# Latest papers in fluid mechanics

### A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries

A simple parameter, called the Aneurysm number (An) which is defined as the ratio of transport to vortex time scales, has been shown to classify the flow mode in simplified aneurysm geometries. Our objective is to test the hypothesis that An can classify the flow in patient-specific intracranial aneurysms (IA). Therefore, the definition of this parameter is extended to anatomic geometries by using hydraulic diameter and the length of expansion area in the approximate direction of the flow. The hypothesis is tested using image-based flow simulations in five sidewall and four bifurcation geometries, i.e., if An ≲ 1 (shorter transport time scale), then the fluid is transported across the neck before the vortex could be formed, creating a quasi-stationary shear layer (cavity mode). By contrast, if An ≳ 1 (shorter vortex time scale), a vortex is formed. The results show that if An switches from An ≲ 1 to An ≳ 1, then the flow mode switches from the cavity mode to the vortex mode. However, if An does not switch, then the IAs stay in the same mode. It is also shown that IAs in the cavity mode have significantly lower An, temporal fluctuations of wall shear stress and oscillatory shear index (OSI) compared to the vortex mode (p < 0.01). In addition, OSI correlates with An in each flow mode and with pulsatility index in each IA. This suggests An to be a viable hemodynamic parameter which can be easily calculated without the need for detailed flow measurements/ simulations.

### A non-dimensional parameter for classification of the flow in intracranial aneurysms. I. Simplified geometries

Non-dimensional parameters are routinely used to classify different flow regimes. We propose a non-dimensional parameter, called Aneurysm number (An), which depends on both geometric and flow characteristics, to classify the flow inside aneurysm-like geometries (sidewalls and bifurcations). The flow inside aneurysm-like geometries can be widely classified into (i) the vortex mode in which a vortex ring is formed and (ii) the cavity mode in which a stationary shear layer acts similar to a moving lid of a lid-driven cavity. In these modes, two competing time scales exist: (a) a transport time scale, Tt, which is the time scale to develop a shear layer by transporting a fluid particle across the expansion region, and (b) the vortex formation time scale, [math]. Consequently, a relevant non-dimensional parameter is the ratio of these two time scales, which is called Aneurysm number: An = Tt/[math]. It is hypothesized, based on this definition, that the flow is in the vortex mode if the time required for vortex ring formation [math] is less than the transport time Tt (An ≳ 1). Otherwise, the flow is in the cavity mode (An ≲ 1). This hypothesis is systematically tested through numerical simulations on simplified geometries and shown to be true through flow visualizations and identification of the main vortex and shear layer. The main vortex is shown to evolve when An ≳ 1 but stationary when An ≲ 1. In fact, it is shown that the flows with An ≲ 1 (cavity mode) are characterized by much smaller fluctuations of wall shear stress and oscillatory shear index relative to flows with An ≳ 1 (vortex mode) because of their quasi-stationary flow pattern (cavity mode) compared to the evolution and breakdown of the formed vortex ring (vortex mode).

### Elastohydrodynamics of swimming helices: Effects of flexibility and confinement

Author(s): John LaGrone, Ricardo Cortez, and Lisa Fauci

We examine the swimming of an elastic helix rotated by a torque at its base, both in free-space and confined to a tube. The image depicts the envelope of an excursion of a filament centerline over one rotation; the blue is the surface of the finite-radius helical filament at one snapshot in time.

[Phys. Rev. Fluids 4, 033102] Published Mon Mar 25, 2019

### Experimental study of convection in the compressible regime

Author(s): Rémi Menaut, Yoann Corre, Ludovic Huguet, Thomas Le Reun, Thierry Alboussière, Michael Bergman, Renaud Deguen, Stéphane Labrosse, and Marc Moulin

Compressible thermal convection is experimentally studied. In the large apparent gravity of a rotor centrifuge, using xenon gas, an adiabatic temperature difference of 14 °C over a height equal to 4 cm is obtained. Large Coriolis forces impose a quasigeostrophic regime.

[Phys. Rev. Fluids 4, 033502] Published Mon Mar 25, 2019

### Diffusion-driven transition between two regimes of viscous fingering

Author(s): Thomas E. Videbæk and Sidney R. Nagel

Diffusion between miscible fluids in the viscous-fingering instability produces an unexpected transition into a novel pattern. Usually thought of as a two-dimensional phenomena, this works shows the importance of three-dimensional structure to the patterns that form.

[Phys. Rev. Fluids 4, 033902] Published Mon Mar 25, 2019

### Inviscid flow separation at the crest of an erodible dune

Author(s): F. Charru and P. Luchini

Potential flow analysis is used to find the elevation profile of traveling dunes of given volume and locate the brink point where the flow separates without singularity.

[Phys. Rev. Fluids 4, 034304] Published Mon Mar 25, 2019

### Streamline segment statistics propagation in inhomogeneous turbulence

Author(s): A. Rubbert, M. Albers, and W. Schröder

Streamline segment statistics are collected from tomographic particle image velocimetry and direct numerical simulation data of a turbulent wavy channel flow. The model equation for such statistics is adapted for inhomogeneous turbulence. The novel formulation is applied to explain the observations and identify the locally acting mechanisms.

[Phys. Rev. Fluids 4, 034605] Published Mon Mar 25, 2019

### Vorticity dynamics of the three-dimensional Taylor-Green vortex problem

The three-dimensional (3D) Taylor-Green Vortex (TGV) flow problem has been used to study turbulence from genesis to eventual decay governed by the 3D Navier-Stokes equation. The evolution of the TGV shows that the solution becomes unstable at very early times and eventually becomes turbulent, but a study of this transition has not been advanced so far. The computations are performed using a high accuracy compact scheme on a uniform grid, with the fourth-order Runge-Kutta time integration method. The vector potential-vorticity ([math])-formulation of the governing equations is solved in a cubic periodic domain with one complete basic unit of a TGV cell in the interior of the domain at t = 0. The TGV problem allows one to study the vorticity dynamics using highly accurate formulation because of periodic boundary conditions. Simulations performed for different Reynolds numbers and grid resolutions reveal that numerical error in computations induce a period-doubling bifurcation, which leads to new spatial symmetries maintained up to intermediate times, followed by simultaneous stretching and fragmentation of vortices resulting in a decaying turbulent flow. The compensated energy spectrum of the 3D TGV flow displays inertial subrange at t = 9, after which the generated turbulence starts decaying. The power law for turbulent kinetic energy decay is analyzed, and the decay exponent is noted to approach unity as time increases.

### Thermal effects on the instability of coaxial liquid jets in the core of a gas stream

The breakup of coaxial liquid jets in a co-flowing gas stream under the radial thermal field is studied by the linear instability theory. A simplified physical model is established, and an analytical dimensionless dispersion relation for temporally axisymmetric perturbations is derived and solved numerically. The outer liquid-gas surface tension coefficient is assumed to be a linear function of temperature. Due to the radial temperature gradients, the time-dependent spatial variation of surface tension gives rise to a shear stress and induces Marangoni force upon the flow. The effects of different process parameters on the characteristics of unstable modes including the para-sinuous mode and the para-varicose mode are explored. It is found that the para-sinuous mode always dominates the jet instability in the parametric regions and the increasing temperature ratio of the surrounding gas stream and the inner liquid jet (T31) can reduce the maximum growth rates of unstable modes and corresponding dominant wavenumbers. The Reynolds number destabilizes the jet instability, and the Weber number suppresses it at relatively long wavelengths for both isothermal and non-isothermal situations. The Marangoni number and the Peclet number have a destabilizing effect for T31 < 1, but it is opposite for T31 > 1. These theoretical predictions would provide insight into underlying physical mechanisms of thermal jet breakup and compound droplet formation.

### Erratum: “A sharp interface immersed boundary method for vortex-induced vibration in the presence of thermal buoyancy” [Phys. Fluids 30, 023603 (2018)]

### Publisher’s Note: “Advection of droplet collision in centrifugal microfluidics” [Phys. Fluids 31, 032003 (2019)]

### Temperature dependence of shock wave structure in helium and neon

Temperature dependence of a planar shock wave in helium and neon is studied by the direct simulation Monte Carlo method based on ab initio potentials. A quantum approach to interatomic interactions used here allows us to carry out calculations over a wide temperature range beginning from 1 K up to 5000 K. Moreover, for high temperatures, the quantum approach requires less computational effort than the classical one. Three gaseous species are considered: helium-3, helium-4, and neon. The problem is solved for three values of the Mach number Ma = 2, 5, 10. No influence of the quantum effects has been detected within the numerical error for the temperature of 300 K and higher. For temperatures lower than 300 K, the influence of the quantum effects in helium exceeds the numerical error and reaches 230%. In the case of neon, the quantum effect does not exceed 2% in the whole temperature range considered in the present work. A comparative analysis of flow-fields in shock waves at various temperatures points out a strong influence of the temperature ahead of a shock wave on its structure. The numerical data provided in the supplementary material can be used to model any flow of helium and neon in a wide range of temperatures.

### Wave breaking in undular bores generated by a moving weir

If a weir is dragged through a wave flume, the upstream flow takes the form of an undular bore propagating ahead of the weir. It was found previously in the work of Wilkinson and Banner (“Undular bores,” in 6th Australian Hydraulics and Fluid Mechanics Conference, Adelaide, Australia, 1977) that the leading wave of the undular bore will break if the bore strength given by the ratio of downstream to upstream flow depth exceeds a certain value. In the present work, a Boussinesq system is used to study the situation in a numerical wave tank. It is found that if a convective breaking criterion is used to indicate wave breaking, then the critical bore strength of the numerical model agrees with the experimental value of Wilkinson and Banner up to an error of less than 2%.

### Effect of soluble surfactants on vertical liquid film drainage

A mathematical model is established to investigate the gravity-driven drainage of vertical films containing a soluble surfactant by considering the coupling effect of surface elasticity, adsorption coefficient, and surfactant solubility. The lubrication theory is applied to derive the four coupled nonlinear partial differential equations describing the film thickness, surface velocity, and surfactant concentration on the surface and in the bulk. Simulated results showed that the surface elasticity, adsorption coefficient, and surfactant solubility are indispensable factors in the drainage process of a liquid film containing a soluble surfactant. In the initial stage of the drainage, the initial film thickness increases with increasing surface elasticity and the film surface tends to be more rigid. With further drainage, the liquid film exhibits different notable features for high and low elasticity. For low surface elasticity, the surfactant distribution produces a positive Marangoni effect, which counteracts gravity. However, for high surface elasticity, the film surface exhibits a reverse Marangoni effect, which accelerates the drainage and leads to an unstable film. As the solubility decreases, both the film stability and initial surface elasticity enhance. The surface elasticity gradually approaches a limiting dilational elasticity modulus owing to the film thinning. For a large Ks, the film surface is insufficient to produce a strong Marangoni effect and then the liquid film tends to easily destabilize. For a small Ks, the soluble surfactant is similar to an insoluble surfactant, and the film is much thicker in the later stage of the drainage.

### Dynamic behavior of water drops impacting on cylindrical superhydrophobic surfaces

This paper investigates the impact behavior between water drops with different velocities and cylindrical superhydrophobic surfaces with various diameters and presents two possible outcomes of drop impact, which are asymmetric rebound and stretched breakup. Due to the special cylindrical topology of the surface, drops undergo an asymmetric spreading and retracting process in the azimuthal and the axial direction, which results in three types of asymmetric rebound, including jug-like rebound, wing-like rebound, and rebound breakup. The stretched breakup is observed in the collision of drops with higher impact velocities and smaller cylinder diameters. The diameter ratio D* and Weber number We are found to be the determinants of the bouncing patterns. With the decrease in the diameter ratio D* or the increase in the Weber number We, the bouncing patterns transformed from jug-like rebound through wing-like rebound and finally to stretched breakup. We put forward a modification form of the Weber number (α = We/D*) affected by the diameter ratio D*, indicating the ratio between the inertia force and the surface tension, as the criterion to distinguish the upward rebound from the downward stretch, which helps obtain the linear relation of critical Wecr and D*cr. Furthermore, asymmetric rebound and stretched breakup could effectively shorten the contact time between drops and substrates. The contact time is found to be mainly determined by the dimensionless parameter α. The correlation between the dimensionless contact time and the dimensionless parameter α is demonstrated to be τc ∝ αn.

### Phase-field modeling of an immiscible liquid-liquid displacement in a capillary

Author(s): S. Prokopev, A. Vorobev, and T. Lyubimova

We develop a numerical model for a two-phase flow of a pair of immiscible liquids within a capillary tube. We assume that a capillary is initially saturated with one liquid and the other liquid is injected via one of the capillary's ends. The governing equations are solved in the velocity-pressure f...

[Phys. Rev. E 99, 033113] Published Thu Mar 21, 2019

### Flow structures govern particle collisions in turbulence

Author(s): Jason R. Picardo, Lokahith Agasthya, Rama Govindarajan, and Samriddhi Sankar Ray

Direct numerical simulations find that rapid head-on collisions of particles mostly occur in regions of straining compared to vortical regions, and that intense vortex tubes conspire with enveloping straining sheets, in the form of vortex-strain worm-rolls, to generate violent collisions.

[Phys. Rev. Fluids 4, 032601(R)] Published Thu Mar 21, 2019

### Scattering of liquid droplets from axisymmetric targets

Author(s): Jacob Hale and Jacob Boudreau

A meniscus formed around a vertical cylinder looks and behaves like a repulsive central potential, deflecting noncoalescent droplets analogous to Rutherford scattering. The scattering behavior is used to probe the potential of the cylindrical meniscus, confirming theoretical models for its shape.

[Phys. Rev. Fluids 4, 033602] Published Thu Mar 21, 2019

### Modal analysis with proper orthogonal decomposition of hypersonic separated flows over a double wedge

Author(s): Ozgur Tumuklu, Deborah A. Levin, and Vassilis Theofilis

A study combining direct simulation Monte Carlo simulations with window proper orthogonal decomposition investigates the temporal characteristics of unsteady, laminar shock boundary-layer interactions for different gas mixtures for an Edney type-IV flow.

[Phys. Rev. Fluids 4, 033403] Published Tue Mar 19, 2019

### Imbibition and evaporation of droplets of colloidal suspensions on permeable substrates

Author(s): Truong Pham and Satish Kumar

Colloidal particles inside an evaporated droplet on a solid substrate are often preferentially deposited at the droplet contact line, a phenomenon known as the coffee-ring effect. A study shows how this phenomenon is affected by the permeability of the substrate.

[Phys. Rev. Fluids 4, 034004] Published Tue Mar 19, 2019