Volume 27, Issue 7, July 2015
Index of content:

Complex, unsteady fluid flow phenomena in the arteries arise due to the pulsations of the heart that intermittently pumps the blood to the extremities of the body. The many different flow waveform variations observed throughout the arterial network are a result of this process and a function of the vessel properties. Large scale secondary flow structures are generated throughout the aortic arch and larger branches of the arteries. An experimental 180° curved artery test section with physiological inflow conditions was used to validate the computational methods implemented in this study. Good agreement of the secondary flow structures is obtained between experimental and numerical studies of a Newtonian bloodanalog fluid under steadystate and pulsatile, carotid artery flow rate waveforms. Multiple vortical structures, some of opposite rotational sense to Dean vortices, similar to Lynetype vortices, were observed to form during the systolic portion of the pulse. Computational tools were used to assess the effect of bloodanalog fluid rheology (i.e., Newtonian versus nonNewtonian). It is demonstrated that nonNewtonian, bloodanalog fluid rheology results in shear layer instabilities that alter the formation of vortical structures during the systolic deceleration and onwards during diastole. Additional vortices not observed in the Newtonian cases appear at the inside and outside of the bend at various times during the pulsation. The influence of bloodanalog shearthinning viscosity decreases mean pressure losses in contrast to the Newtonian blood analog fluid.
 LETTERS


Velocity derivative skewness in fractalgenerated, nonequilibrium grid turbulence
View Description Hide DescriptionThe evolution of the velocity derivative skewness, S(∂u/∂x), is investigated along two streamwise axes and four transverse positions in the wake of a squarefractalelement grid. In the nearfield, the produced turbulence exhibits nonequilibrium characteristics including . In the farfield, the turbulence agrees with canonical grid turbulence results and C ϵ is approximately constant. It is found that in the nonequilibrium region, the value of −S(∂u/∂x) is dependent on both streamwise and transverse positions, but after a sufficient decay period, it takes on a near constant value in the farfield. It is demonstrated that the evolution C ϵ approximately corresponds to that of −S(∂u/∂x), which is suggestive that some of the nonequilibrium properties are likely a result of residual strain from the turbulence generating conditions.

Viscous flow separation caused by the Marangoni effect in competition with capillary flow
View Description Hide DescriptionThis letter provides an analytical model that describes the viscous flow separation in a drying thin polymer solution film. While conventional flow separation occurs due to an adverse pressure gradient opposing fluid inertia, here we show that flow separation can also be caused by the Marangoni effect in an evaporationdriven creeping flow. The flow separation behavior strongly depends on the surface tension distribution and the interface profile. Viscous flow separation adds to the current understanding of flow physics during the drying of thin films, in addition to the wellknown capillary transport and the Marangoni effect.

 ARTICLES

 Biofluid Mechanics

NonNewtonian perspectives on pulsatile bloodanalog flows in a 180° curved artery model
View Description Hide DescriptionComplex, unsteady fluid flow phenomena in the arteries arise due to the pulsations of the heart that intermittently pumps the blood to the extremities of the body. The many different flow waveform variations observed throughout the arterial network are a result of this process and a function of the vessel properties. Large scale secondary flow structures are generated throughout the aortic arch and larger branches of the arteries. An experimental 180° curved artery test section with physiological inflow conditions was used to validate the computational methods implemented in this study. Good agreement of the secondary flow structures is obtained between experimental and numerical studies of a Newtonian bloodanalog fluid under steadystate and pulsatile, carotid artery flow rate waveforms. Multiple vortical structures, some of opposite rotational sense to Dean vortices, similar to Lynetype vortices, were observed to form during the systolic portion of the pulse. Computational tools were used to assess the effect of bloodanalog fluid rheology (i.e., Newtonian versus nonNewtonian). It is demonstrated that nonNewtonian, bloodanalog fluid rheology results in shear layer instabilities that alter the formation of vortical structures during the systolic deceleration and onwards during diastole. Additional vortices not observed in the Newtonian cases appear at the inside and outside of the bend at various times during the pulsation. The influence of bloodanalog shearthinning viscosity decreases mean pressure losses in contrast to the Newtonian blood analog fluid.

The dynamics of a capsule in a wallbounded oscillating shear flow
View Description Hide DescriptionThe motion of an initially spherical capsule in a wallbounded oscillating shear flow is investigated via an accelerated boundary integral implementation. The neoHookean model is used as the constitutive law of the capsule membrane. The maximum wallnormal migration is observed when the oscillation period of the imposed shear is of the order of the relaxation time of the elastic membrane; hence, the optimal capillary number scales with the inverse of the oscillation frequency and the ratio agrees well with the theoretical prediction in the limit of highfrequency oscillation. The migration velocity decreases monotonically with the frequency of the applied shear and the capsulewall distance. We report a significant correlation between the capsule lateral migration and the normal stress difference induced in the flow. The periodic variation of the capsule deformation is roughly in phase with that of the migration velocity and normal stress difference, with twice the frequency of the imposed shear. The maximum deformation increases linearly with the membrane elasticity before reaching a plateau at higher capillary numbers when the deformation is limited by the time over which shear is applied in the same direction and not by the membrane deformability. The maximum membrane deformation scales as the distance to the wall to the power 1/3 as observed for capsules and droplets in nearwall steady shear flows.
 Micro and Nanofluid Mechanics

Lubrication analysis of interacting rigid cylindrical particles in confined shear flow
View Description Hide DescriptionLubrication analysis is used to determine analytical expressions for the elements of the resistance matrix describing the interaction of two rigid cylindrical particles in twodimensional shear flow in a symmetrically confined channel geometry. The developed model is valid for nonBrownian particles in a lowReynoldsnumber flow between two sliding plates with thin gaps between the two particles and also between the particles and the walls. Using this analytical model, a comprehensive overview of the dynamics of interacting cylindrical particles in shear flow is presented. With only hydrodynamic interactions, rigid particles undergo a reversible interaction with no crossstreamline migration, irrespective of the confinement value. However, the interaction time of the particle pair substantially increases with confinement, and at the same time, the minimum distance between the particle surfaces during the interaction substantially decreases with confinement. By combining our purely hydrodynamic model with a simple on/off nonhydrodynamic attractive particle interaction force, the effects of confinement on particle aggregation are qualitatively mapped out in an aggregation diagram. The latter shows that the range of initial relative particle positions for which aggregation occurs is increased substantially due to geometrical confinement. The interacting particle pair exhibits tangential and normal lubrication forces on the sliding plates, which will contribute to the rheology of confined suspensions in shear flow. Due to the combined effects of the confining walls and the particle interaction, the particle velocities and resulting forces both tangential and perpendicular to the walls exhibit a nonmonotonic evolution as a function of the orientation angle of the particle pair. However, by incorporating appropriate scalings of the forces, velocities, and doublet orientation angle with the minimum free fraction of the gap height and the plate speed, master curves for the forces versus orientation angle can be constructed.

Investigation of coldtohot transfer and thermal separation zone through nano step geometries
View Description Hide DescriptionNanosteps form once nanochannels of various diameters connect to each other. The focus of this paper is to investigate the heat transfer and hydro/thermal field behavior in nanostep geometries using direct simulation Monte Carlo. The effects of the hydrodynamics separation on the pressure field and heat lines are reported, i.e., we show that the length of the hydrodynamics separation zone is different from the positive pressure gradient and thermal separation zones. Interestingly, cold to hot transfer is observed when the wall temperatures and inlet temperature are close to each other. We show that cold to hot heat transfer appears due to the interplay between the higher order term of the heat flux formula, which is a function of the second derivate of the velocity, with the Fourier term; the cold to hot transfer effect is omitted as the wall temperature or Knudsen number increases. In addition, the impact of different parameters, such as pressure ratio, Knudsen number, and wall temperature adjacent to the separation zone, are investigated. The dependence of the mass flow rate and the length of the separation zone on the wall temperature and the channel pressure ratio is considered. We show that Knudsen minimum is not observed in the step geometry for both isothermal and nonisothermal wall conditions.

Diffusion dependent focusing regimes in peak mode counterflow isotachophoresis
View Description Hide DescriptionWe present an analytical, numerical, and experimental study of pressure driven counterflow isotachophoresis (ITP). We study solutions to the NernstPlanck equations in the axisymmetric and radially dependent case, in the leading order of negligible body forces. We provide a simple model that describes the ITP interface shape for Poiseuilletype counterflows, and an asymptotic model which captures two distinct sample focusing regimes of peak mode ITP. We validate the existence of these regimes using numerical simulations and map the conditions under which each of the focal regions dominates. In particular, we demonstrate numerically that a species diffusivity is a key parameter determining its focusing regime. We experimentally show that this allows spatial separation of cofocusing species having distinctly different diffusivities. We further demonstrate that while dispersion associated with counterflow is typically considered to reduce peak concentrations, certain focusing regimes allow a net gain in sample concentration over the nondispersed case.
 Interfacial Flows

Wave drag on a submerged sphere
View Description Hide DescriptionWe measure the wave drag acting on fully submerged spheres as a function of their depth and velocity, with an apparatus that measures only the component of the drag due to the proximity of the free surface. We observe that close to the surface the wave drag is of the order of the hydrodynamic drag. In our range of study, the measured force is more than one order smaller than predictions based on linear response. In order to investigate this discrepancy, we measure the amplitude of the waves at the origin of the wave drag, comparing the measurement with a theoretical model. The model captures the measurements at “large depth” but the wave’s amplitude saturates at “small depth,” an effect that partially accounts for the difference between the predicted and measured wave drag.

Floating and sinking of selfassembled spheres on liquidliquid interfaces: Rafts versus stacks
View Description Hide DescriptionThe floating and sinking of objects on fluidfluid interfaces occurs in nature and has many important implications in technology. Here, we study the stability of floating selfassembled spheres on an oilwater interface, and how the sphere deposition geometry affects the size limits of the assemblies before they collapse and sink through the interface. Specifically, we compare the critical size of particle rafts to particle stacks. We show that, on liquidliquid interfaces, monolayer rafts and stacked spheres exhibit different scaling of the critical number of spheres to the Bond number—the dimensionless ratio of buoyancy to interfacial tension effects. Our results indicate that particle stacks will sink with a lower threshold number of particles than particle rafts. This finding may have important implications to engineering applications where interfacial assemblies are not monolayers.

Onset of convection in a two–phase binary mixture with the Soret effect in weightlessness
View Description Hide DescriptionThe linear stability of mechanical equilibrium in a two–layer system formed by different phases of the same binary mixture is investigated. The temperature difference is applied to the layers by heating and cooling the opposite rigid boundaries. In the state of mechanical equilibrium, the applied temperature gradient induces concentration gradients due to the Soret effect. The conservation of mass for the mixture components leads to the dependence of layer thicknesses on the applied temperature difference. In weightlessness, the main mechanisms of instability in the considered system are related to phase change and Marangoni effect. The calculations are performed for cyclohexane–methanol binary mixture, which has a liquid–liquid miscibility gap. The analytical solution of amplitude equations for monotonic perturbations is found and expression for the critical temperature difference is derived. It is shown that the phase change instability is long–wave and favoured when the difference between interfacial concentrations in the basic state decreases. When the Marangoni effect is taken into account, additional monotonic and oscillatory modes appear. They result from the interplay between thermocapillarity and phase change with latent heat release/absorption. The most unstable monotonic and oscillatory modes are identified depending on the heating regime and relative thickness of the layers.

Strongly coupled interaction between a ridge of fluid and an inviscid airflow
View Description Hide DescriptionThe behaviour of a steady thin sessile or pendent ridge of fluid on an inclined planar substrate which is strongly coupled to the external pressure gradient arising from an inviscid airflow parallel to the substrate far from the ridge is described. When the substrate is nearly horizontal, a very wide ridge can be supported against gravity by capillary and/or external pressure forces; otherwise, only a narrower (but still wide) ridge can be supported. Classical thinaerofoil theory is adapted to obtain the governing singular integrodifferential equation for the profile of the ridge in each case. Attention is focused mainly on the case of a very wide sessile ridge. The effect of strengthening the airflow is to push a pinned ridge down near to its edges and to pull it up near to its middle. At a critical airflow strength, the upslope contact angle reaches the receding contact angle at which the upslope contact line depins, and continuing to increase the airflow strength beyond this critical value results in the depinned ridge becoming narrower, thicker, and closer to being symmetric in the limit of a strong airflow. The effect of tilting the substrate is to skew a pinned ridge in the downslope direction. Depending on the values of the advancing and receding contact angles, the ridge may first depin at either the upslope or the downslope contact line but, in general, eventually both contact lines depin. The special cases in which only one of the contact lines depins are also considered. It is also shown that the behaviour of a very wide pendent ridge is qualitatively similar to that of a very wide sessile ridge, while the important qualitative difference between the behaviour of a very wide ridge and a narrower ridge is that, in general, for the latter one or both of the contact lines may never depin.
 Particulate, Multiphase, and Granular Flows

On the mixing induced by tightly confined spheres in bounded shear flows
View Description Hide DescriptionThe mixing of solute tracers produced by a dilute suspension of spheres undergoing shear flow is examined in the limit that the gap between the sphere and the bounding walls becomes vanishingly small. Such tight confinement produces an envelope of flipping trajectories in the vicinity of the sphere giving rise to swift mixing of an antisymmetric concentration distribution across the central plane of the gap. The size of this flipping envelope is demonstrated to be only weakly dependent on the angular velocity of the sphere and is accurately approximated by a two parameter model. This model can be used to calculate the additional mass transfer arising due to flipping. The degree of mixing in the system is directly related to the intensity of flipping which is shown to be a function of a single parameter χ given by where is the shear rate, a is the radius of the sphere, ϕs is the volume fraction of the spheres, and D is the diffusivity. As χ varies from 0 to ∞, the concentration distribution across the gap goes from being linear everywhere to being uniform across the flipping envelope, with the overall flux increasing by a factor of ∼3.

Coalescence and breakup of large droplets in turbulent channel flow
View Description Hide DescriptionCoalescence and breakup of large deformable droplets dispersed in a wallbounded turbulent flow are investigated. Droplets much larger than the Kolmogorov length scale and characterized by a broad range of surface tension values are considered. The turbulent field is a channel flow computed with pseudospectral direct numerical simulations, while phase interactions are described with a phase field model. Within this physically consistent framework, the motion of the interfaces, the capillary effects, and the complex topological changes experienced by the droplets are simulated in detail. An oilwater emulsion is mimicked: the fluids are considered of same density and viscosity for a range of plausible values of surface tension, resulting in a simplified system that sets a benchmark for further analysis. In the present conditions, the Weber number (We), that is, the ratio between inertia and surface tension, is a primary factor for determining the droplets coalescence rate and the occurrence of breakups. Depending on the value of We, two different regimes are observed: when We is smaller than a threshold value (We < 1 in our simulations), coalescence dominates until dropletdroplet interactions are prevented by geometric separation; when We is larger than the threshold value (We > 1), a permanent dynamic equilibrium between coalescence and breakup events is established.

Flow of immiscible ferrofluids in a planar gap in a rotating magnetic field
View Description Hide DescriptionAnalytical solutions are obtained for the steady, fully developed flow of two layers of immiscible ferrofluids of different thicknesses between two parallel plates. Interfacial linear and internal angular momentum balance relations are derived for the case when there is a ferrofluidferrofluid interface to obtain the translational and spin velocity profiles in the gap. As expected for the limit of low applied field amplitude, the magnitude of the translational velocity is directly proportional to the frequency of the applied magnetic field and to the square of the magnetic field amplitude. Expressions for the velocity profiles are obtained for the zero spin viscosity and nonzero spin viscosity cases and the effect of applied pressure gradient on the flows is studied. The spin velocity in both ferrofluid phases is in the direction of the rotating magnetic field, except for cases of extreme applied pressure gradients for which the fluid vorticity opposes the spin. We find that for the case of nonzero spin viscosity, flow reversals are predicted using representative ferrofluid property values and field conditions. The unique predictions of the solution with nonzero spin viscosity could be used to experimentally test the existence of couple stresses in ferrofluids and the validity of previously reported values of the socalled spin viscosity.

Standing jumps in shallow granular flows down smooth inclines
View Description Hide DescriptionThe shapes of standing jumps formed in shallow granular flows down an inclined smoothbased chute are analysed in detail, by varying both the slope and mass discharge. Laboratory tests and analytic jump solutions highlight two important transitions. First, for dense flows at high mass discharge, we observe a transition between steep jumps and more diffuse jumps. The traditional shallowwater equation offers a valid prediction for the thickness of the steep waterlike jumps. Diffuse frictional jumps require a more general equation accounting for the forces acting inside the jump volume. Second, moving from dense to dilute flows produces another transition between incompressible and compressible jumps. The observed jump height decrease may be reproduced for a more dilute incoming flow by including experimentally measured density variation in the jump equation. Finally, we briefly discuss the likely relevance to avalanche protection dam design that currently utilises traditional shock equations for incompressible frictionless fluids.

Analysis of the correlation dimension for inertial particles
View Description Hide DescriptionWe obtain an implicit equation for the correlation dimension which describes clustering of inertial particles in a complex flow onto a fractal measure. Our general equation involves a propagator of a nonlinear stochastic process in which the velocity gradient of the fluid appears as additive noise. When the longtime limit of the propagator is considered our equation reduces to an existing largedeviation formalism from which it is difficult to extract concrete results. In the shorttime limit, however, our equation reduces to a solvability condition on a partial differential equation. In the case where the inertial particles are much denser than the fluid, we show how this approach leads to a perturbative expansion of the correlation dimension, for which the coefficients can be obtained exactly and in principle to any order. We derive the perturbation series for the correlation dimension of inertial particles suspended in threedimensional spatially smooth random flows with whitenoise time correlations, obtaining the first 33 nonzero coefficients exactly.

Direct numerical simulation of moderateReynoldsnumber flow past arrays of rotating spheres
View Description Hide DescriptionDirect numerical simulations with an immersed boundarylattice Boltzmann method are used to investigate the effects of particle rotation on flows past random arrays of monodisperse spheres at moderate particle Reynolds numbers. This study is an extension of a previous study of the authors [Q. Zhou and L.S. Fan, “Direct numerical simulation of lowReynoldsnumber flow past arrays of rotating spheres,” J. Fluid Mech. 765, 396–423 (2015)] that explored the effects of particle rotation at low particle Reynolds numbers. The results of this study indicate that as the particle Reynolds number increases, the normalized Magnus lift force decreases rapidly when the particle Reynolds number is in the range lower than 50. For the particle Reynolds number greater than 50, the normalized Magnus lift force approaches a constant value that is invariant with solid volume fractions. The proportional dependence of the Magnus lift force on the rotational Reynolds number (based on the angular velocity and the diameter of the spheres) observed at low particle Reynolds numbers does not change in the present study, making the Magnus lift force another possible factor that can significantly affect the overall dynamics of fluidparticle flows other than the drag force. Moreover, it is found that both the normalized drag force and the normalized torque increase with the increase of the particle Reynolds number and the solid volume fraction. Finally, correlations for the drag force, the Magnus lift force, and the torque in random arrays of rotating spheres at arbitrary solids volume fractions, rotational Reynolds numbers, and particle Reynolds numbers are formulated.
 Laminar Flows

Dynamics of an inverted flexible plate in a uniform flow
View Description Hide DescriptionThe dynamics of an inverted flexible plate with a free leadingedge and a fixed trailingedge in a uniform flow has been studied numerically by an immersed boundarylattice Boltzmann method for the fluid flow and a finite element method for the plate deformation. Mechanisms underlying the dynamics of the fluidplate system are elucidated systematically. A series of distinct states of the plate deformation and motion are identified and can be described as straight, flapping, deflected, deflectedflapping, and asymmetricflapping states. Which state to occur depends mainly on the bending stiffness and aspect ratio of the plate. The forces exerted on the plate and the elastic strain energy of the plate are analyzed. It is found that the flapping state can improve the conversion of fluid kinetic energy to elastic strain energy. In addition, the effects of the mass ratio of the plate and the fluid, the Reynolds number, and the angle of attack of the uniform flow on the dynamics and the elastic strain energy of flexible plate are also investigated in detail. The vortical structures around the plate are given to discuss the connection of the evolution of vortices with the plate deformation and motion. The results obtained in this study provide physical insight into the understanding of the mechanisms on the dynamics of the fluidplate system.

Vortex flow structures and interactions for the optimum thrust efficiency of a heaving airfoil at different mean angles of attack
View Description Hide DescriptionThe thrust efficiency of a twodimensional heaving airfoil is studied computationally for a low Reynolds number using a vortex force decomposition. The auxiliary potentials that separate the total vortex force into lift and drag (or thrust) are obtained analytically by using an elliptic airfoil. With these auxiliary potentials, the addedmass components of the lift and drag (or thrust) coefficients are also obtained analytically for any heaving motion of the airfoil and for any value of the mean angle of attack α. The contributions of the leading and trailingedge vortices to the thrust during their down and upstroke evolutions are computed quantitatively with this formulation for different dimensionless frequencies and heave amplitudes (Stc and Sta ) and for several values of α. Very different types of flows, periodic, quasiperiodic, and chaotic described as Stc , Sta , and α, are varied. The optimum values of these parameters for maximum thrust efficiency are obtained and explained in terms of the interactions between the vortices and the forces exerted by them on the airfoil. As in previous numerical and experimental studies on flapping flight at low Reynolds numbers, the optimum thrust efficiency is reached for intermediate frequencies (Stc slightly smaller than one) and a heave amplitude corresponding to an advance ratio close to unity. The optimal mean angle of attack found is zero. The corresponding flow is periodic, but it becomes chaotic and with smaller average thrust efficiency as α becomes slightly different from zero.
 Instability and Transition

Instability mechanisms in a lowMachnumber reacting flow from coupled convectionreactiondiffusion equations
View Description Hide DescriptionIn this paper, instability mechanisms in a low Mach number reacting flow are investigated. Here, the emphasis is on the growth or decay of acoustic oscillations which arise from the acoustichydrodynamic interaction in a low Mach number reacting flow. Motivated by the studies in magnetohydrodynamics and atmospheric flows, we propose to investigate the acoustichydrodynamic coupling as a system of wavemean flow interaction. For example, a comparison with the heat fluctuation modified hydrodynamics associated with magnetohydrodynamics is useful in understanding this coupling. The wavelike acoustic disturbance is introduced here as a compressibility correction to the mean flow. Accounting for the multiple scales introduced by the weak compressibility, we derive a set of equations governing wavemean flow interaction in a reacting low Mach number flow. Sources such as volume expansion (which, in atmospheric flows arises due to the density variation with altitude) occur in reacting flows due to the heat release rate. This heat release rate, when coupled with the acoustic field, often leads to selfsustained thermoacoustic oscillations. In the study of such oscillations, we discover a relation between the acoustic pressure and second order thermal fluctuations. Further, using this relation, we discover the nonlinear coupling mechanism that would lead to selfsustained oscillations in a reacting low Mach number flow. This mechanism, represented by a coupled convection reaction diffusion system, is presented here for the first time. In addition to the acoustic pressure and temperature fields, we also discover the role of acoustic velocity field in the acoustichydrodynamic interaction through a convective and liftup mechanism.