses at a certain distance downstream of the cylinder. The average drag coefficient is found to be independent of A and KC, and depends only on Re. However, for A > 0.4, for a fraction of the pulsatile cycle, the instantaneous drag coefficient is negative indicating a thrust production.

Ideal stochastic forcing for the motion of particles in largeeddy simulation extracted from direct numerical simulation of turbulent channel flow
View Description Hide DescriptionThe motion of small particles in turbulent conditions is influenced by the entire range of length and timescales of the flow. At high Reynolds numbers this range of scales is too broad for direct numerical simulation (DNS). Such flows can only be approached using largeeddy simulation (LES), which requires the introduction of a subfilter model for the momentum dynamics. Likewise, for the particle motion the effect of subfilter scales needs to be reconstructed approximately, as there is no explicit access to turbulent subfilter scales. To recover the dynamic consequences of the unresolved scales, partial reconstruction through approximate deconvolution of the LESfilter is combined with explicit stochastic forcing in the equations of motion of the particles. We analyze DNS of highReynolds turbulent channel flow to a priori extract the ideal forcing that should be added to retain correct statistical properties of the dispersed particle phase in LES. The probability density function of the velocity differences that need to be included in the particle equations and their temporal correlation display a striking and simple structure with little dependence on Reynolds number and particle inertia, provided the differences are normalized by their RMS, and the correlations expressed in wall units. This is key to the development of a general “standalone” stochastic forcing for inertial particles in LES.

Fluid elasticity can enable propulsion at low Reynolds number
View Description Hide DescriptionConventionally, a microscopic particle that performs a reciprocal stroke cannot move through its environment. This is because at small scales, the response of simple Newtonian fluids is purely viscous and flows are timereversible. We show that by contrast, fluid elasticity enables propulsion by reciprocal forcing that is otherwise impossible. We present experiments on rigid objects actuated reciprocally in viscous fluids, demonstrating for the first time a purely elastic propulsion set by the object's shape and boundary conditions. We describe two different artificial “swimmers” that experimentally realize this principle.

 ARTICLES


Biofluid Mechanics

Characterization of the transport topology in patientspecific abdominal aortic aneurysm models
View Description Hide DescriptionAbdominal aortic aneurysm (AAA) is characterized by disturbed blood flow patterns that are hypothesized to contribute to disease progression. The transport topology in six patientspecific abdominal aortic aneurysms was studied. Velocity data were obtained by imagebasedcomputational fluid dynamics modeling, with magnetic resonance imaging providing the necessary simulation parameters. Finitetime 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 flowtopology in the aneurysm. It was difficult to predict the vortex dynamics from the aneurysm morphology, motivating the application of imagebasedflow modeling.

Liquid injection in confined coflow: Application to portal vein embolization by glue injection
View Description Hide DescriptionDrop formation in liquidliquid systems has received considerable attention over the last century owing to its many industrial applications. More recent applications may be found in the field of endovascular/percutaneous treatments. The present study focuses on portal vein embolization (PVE), which consists in the blockage of part of the portal trunk though the injection of surgical glue. The shorttime injection is dominated by fluid dynamic effects: the influence of polymerization is secondary owing to the presence of ethiodized oil in the injected mixture. If the mechanism of liquid injection is well understood for injections in unconfined fluids at rest, fewer studies have so far considered the case of outer liquids flowing in confined environments. The objective is therefore to conduct a large range parametric study of liquid injections in confined coflows. An experimental setup has been designed to simulate in vitro the injection in an immiscible liquid flowing in a cylindrical tube. The transition from the dripping to the jetting regimes is found to be independent of confinement, but to depend on the ratio of the inertial forces of the injected liquid to the surface tension, i.e., the Weber number of the inner flowWe _{ i }. The confinement, however, has an influence on the drop size in the dripping regime. Its influence diminishes in the first phase of the jetting regime, as the drop size largely decreases. In the fully established jetting regime, the drop size is finally only a function of the ejection tube diameter. To predict the size of the drops in the dripping regime, we have developed a semiempirical model that takes into account the effects of both the tube confinement and outer flow. It will help the interventional radiologists predict the drop size depending on the geometrical and velocimetric conditions at the site of embolization. All these results can then serve as a base to optimize the PVE technique during clinical practice.

A lowdimensional deformation model for cancer cells in flow
View Description Hide DescriptionA lowdimensional parametric deformation model of a cancercell under shear flow is developed. The model is built around an experiment in which MDAMB231 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 postprocess 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 } (xwidth), and σ_{ y } (ywidth). 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 lowdimensional 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.

Micro and Nanofluid Mechanics

The dynamics of liquid drops and their interaction with solids of varying wettabilities
View Description Hide DescriptionMicrodrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation freesurface flows is confirmed by a comparison with previous numerical studies for the large amplitude oscillations of free liquiddrops. Our code's ability to produce high resolution benchmark calculations for dynamic wetting flows is then demonstrated by simulating microdrop impact and spreading on surfaces of greatly differing wettability. The simulations allow one to see features of the process which go beyond the resolution available to experimental analysis. Strong interfacial effects which are observed at the microfluidic scale are then harnessed by designing surfaces of varying wettability that allow new methods of flow control to be developed.

Ferrofluid flow in a spherical cavity under an imposed uniform rotating magnetic field: Spherical spinup flow
View Description Hide DescriptionAn analytical solution is obtained for the ferrohydrodynamic problem of flow of a ferrofluid in a spherical cavity under the influence of a uniform rotating magnetic field produced by a fluxball winding. The ferrohydrodynamics equations are decoupled for low values of the applied magnetic field amplitude to allow analytical solution. A governing equation for the divergence of spin velocity is obtained and used to demonstrate that the divergence of the spin velocity is zero under conditions of small uniform magnetic field. The condition of zero spin viscosity results in no flow being predicted in the cavity. For the case of nonzero spin viscosity the condition of zero divergence of spin results in the inability of the ferrohydrodynamics equations to satisfy boundary conditions for both the normal and tangential components of the spin velocity at the sphere wall. Solutions are obtained for cases where boundary conditions are imposed on either the normal or tangential component of the spin velocity. In both cases, the solutions predict that the ferrofluid rotates rigidbodylike about the axis of field rotation in the core and there is a region near the outer wall where flow reduces to satisfy the no slip boundary condition on the translational velocity. However, the two solutions differ in their asymptotic behavior when the spin viscosity vanishes. It is found that when the boundary condition is applied to the tangential component of the spin velocity, the zero spin viscosity solution is recovered as η^{′} → 0, whereas when the boundary condition is applied to the normal component of the spin velocity the solution diverges as η^{′} → 0. The results indicate that studying the flow of ferrofluids in a spherical cavity could yield important tests of longheld, arguably ad hoc assumptions surrounding the governing equations and boundary conditions of ferrofluidflow.

Alternating current inducedcharge electrophoresis of leaky dielectric Janus particles
View Description Hide DescriptionWe hereby provide a semianalytic and numerical solution for the nonlinear, inducedcharge electrophoretic motion of an electrically inhomogeneous Janus sphere—comprising two hemispheres with differing dielectric permittivities—under the application of a uniform, timedependent (ac)electric field. No assumptions are made regarding the size of the electric double layer(EDL) and thus the analysis remains valid even in the case of nanoparticles where the particle radius can be of the same order as the EDL thickness. We consider a number of practical and realistic configurations of metallic and dielectric hemispheres and predict the variations in particle mobility as a function of the conductivity of the two hemispheres and the electrolyte, the frequency of the applied electric field and the EDL length. It is determined that there exist critical values for the conductivity of each hemisphere and the frequency of the applied field, which when exceeded, can cause the mobility to decay rapidly to zero.

The contribution of diffusion to gas microflow: An experimental study
View Description Hide DescriptionModerately rarefied gasflows are clearly distinguished from viscous flow in the continuum regime and from molecular diffusion at high rarefaction. They are an intermediate of the two border cases referred to as slip flow and transition regime flow. Here, we present a new pencilandpaper approach for modeling flows in these regimes by a superposition of convection and Fickian diffusion. It allows us to predict mass flows for helium, argon, nitrogen, and carbon dioxide in microducts with parallel walls and with slightly varying cross section. The model was validated by measurement series taken from literature and by own permeation experiments on tapered microchannels. Analytical investigation of the approach showed that the diffusive flow is proportional to the crosssectional area at the channel entrance. Hence, the mass flow in a tapered channel is unequal in both directions when diffusion dominates due to increased rarefaction. In contrary to the common Maxwellian slip approach the superposition model describes the data reliably. From this we conclude that deviations from continuum behavior in the intermediate cannot be explained by slip flow at the walls and tangential momentum accommodation, but by Fickian diffusion. Now predictions are possible without any usage of fitted parameters such as the tangential momentum accommodation coefficient.

Dielectricsolid polarization at strong fields: Breakdown of Smoluchowski's electrophoresis formula
View Description Hide DescriptionWe investigate the thindoublelayer electrophoretic drift of a uniformly charged dielectric particle, driven by an intense electric field comparable to the transverse Debyelayer field. Under these circumstances, solid polarization affects the leadingorder electrokinetic transport in the fluid by inducing a nonuniform zetapotential distribution. The resulting expression for the particle velocity is accordingly nonlinear in the applied field. The electrophoretic “mobility”—the ratio of this velocity and the applied field—depends upon two parameters, the first quantifying the surfacecharge density, and the second constituting the product of the solidtoliquid permittivity ratio and the scaled appliedfield magnitude. At weak values of this product, solid polarization results in fieldcubed deviations from Smoluchowski's velocity; at large values of it, the particle velocity is a slowly increasing function of the applied field, essentially varying with its logarithm. The transition between these two limits features a shift from zetapotential proportionality to a chargedensity proportionality. For all values of the two governing parameters solid polarization acts so as to reduce the electrophoretic velocity relative to the Smoluchowski limit.

Interfacial Flows

Coalescence of surfactant covered drops in extensional flows: Effects of the interfacial diffusivity
View Description Hide DescriptionBoundary integral simulations and scaling theory were employed to study the effects of insoluble surfactantsurface diffusivity D _{ s } and concentration Γ on the coalescence process of two equalsized viscous drops. The drops underwent headon collisions in a biaxial extensional flow, in the Stokes flow limit and low capillary numbers. The simulations were compared with the drainage time experiments of Yoon et al. [Phys. Fluids19, 023102 (2007)10.1063/1.2409735] concerned with a polymeric system, polybutadiene (PBd) drops in a polydimethylsyloxane (PDMS) matrix, stabilized by blockcopolymers acting as insoluble surfactants to explain the mechanism underneath their findings. An ad hocequation of state, derived by mean field theory, specific for the blockcopolymers in the experiments of Yoon et al., able to match the experimental surface tension data without fitting parameters, was used. We were able to reproduce the experimental drainage time data, although an additional attractive force, besides the usual van der Waals interactions, had to be introduced for high blockcopolymer concentrations, probably as a result of the entropic attraction between the two facing dry brushes formed in the thin film between the two drops. According to simulations, the puzzling experimental drainage time transition for low surfactant concentrations, from high drainage time to low drainage time as Ca increases, was a consequence of the oscillating behavior of the minimum film thickness, which takes place for Marangoni numbers Ma < 5 and surface Peclet number Pe _{ s } > 60. In this regard, a master curve was obtained for the scaled relative minimum film thickness attained during the oscillation as a function of Ma. This enabled to determine both the minimum value of the dimensionless attractive forces to avoid coalescence for each concentration studied and the range of Ma that favors early coalescence. The coalescence process was found very sensitive to Pe _{ s } and for Pe _{ s } O(100–1000) even trace amounts of surfactants can be as effective stabilizers as high surfactant concentrations. Moreover, for the polymeric system of interest, the range of D _{ s } in which the drainage time changes from the saturation value to the clean interface value was computed as a function of the surfactant concentration. In the specific, for the PDMS/PBd system of interest the D _{ s } range studied was O(10^{−12}–10^{−5} cm^{2} s^{−1}). Additionally, our scaling analysis further validates our simulations, also highlighting the effect on the drainage process of the different parameters, in particular, of the external pushing force, which is increased compared to a clean interface system, as Pe _{ s } is increased or as the surfactant concentration is increased, because of the reduction in the interfacial mobility of the drop. Finally, our study suggests that matching simulations with fourroll mill drainage time experiments can be an effective method to determine blockcopolymer surface diffusivity.

Free vibrations of a spherical drop constrained at an azimuth
View Description Hide DescriptionTwo droplets coupled through a liquid filled (a) hole in a plate or (b) tube is referred to as a double droplet system (DDS) or a capillary switch. Such capillary systems are gaining increasing attention due to their utility in applications. A particularly exciting application is one where a DDS is employed as a liquid lens, one flavor of which entails using a DDS as a variable focus lens by keeping it under sustained oscillations at its natural frequencies. The natural modes of oscillation of a DDS are determined analytically here in the limit in which the plate thickness (or tube length) is vanishingly small and when the effect of gravity is negligible compared to that of surface tension. In this limit, a DDS at rest reduces to two spherical caps that are pinned to and coupled along a common circular ring of contact of negligible thickness. Here, the caps are taken to be complementary pieces of a sphere so that the equilibrium state of the system is a sphere that is constrained by a ring of negligible thickness at an azimuthal angle with respect to the center of the sphere. Both the constrained drop and the fluid exterior to it are taken to be inviscid fluids undergoing irrotational flow. Similar to the linear oscillations of a free drop first studied by Rayleigh, the analytical formulation of the linear oscillations of the constrained drop results in a linear operator eigenvalue problem but with one additional boundary condition, i.e., that which accounts for zero shape perturbation along the circle of contact. Exploiting properties of linear operators, an implicit expression is obtained for the frequency of each mode of oscillation, a feat that appears not to have been accomplished to date in any problem involving oscillations of constrained drops. An extension of a method based on Green's functions that was developed to analyze the linear oscillations of a drop in contact with a spherical bowl [M. Strani and F. Sabetta, “Freevibrations of a drop in partial contact with a solid support,” J. Fluid Mech.141, 233–247 (1984)]10.1017/S0022112084000811 is also employed to verify the aforementioned results. Results obtained from these two approaches are then compared to those reported by Bostwick and Steen [“Capillary oscillations of a constrained liquid drop,” Phys. Fluids21, 032108 (2009)]10.1063/1.3103344. Careful examination of flow fields within drops reveals that by pinning a drop, it should be possible to selectively excite just a portion of a drop'ssurface.

Numerical study on the effects of nondimensional parameters on dropondemand droplet formation dynamics and printability range in the upscaled model
View Description Hide DescriptionThe dropletformationdynamics from a dropondemand printhead is numerically investigated with regard to the printability range. The numerical simulation is carried out using a volumeoffluid model, and the qualitative effects of nondimensional parameters on the dropletformationdynamics are evaluated. To determine the printability range, within which the droplet is ejected in a stable manner without satellite droplets, extensive numerical simulations are carried out by varying the viscosity and surface tension. Generally, the printability range is determined by a Z number, which is the inverse of the Ohnesorge number (Oh). However, it is found that the Z number alone is insufficient for describing the dropletformationdynamics. Other important nondimensional parameters such as the Reynolds number (Re), Weber number (We), and capillary number (Ca) should also be taken into consideration. For studying the printability, the dropletformationdynamics are divided into five different regimes, and a regime map based on the Z, We, and Ca is proposed.

Forces on a boiling bubble in a developing boundary layer, in microgravity with gjitter and in terrestrial conditions
View Description Hide DescriptionTerrestrial and microgravityflow boiling experiments were carried out with the same test rig, comprising a locally heated artificial cavity in the center of a channel near the frontal edge of an intrusive glass bubble generator. Bubble shapes were in microgravity generally not far from those of truncated spheres, which permitted the computation of inertial lift and drag from potential flow theory for truncated spheres approximating the actual shape. For these bubbles, inertial lift is counteracted by drag and both forces are of the same order of magnitude as gjitter. A generalization of the Laplace equation is found which applies to a deforming bubble attached to a plane wall and yields the pressure difference between the hydrostatic pressures in the bubble and at the wall, Δp. A fully independent way to determine the overpressure Δp is given by a second EulerLagrange equation. Relative differences have been found to be about 5% for both terrestrial and microgravity bubbles. A way is found to determine the sum of the two counteracting major force contributions on a bubble in the direction normal to the wall from a single directly measurable quantity. Good agreement with expectation values for terrestrial bubbles was obtained with the difference in radii of curvature averaged over the liquidvapor interface, ⟨(1/R _{2} − 1/R _{1})⟩, multiplied with the surface tension coefficient, σ. The new analysis methods of force components presented also permit the accounting for a surface tension gradient along the liquidvapor interface. No such gradients were found for the present measurements.

Slip or not slip? A methodical examination of the interface formation model using twodimensional droplet spreading on a horizontal planar substrate as a prototype system
View Description Hide DescriptionWe consider the spreading of a thin twodimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphase Flow19, 589–610 (1993)]10.1016/03019322(93)90090H, to the more commonly used continuum fluid dynamical equations augmented with the Navierslip condition. Considering quasistatic droplet evolution and using the method of matched asymptotics, we find that the evolution of the droplet radius using the interface formationmodel reduces to an equivalent expression for a slip model, where the prescribed microscopic dynamic contact angle has a velocity dependent correction to its static value. This result is found for both the original interface formationmodel formulation and for a more recent version, where mass transfer from bulk to surface layers is accounted for through the boundary conditions. Various features of the model, such as the pressure behaviour and rolling motion at the contact line, and their relevance, are also considered in the prototype system we adopt.

Turbulent mixing and wave radiation in nonBoussinesq internal bores
View Description Hide DescriptionBores, or hydraulic jumps, appear in many natural settings and are useful in many industrial applications. If the densities of the two fluids between which a bore propagates are very different (i.e., water and air), the less dense fluid can be neglected when modeling a bore analytically—a singlelayer hydraulicmodel will accurately predict a bore's speed of propagation. A twolayer model is required, however, if the densities are more similar. Mass is conserved separately in each layer and momentum is conserved globally, but the model requires for closure an assumption about the loss of energy across a bore. In the Boussinesq limit, it is known that there is a decrease of the total energy flux across a bore, but in the expanding layer, turbulentmixing at the interface entrains high speed fluid from the contracting layer, resulting in an increase in the flux of kinetic energy across the expanding layer of a bore. But it is unclear if this finding will extend to nonBoussinesq bores. We directly examine the flux of energy within nonBoussinesq bores using twodimensional direct numerical simulations and find that a gain of energy across the expanding layer only occurs for bores where the density ratio, defined as the ratio of the density of the lighter fluid to the heavier fluid, is greater than approximately one half. For smaller density ratios, undular waves generated at the bore's front dominate over the effects of turbulentmixing, and the expanding layer loses energy across the bore. Based on our results, we show that if one can predict the amount of energy radiated by bores through undular waves, it is possible to derive an accurate model for the propagation of nonBoussinesq bores.

Effects of streamwise rotation on the dynamics of a droplet
View Description Hide DescriptionAn initially streamwise rotating droplet released into a uniform cross flow is studied numerically. The computations are performed using a finite volume Navier–Stokes solver which employs a moving mesh interface tracking scheme to locate the interface. With a large initial Weber number (We _{ i } = 40) the streamwise rotating droplet flattens along the free stream direction more quickly as rotation rate () increases, and leads to a dramatic increase in the dynamic drag coefficient (C _{ D }/A*, where A* is the dimensionless frontal area). On the other hand, for We _{ i } = 4 and 0.4 at , the flattening of the droplet is less pronounced and the droplet even restores to spherical shape, hence, C _{ D }/A* decreases sharply. The dynamic drag coefficient even becomes negative for We _{ i } = 4 and 0.4 at . At the largest deformation, the droplet can be classified into three major shapes: biconvex, convexconcave, and biconcave. One dominant feature of the wake downstream of the droplet is the formation and convection of vortex rings. The shape and deformation of the droplet is dependent not only on the size of the vortex ring, but also upon the free stream dynamic pressure and droplet pressure. The detachment of vortex ring in the wake leads to a substantial drag reduction, and this detachment occurs at Re ≈ 28.

Bubble pinchoff and scaling during liquid drop impact on liquid pool
View Description Hide DescriptionSimulations are performed to show entrapment of air bubble accompanied by high speed upward and downward water jets when a waterdropimpacts a pool of watersurface. A new bubble entrapment zone characterised by small bubble pinchoff and long thick jet is found. Depending on the bubble and jet behaviour, the bubble entrapment zone is subdivided into three subregimes. The entrapped bubble size and jet height depends on the crater shape and its maximum depth. During the bubble formation, bubble neck develops an almost singular shape as it pinches off. The final pinchoff shape and the power law governing the pinching, r _{neck} ∝ A(t _{0} − t)^{α}varies with the Weber number. Weber dependence of the function describing the radius of the bubble during the pinchoff only affects the coefficient A and not the power exponent α.
