Physical Review Fluids

Emergence of metachronal waves in active microtubule arrays

Stephen E. Martin, Matthew E. Brunner, and Joshua M. Deutsch

Phys. Rev. Fluids 4, 103101 (2019) - Published 28 October, 2019

Groups of active microtubule bundles spontaneously form wavelike patterns, and the physical mechanism for this hasn’t been well understood. We present a first-principles model that exhibits these waves with only a handful of inputs, and predicts how observations depend on experimental conditions.

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The physical mechanism behind the spontaneous formation of metachronal waves in microtubule arrays in a low-Reynolds-number fluid has been of interest for the past several years, yet is still not well understood. We present a model implementing the hydrodynamic coupling hypothesis from first principles and use this model to simulate kinesin-driven microtubule arrays and observe their emergent behavior. The results of simulations are compared with known experimental observations by Sanchez et al. [Science 333, 456 (2011)]. By varying parameters, we determine regimes in which the metachronal wave phenomenon emerges and categorize other types of possible microtubule motion outside these regimes.

Stability of two-layer miscible convection

Fryderyk Wilczynski and David W. Hughes

Phys. Rev. Fluids 4, 103502 (2019) - Published 28 October, 2019

We study the onset of convection in two superposed fluid layers that have different properties. Depending on the parameters of the problem, the most unstable mode can take one of three distinct forms: whole layer solutions, localized solutions, and segregated solutions.

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The dynamics at the edge of fusion confinement devices involves the motion of plasma across two regions—the core and the scrape-off layer—that may have very different properties. Motivated by this problem, and exploiting the analogy between the equations governing plasma interchange dynamics and those of classical Rayleigh-Bénard convection, we consider the linear stability of two-dimensional, two-layer miscible convection. We focus specifically on the influence of three particular parameters: the ratio of the viscosities in the two layers, the ratio of the thermal diffusivities, and the ratio of the depths of the two layers. The key result is that, depending on the parameters of the problem, the most unstable mode can take one of three quite distinct forms: whole layer solutions, in which the eigenfunctions of the stream function and temperature extend over both layers of fluid; localized solutions, with the velocity cells or the temperature perturbation (or both) confined to just one of the layers; and segregated solutions, in which the fluid motion and temperature perturbation are confined to different fluid layers.

Modeling Ekman and quasi-static magnetohydrodynamic turbulence using Pao's hypothesis

Mohammad Anas and Mahendra K. Verma

Phys. Rev. Fluids 4, 104611 (2019) - Published 28 October, 2019

We generalize Pao’s hypothesis for hydrodynamic turbulence to derive the energy spectrum for two-dimensional Ekman turbulence. The model captures the steepening of the spectrum caused by Ekman friction. The paper also covers a similar model for quasi-static magnetohydrodynamic turbulence.

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Two-dimensional (2D) turbulence with Ekman friction and quasi-static magnetohydrodynamic (QS MHD) turbulence are complex flows. In this paper, we present models for these flows by extending Pao's hypothesis [Phys. Fluids 8, 1063 (1965)] for hydrodynamic turbulence to them. For 2D Ekman turbulence, the energy spectrum predicted by the model is steeper than its hydrodynamic counterpart due to Ekman friction. The model predictions are consistent with earlier theoretical predictions and experimental and numerical results. Similarly, the model for QS MHD turbulence predicts a steeper energy spectrum due to Joule dissipation; the model predictions fit with earlier numerical results quite well.

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Density contrast matters for drop fragmentation thresholds at low Ohnesorge number

Florence Marcotte and Stéphane Zaleski

Phys. Rev. Fluids 4, 103604 (2019) - Published 25 October, 2019

Droplet breakup is classically controlled by the ratio of flow kinetic to surface energy (Weber number). From axisymmetric simulations and simple model-scaling arguments we show how the critical Weber numbers for breakup and bursting/stripping transition depend on the droplet/carrier density ratio.

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We address numerically the deformation and fragmentation dynamics of a single liquid drop subject to impulsive acceleration by a unidirectional gas stream. The density ratio between the liquid and gaseous phases is varied in the $10 - 2000$ range and comparisons are made with recent drop breakup experiments. We show for low Ohnesorge numbers that the liquid-gas density contrast significantly modifies the critical Weber number for the transition between bursting and stripping fragmentation regimes, on the one hand, and for drop fragmentation, on the other hand. We suggest a simple theoretical argument to predict the transitional Weber number as a function of the density contrast and show that the stabilizing influence of small contrasts can be explained by inertial effects in the nonlinear coupling between drop stretching and centroid acceleration.

Convective dispersion of particles in a segmented flow

Wafa Bouhlel, S. Danial Naghib, Jérôme Bibette, and Nicolas Bremond

Phys. Rev. Fluids 4, 104303 (2019) - Published 25 October, 2019

Experiments show that a suspension confined between two bubbles and flowing in a pipe may become heterogeneous when liquid inertia comes into play. Indeed, inertial migration of the particles along the radial direction modifies the axial flux of particles linked to the Poiseuille flow.

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Convective dispersion of solutes is inherent to flow in channels because of the nonuniformity of the velocity profile. When diffusion is negligible, for large particles for example, the trajectory of particles can be solely described by a kinematic approach. Here, we investigate such a phenomenon for micrometer-size beads flowing in a circular pipe. We show that the presence of large bubbles, namely in the case of a segmented flow, either prevents the convective dispersion or leads to the accumulation of particles at the rear of the bubble moving in front. The destabilization of the initially homogeneous suspension occurs when liquid inertia comes into play. Indeed, for moderate Reynolds number of the particles, particles move away from the wall, thus exploring different flow lines that finally impact the axial dispersion features. Moreover, since the bubbles impose an axial boundary condition of the mean velocity, a net flux of particles directed along the flow direction is built up above a critical particle Reynolds number. This work is motivated by the understanding of the flow behavior of biological samples, and especially in the context of cell encapsulation.

Passive propulsion in turbulent flows

J. Yang, M. Davoodianidalik, H. Xia, H. Punzmann, M. Shats, and N. Francois

Phys. Rev. Fluids 4, 104608 (2019) - Published 25 October, 2019

The ability of a device to exploit the energy of a flow to generate thrust is the essence of passive propulsion. Such energy conversion is challenging when a flow is turbulent. Our study sheds light on turbulence-driven propulsion and its consequences for turbulent transport of anisotropic objects.

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The ability of a device to exploit the energy of a flow to generate thrust is the main feature of passive propulsion. In a turbulent flow, such energy conversion is challenging due to the unpredictable and disordered fluid motion. In wave-driven turbulence, it has recently been demonstrated that asymmetric floating rotors can tap the energy of ambient fluctuations to fuel directed rotation. Here we report on the dynamics of asymmetric floating vehicles capable of passively propelling themselves in two-dimensional turbulence. We show experimentally how the shape of a floater and its rotational dynamics conspire to allow harvesting energy of the turbulent fluid motion. The translation and rotation of the floater are shown to be strongly coupled. The propulsion velocity and the rotational diffusion timescale depend on the relative size of the floating vehicle with respect to the turbulence forcing scale. The geometry of the floater is investigated in the range of circular-sector-shaped objects and a shape optimizing its propulsion is identified. At times larger than the rotational diffusion timescale, our results shed light on a substantial increase of the turbulent diffusion coefficient of anisotropic objects due to the coupling between propulsion and rotational diffusion.

High-resolution Navier-Stokes simulations of Richtmyer-Meshkov instability with reshock

Man Long Wong, Daniel Livescu, and Sanjiva K. Lele

Phys. Rev. Fluids 4, 104609 (2019) - Published 25 October, 2019

Variable-density effects at a twice shocked mixing layer between gases are studied through Navier-Stokes adaptive mesh refinement simulations. Development of instability after first shock and chaotic mixing after reshock are discussed for 2D and 3D cases and as a function of the Reynolds number.

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The interaction of a Mach-1.45 shock wave with a perturbed planar interface between sulfur hexafluoride and air is studied through high-resolution two-dimensional (2D) and three-dimensional (3D) shock-capturing adaptive mesh refinement simulations of multispecies Navier-Stokes equations. The sensitivities of time-dependent statistics on grid resolution for 2D and 3D simulations are evaluated to ensure the accuracy of the results. The numerical results are used to examine the differences between the development of 2D and 3D Richtmyer-Meshkov instability during two different stages: (1) initial growth of hydrodynamic instability from multimode perturbations after first shock and (2) transition to chaotic or turbulent state after reshock. The effects of the Reynolds number on the mixing in 3D simulations are also studied through varying the transport coefficients.

Small-scale energy cascade in homogeneous isotropic turbulence

Mohamad Ibrahim Cheikh, James Chen, and Mingjun Wei

Phys. Rev. Fluids 4, 104610 (2019) - Published 25 October, 2019

The relationship between the energy flow and kinematics of the small-scale is investigated in homogeneous isotropic turbulence. The study employs a high order continuum theory to decouple the rotational motion from the translational motion and investigate the contribution of each field alone.

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The dynamics behind the multiscale energy transfer in turbulent flows is investigated in a numerical simulation of homogeneous isotropic turbulence (HIT). The investigation relies on conservation laws derived from the incompressible morphing continuum theory on the basis of the Boltzmann-Curtiss kinetic theory. The resulting conservation laws reveal the existence of small-scale routes for the flow of energy, which broadens the view on energy cascade (forward or inverse). The comparison of the turbulence characteristic with the reference study indicates that the turbulence features in both frameworks are equivalent at the global and small-scales; however, the presented framework shows a more detailed energy flow mechanism, while maintaining the same global dissipation rate. The study reveals that the theoretical small-scale structures can represent the small-scale structures in the turbulent flow. Finally, the energy analysis is carried out based on the presented conservation laws. The analysis reveals that at the small-scale both forward and inverse energy cascade exist in HIT; however, an overall negative energy flux (forward cascade) is present globally. Finally, the energy analysis shows that the energy cascade is highly dependent on the rotation of the small-scale structure as well as their translational motion.

Editorial: Introduction to the 36th Annual Gallery of Fluid Motion and Summary of 19 Years of Winners (Atlanta, Georgia, USA 2018)

David Hu, Brian Thurow, Ken Kiger, and Alexander Lee

Phys. Rev. Fluids 4, 100002 (2019) - Published 24 October, 2019

Shaky life of a water drop in an anise oil-rich environment

Óscar R. Enríquez, Daniel Robles, Pablo Peñas-López, and Javier Rodríguez-Rodríguez

Phys. Rev. Fluids 4, 100502 (2019) - Published 24 October, 2019

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Premixed-flame oscillations in narrow channels

Daniel Martínez-Ruiz, Fernando Veiga-López, and Mario Sánchez-Sanz

Phys. Rev. Fluids 4, 100503 (2019) - Published 24 October, 2019

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Dripping down the rivulet

Gaétan Lerisson, Pier Giuseppe Ledda, Gioele Balestra, and François Gallaire

Phys. Rev. Fluids 4, 100504 (2019) - Published 24 October, 2019

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This paper is associated with a video winner of a 2018 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2018.GFM.V0070.