# Latest papers in fluid mechanics

### Boundary slip phenomena in multicomponent gas mixtures

The slip phenomena in multicomponent gas mixtures are studied. The moment equations, derived from the linearized Boltzmann equation by using the 13-moment approximation of the Grad’s method, are used to obtain the full (containing the contribution from the Knudsen layer) and asymptotic (valid far from the plane physical boundary of the domain) expressions for the nonequilibrium macroscopic parameters of the mixture species. The latter relations are employed to deduce the expressions for the mixture slip velocity and the viscous, thermal, and diffusion slip coefficients by using the modified Maxwell method and the diffuse-specular model of molecule scattering on the wall. The derived relations for the slip coefficients are given in the convenient form expressed in terms of basic transport coefficients, such as partial viscosity and thermal conductivity coefficients, diffusion and thermal diffusion coefficients, and coefficients of molecule momentum accommodation at the wall. The expressions found are used to calculate the slip coefficients for binary (He-Ar) and ternary (He-Ar-Xe) gas mixtures. The numerical results are in good agreement with the data calculated by using other methods.

### Effects of surfactant transport on electrodeformation of a viscous drop

Author(s): Herve Nganguia, On Shun Pak, and Y.-N. Young

In this work we quantify the effects of surfactant transport on the deformation of a viscous drop under a DC electric field. We study how convective and diffusive transport of surfactants at drop surfaces influence the equilibrium and dynamic deformation of a leaky dielectric drop and a conducting d...

[Phys. Rev. E 99, 063104] Published Mon Jun 10, 2019

### Minimal surfaces in porous media: Pore-scale imaging of multiphase flow in an altered-wettability Bentheimer sandstone

Author(s): Qingyang Lin, Branko Bijeljic, Steffen Berg, Ronny Pini, Martin J. Blunt, and Samuel Krevor

High-resolution x-ray imaging is used in combination with measurements of permeability and capillary pressure to study multiphase flow in a porous sample. The authors characterized interfaces between brine and oil in a sandstone sample under a variety of conditions. Similar experimental approaches could be useful for other studies.

[Phys. Rev. E 99, 063105] Published Mon Jun 10, 2019

### Lagrangian acceleration timescales in anisotropic turbulence

Author(s): Peter D. Huck, Nathanael Machicoane, and Romain Volk

In a Lagrangian point of view, anisotropy in small time scales of turbulent flow is not yet well understood. Using Particle Tracking Velocimetry over nearly a decade in Taylor-scale based Reynolds numbers, we theoretically predict anisotropic acceleration correlation times of tracer particles in turbulent flow.

[Phys. Rev. Fluids 4, 064606] Published Mon Jun 10, 2019

### Kinetic energy budget of the largest scales in turbulent pipe flow

Author(s): C. Bauer, A. von Kameke, and C. Wagner

Very-large-scale motions contribute significantly to the kinetic energy in turbulent pipe flow. An analysis of the scale energy budget reveals a similar production mechanism compared to the small scales, but the interscale energy exchange is found to be quite different.

[Phys. Rev. Fluids 4, 064607] Published Mon Jun 10, 2019

### Flow and air-entrainment around partially submerged vertical cylinders

Author(s): Valentin Ageorges, Jorge Peixinho, and Gaële Perret

When a partially submerged vertical cylinder is moved at constant speed through water, the motion induces a turbulent wake, free-surface deformations up to the rupture, and air entrainment within the flow. Two modes of air entrainment are uncovered and the critical velocity is compared to a model.

[Phys. Rev. Fluids 4, 064801] Published Mon Jun 10, 2019

### Startup steady shear flow from the Oldroyd 8-constant framework

One good way to explore fluid microstructure, experimentally, is to suddenly subject the fluid to a large steady shearing deformation and to then observe the evolving stress response. If the steady shear rate is high enough, the shear stress and also the normal stress differences can overshoot, and then they can even undershoot. We call such responses nonlinear and this experiment shear stress growth. This paper is devoted to providing exact analytical solutions for interpreting measured nonlinear shear stress growth responses. Specifically, we arrive at the exact solutions for the Oldroyd 8-constant constitutive framework. We test our exact solution against the measured behaviors of two wormlike micellar solutions. At high shear rates, these solutions overshoot in stress growth without subsequent undershoot. The micellar solutions present linear behavior at low shear rates; otherwise, their behavior is nonlinear. Our framework provides slightly early underpredictions of the overshoots at high shear rates. The effect of salt concentration on the nonlinear parameters is explored.

### On the concept and theory of induced drag for viscous and incompressible steady flow

For steady flow, one usually decomposes the total drag into different components by wake-plane integrals and seeks their reduction strategies separately. Unlike the body-surface stress integral, the induced drag as well as the profile drag has been found to depend on the streamwise location of the wake plane used for drag estimate. It gradually diminishes as the wake plane moves downstream, which was often attributed to numerical dissipation. In this paper, we present an exact general force-breakdown theory and its numerical demonstrations for viscous incompressible flow over an arbitrary aircraft to address this puzzling issue. Based on the theory, the induced and profile drags do depend inherently on the wake-plane location rather than being merely caused by numerical dissipation. The underlying mechanisms are identified in terms of the components, moments, and physical dissipation of the Lamb-vector field produced by the aircraft motion. This theoretical prediction is fully consistent with the linear far-field force theory that the induced drag finally vanishes and the profile drag increases to the total drag at an infinitely far field for viscous flow. Moreover, as a product of this exact theory, a new compact midwake approximation for the induced drag is proposed for the convenience of routine wake survey in industry. Its prediction is similar to conventional formulas for attached flow but behaves much better for separated flow.

### Drag coefficient for a sedimenting and rotating sphere in a viscoelastic fluid

Author(s): Alfonso Castillo, William L. Murch, Jonas Einarsson, Baltasar Mena, Eric S. G. Shaqfeh, and Roberto Zenit

The image shows the flow field around a sphere that sediments and rotates simultaneously in a viscoelastic liquid.

[Phys. Rev. Fluids 4, 063302] Published Fri Jun 07, 2019

### Anomalous percolation flow transition of yield stress fluids in porous media

Author(s): Nicolas Waisbord, Norbert Stoop, Derek M. Walkama, Jörn Dunkel, and Jeffrey S. Guasto

Microfluidic experiments and simulations reveal an anomalous percolation transition for the flow of a yield stress fluid through a random porous medium. The evolution of the fluidized network results in a highly nonlinear flow conductivity and reveals a novel dispersion mechanism.

[Phys. Rev. Fluids 4, 063303] Published Fri Jun 07, 2019

### Computational study of the collapse of a cloud with $12\phantom{\rule{0.16em}{0ex}}500$ gas bubbles in a liquid

Author(s): U. Rasthofer, F. Wermelinger, P. Karnakov, J. Šukys, and P. Koumoutsakos

The collapse of a spherical cloud composed of 12 500 gas bubbles in water is studied. Wave propagation is captured and compared to existing reduced order models. Microjet formation is quantified and a dependence between microjet velocity magnitude and the strength of the collapse wave is identified.

[Phys. Rev. Fluids 4, 063602] Published Fri Jun 07, 2019

### Sensitivity of vortex pairing and mixing to initial perturbations in stratified shear flows

Author(s): Wenjing Dong, E. W. Tedford, M. Rahmani, and G. A. Lawrence

An investigation of the phase relationship between the Kelvin-Helmholtz mode and its subharmonic mode finds that it has important implications for vortex pairing and mixing in the flow by ensuring the instability. Results are consistent with laboratory observations for suppression of the subharmonic mode near an unfavorable phase.

[Phys. Rev. Fluids 4, 063902] Published Fri Jun 07, 2019

### On heat transport and energy partition in thermal convection with mixed boundary conditions

A two-dimensional square enclosure thermally insulated on the vertical walls and heated nonuniformly on the horizontal walls is numerically studied in comparison with the classical Rayleigh-Bénard (RB) convection in the range of Rayleigh number 105 ≤ Ra ≤ 109. Two possible configurations, namely, (1) HCCH and (2) HCHC, are studied in which a unit step function describes the conduction wall temperature as a combination of hot (H) and cold (C) temperatures. The first two letters (of HCCH or HCHC) represent the applied thermal conditions on the bottom wall and the last two letters represent those on the top wall. In the mentioned configurations, the average temperature difference between the bottom and top walls is zero, yet the complex convection state is observed. The diagonally aligned large-scale elliptic roll observed in the RB convection for the Rayleigh number Ra = 108 is found to be replaced by a circular roll in HCCH and a square roll in HCHC. The mean and fluctuating temperature fields in cases of HCCH and HCHC are significantly high as compared to the RB case. We found that heat transport is higher for HCCH and HCHC as compared to the RB convection in a range of 105 ≤ Ra < 108. The increase in heat transport is due to (1) an increase in the background potential energy in the case of HCCH and (2) an increase in the available potential energy in the case of HCHC, which is confirmed by using the global energy budget.

### Experimental study on cavity dynamics of projectile water entry with different physical parameters

In this paper, we investigate the influences of nose shape, impact velocity (8–14 m/s), and impact angle (60°–90°) on cavity dynamics when a projectile enters water. The Froude number, which characters the kinetic energy against gravitational potential, ranges from 280 to 850. It is found that the cavity diameter changes for different nose shapes, and an elongated cavity is achieved as the impact speed increases. The cavity pinch-off phenomenon is characterized. Experimental data reveal that the nose shape, impact velocity, and impact angle change the pinch-off depth and pinch-off time slightly by changing the occurrence time of the surface seal. For blunt nose shapes, greater impact velocity speeds up the surface seal and then quickens the pinch-off, thus reducing both the pinch-off depth and pinch-off time. Generally, the pinch-off depth follows the Fr1/3 law in our experiments. Cavity ripples were observed after pinch-off, and the wavelength, amplitude, and rippling frequency were measured. The wavelength of a ripple remains constant throughout, and all ripples are fixed with the experimental frame. The rippling frequencies are approximately identical to the Minnaert frequency. The impact velocity significantly changes the rippling frequency by affecting the radius of the air cavity.

### Electric field-induced pinch-off of a compound droplet in Poiseuille flow

We address the pinch-off dynamics of a compound droplet that is suspended in a carrier fluid in a parallel plate microchannel. The droplet is subjected to a transverse electric field in the presence of an imposed pressure-driven flow. When a concentric compound droplet migrates in a pressure driven flow, the inner droplet deviates from the concentric position and forms an eccentric configuration that finally leads to the pinch-off of the outer shell. Our results reveal that the temporal evolution of droplet eccentricity as well as the kinetics of the thinning of the outer droplet is markedly influenced by the strength of the electric field as well as the electric properties of the fluids. We also bring out the conversion of different modes of droplet pinch-off, such as the equatorial cap breakup or the equatorial hole-puncture mode, by altering the electric field strength and electrical properties of the fluids. We also identify the relevant pointers that dictate the pinch-off time as well as the location of the pinch-off. This, in turn, opens up novel means of modulating the morphology of double emulsion in a confined channel by applying an electric field.

### Exact results on the large-scale stochastic transport of inertial particles including the Basset history term

The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.

### Direct numerical simulation of transitional and turbulent round jets: Evolution of vortical structures and turbulence budget

Direct numerical simulation of transitional and turbulent round jets is reported in a comparative framework. Such a comparison is central toward revealing the roles that molecular viscosity and vorticity intensification play in the evolution of jets. The initial and intermediate evolution is differentiated based on the assessment of the starting jet, roll-up frequency, dynamics of vortex rings, and emergence of the secondary instability. Long-term behavior is differentiated based on the assessment of preferred mode frequency, time averaged vortical structures, half jet-width, and volume flow rate obtained from the time-averaged velocity field. The present study demonstrates that viscous damping of cross-stream vorticity plays a key role in establishing helical instability as the dominant mode in long-term evolution of the transitional jet. On the contrary, varicose mode is dominant in the turbulent jet, despite preferred mode frequency being the same in both cases. Finally, a novel attempt is made toward comparing individual terms constituting turbulence budget between both regimes. Through such a comparison, relative dominance of various transport mechanisms governing the evolution of turbulence kinetic energy [math] is revealed. It is observed that terms accounting for a forward cascade of [math] from inertial to smallest scales are comparatively larger for the turbulent jet, while those accounting for the backscatter of [math] are comparatively larger for the transitional jet. It is also established that turbulence dissipation is evidently the same for both jets. Thus, the property of turbulence dissipation being independent of Reynolds number for turbulent jets can also be extrapolated to transitional jets.

### A new additive decomposition of velocity gradient

To avoid the infinitesimal rotation nature of the Cauchy-Stokes decomposition of velocity gradient, the letter proposes an new additive decomposition in which one part is a SO(3) rotation tensor Q = exp W.

### Salt comets in hand sanitizer: A simple probe of microgel collapse dynamics

Author(s): Arash Nowbahar, Art O'Connor, Vincent Mansard, Patrick Spicer, and Todd M. Squires

A single grain of salt, placed on the surface of everyday hand sanitizer, slowly bores a hole through it, leaving a milky “comet trail” in its wake. The fall speed does not depend on the size of the salt grain, but does depend on salt type, and reveals subtle aspects of collapsing microgels.

[Phys. Rev. Fluids 4, 061301(R)] Published Thu Jun 06, 2019

### Regularized Stokeslet rings: An efficient method for axisymmetric Stokes flow with application to the growing pollen tube

Author(s): J. Tyrrell, D. J. Smith, and R. J. Dyson

The “regularized ringlet,” which is the fundamental solution to axisymmetric Stokes flow driven by a ring of smoothed point forces, is derived and used to model cytosolic flow in the growing pollen tube.

[Phys. Rev. Fluids 4, 063102] Published Thu Jun 06, 2019