# Latest papers in fluid mechanics

### Droplet mobilization at the walls of a microfluidic channel

The mechanism of dynamic wetting and the fluid dynamics during the onset of droplet mobilization driven by a microchannel flow are not clearly understood. In this work, we use microparticle tracking velocimetry to visualize the velocity distribution inside the droplet both prior to and during mobilization. Time-averaged and instantaneous velocity vectors are determined using fluorescent microscopy for various capillary numbers. A circulating flow exists inside the droplet at a subcritical capillary number, in which case the droplet is pinned to the channel walls. When the capillary number exceeds a critical value, droplet mobilization occurs, and this process can be divided into two stages. In the first stage, the location of the internal circulation vortex center moves to the rear of the droplet and the droplet deforms, but the contact lines at the top walls remain fixed. In the second stage, the droplet rolls along the solid wall, with fixed contact angles keeping the vortex center in the rear part of the droplet. The critical capillary number for the droplet mobilization is larger for the droplet fluid with a larger viscosity. A force-balance model of the droplet, considering the effect of fluid properties, is formulated to explain the experimental trends of advancing and receding contact angles with the capillary number. Numerical simulations on internal circulations for the pinned droplet indicate that the reversed flow rate, when normalized by the inlet flow rate and the kinematic viscosity ratio of the wetting and nonwetting phases, is independent of the capillary number and the droplet composition.

### Spreading and penetration of a micro-sized water droplet impacting onto oil layers

This paper describes a theoretical and numerical investigation of the impact dynamics and outcomes of a microsized water droplet falling onto an oil layer. The shape of the water droplet floating on the oil layer is predicted theoretically to understand the balancing of the three interfacial tensions. Direct numerical simulations coupled with a three-phase volume-of-fluid method are performed on an axisymmetric model, considering the balancing and motion of the triple-line. The effects of the impact velocity, viscosity ratio of oil and water, height of the oil layer, and the combination of the three interfacial tensions on the impact dynamics and outcomes are systematically studied. Regime diagrams of the nonpenetration and penetration outcomes are obtained under different combinations of the flow and physical parameters. It is found that the balance among the three interfacial tensions is well maintained at the triple-line due to the low capillary number. The maximum horizontal spreading of the water droplet is proportional to the square root of the Weber number when the impact velocity is low. Moreover, the maximum penetration for high impact velocities is independent of the spreading parameter. To understand the lower transition between nonpenetration and penetration, the critical penetration distance at which the triple-line is about to collapse is obtained from simulation results as a function of the spreading parameter, and these indicate weak dependence on the viscosity ratio. A semiempirical model is used to predict the boundary of lower transitions, and these are in good agreement with the simulations results.

### Experimental investigation of turbulent flow in a rotating straight channel with continuous ribs

We experimentally study the combined effects of continuous ribs and rotations constructed in a square duct on the turbulent flows and flow separation. The ribs obstruct the channel by 10% of its height and are arranged in three different pitch-to-height ratios (P/e) of 10, 12, and 15. The Reynolds number (Re = ρU0D/μ) is fixed at 10 000, and the rotation number (Ro = ΩD/U0) varies from 0 to 0.52. A time-resolved particle image velocimetry system is applied to provide insights into the main flow and turbulence mechanism. Results show that rotation significantly changes main flow and turbulent characteristics. In particular, a main flow phenomenon has been found: on account of the secondary flow near the ribs, velocity profile deflects to the leading side under a low rotation number, and when Ro rises to 0.48 (critical value), velocity profile deflects to the trailing side. It gives an insight into main flow in a ribbed channel. Reattachment law has been investigated, which can optimize heat transfer by optimize rib arrangement. A proper orthogonal decomposition analysis is also considered to identify the spatial characteristics of the superimposed flow fields. Based on the experimental data, the existence of ribs with different P/e ratios and Coriolis forces play significant roles in rib-generated vortices as well as their turbulent activities.

### Small droplet bouncing on a deep pool

Droplet bouncing on liquid surfaces frequently occurs for low-Weber-number impacts. Previous studies typically used large droplets with oscillation initiated by their creation process but without determining the effects of these oscillations. Here, we use small droplets, providing the means to reduce oscillations to show that the probability of the droplet bounce does not depend on the droplet oscillations. The time from the moment of contact to the maximum penetration depth was found to be independent of the Weber number for droplets of fixed diameter but increased with an increase in diameter. Both the maximum penetration depth and the maximum rebound height increased monotonically with the Weber number. A simple model predicting the maximum penetration depth was proposed and validated through comparison with experimental data.

### Accelerating viscous flow past a wedge

This paper presents direct numerical simulations of accelerated viscous flow past an infinite wedge with a focus on the effect of the accelerating rate on vortex dynamics and material transport near the wedge tip. The wedge angle ranges π/3 ≤ βπ ≤ 5π/6 and the acceleration rate is 0 ≤ p ≤ 1. Since the wedge is infinite, the inviscid self-similar analysis predicts that the solution of one viscosity at a time is the same as the solution of a different viscosity at a scaled time. This theoretical prediction is numerically verified in the current work. Evolution of the vorticity, streamlines, and streaklines is shown in great detail. In the vorticity field, hierarchical vortex separations at the wedge tip are observed, which associate with multiple circulating regions in the streamlines. We also compare the solution at varying acceleration rates and wedge angles and explore the scaling laws in the solution. Streaklines are used to illustrate material transport in the fluid flow. The streaklines form two spirals, a major one that corresponds to the starting vortex and a second one that appears near the wedge tip. The formation of both the major and secondary spirals are investigated and diagnosed using the strain rate in the fluid flow.

### A theoretical model of thermo-dynamic interpretation for the Pettit effect and associated heat transport processes

Based on several fundamental preassumptions, a one-dimensional convection-diffusion equation for heat transport inside liquid wedges causing the Pettit effect is proposed. With a hot or cold thermode placed at the middle of the liquid wedge, the average temperature of the liquid wedge determined from the convection-diffusion equation proposed shows a maximum, which corresponds to a particular liquid flow rate. The state achieved at this maximum temperature is believed to be the most stable for its minimum interfacial energy. The theory suggests a thermodynamic mechanism, which drives the liquid to flow in directions corresponding to those observed in experiments. It is believed that this work improves the thermodynamic interpretation proposed previously since the new-form convection-diffusion equation is more rigorously deduced and is thus more accurate. In addition, the work also presents a detailed theoretical analysis for heat transport. The results show that, in practical situations, the manifested heat-transport behaviors of a liquid wedge are governed by conductive heat transfer because convective heat flow is self-balancing due to the restriction by the law of mass conservation. Meanwhile, based on the asymmetric features of the conductive heat flows transiting within two different halves of the liquid wedge, a closed-loop formed by connecting a hot-thermode-driven liquid wedge and a cold-thermode-driven liquid wedge is proposed such that a hot thermode-cold thermode loop can lead to controllable heat transfer with which targeted heating or cooling may be realized. The effect may reveal the technical principles upon which novel small-size thermal engines, pumps, heaters, and coolers can be built.

### Numerical investigation of flow-induced vibrations of two cylinders in tandem arrangement with full wake interference

This paper presents a numerical investigation on flow-induced vibration (FIV) of two elastically mounted cylinders in a tandem arrangement at subcritical Reynolds numbers. The tandem spacing between the cylinder centers is set at four cylinder diameters, placing the FIV problem within the full wake interference regime. A fluid-structure interaction numerical methodology based on a two-dimensional discrete vortex method is developed and applied to the FIV simulation of two cylinders. To investigate the effect of the upstream wake frequency and Reynolds number on the FIV response of the downstream cylinder separately, two experimental cases are designed. In one case, the FIV response is investigated with the Reynolds number varying and the upstream wake frequency fixed. In another case, the Reynolds number is fixed and the upstream wake frequency varies. In both cases, the FIV response of the upstream cylinder roughly resembles the lower branch of the typical vortex-induced vibration response of the single cylinder with the upstream reduced velocity varying from 6 to 9. For the downstream cylinder, the FIV response is characterized by two frequency branches: a dominant frequency branch associated with the wake interference mechanism and a secondary frequency branch associated with the upstream vortex shedding mechanism. It is found that the variation of the vortex shedding frequency in the upstream wake has little effect on the amplitude and dominant frequency of the downstream FIV response but directly causes the variation of the secondary frequency as the secondary frequency strictly follows the upstream vortex shedding frequency. The FIV response amplitude and dominant frequency of the downstream cylinder shows a strong dependence on the Reynolds number. The wake pattern of FIV shows that the FIV vortex shedding of each cylinder is directly related to the motion of itself but slightly modified by the wake of other cylinders for the full wake interference regime. The upstream wake vortices interfering with the downstream motion induce a flow in favor of the downstream FIV response.

### Mixed mass of classical Rayleigh-Taylor mixing at arbitrary density ratios

The accurate prediction of mixed mass induced by turbulent Rayleigh-Taylor mixing is of fundamental importance for many natural phenomena and engineering applications; however, no quantitative theory based on it has been established yet. In this study, we establish a quantitative theory to predict its evolution at arbitrary density ratios by combining the theory of density-ratio-invariant mean species profiles, which was recently developed by us, and the closure model for the turbulent fluctuations presented in this letter. The transformation formula between mixed mass and mixing width is obtained; in addition, the quantitative variation of normalized mixed mass with respect to the density ratio is derived. The theoretical results agreed very well with the direct numerical simulations at varied density ratios. The study sheds light on the quantitative prediction of mixed mass in practical engineering applications such as inertial confinement fusion.

### Immiscible liquid-liquid displacement flows in a Hele-Shaw cell including shear thinning effects

We experimentally studied the viscous fingering instability considering a Newtonian oil displacing viscoelastic shear-thinning liquids and vice versa. The non-Newtonian liquids are aqueous solutions of polyacrylamide and xanthan gum, i.e., flexible and rigid polymers, respectively. A rectangular Hele-Shaw cell, connected by two plenum chambers, was developed to evaluate the displacement of a fixed volume. The experiment consists of analyzing the interface time evolution through a digital camera as a function of the geometric, dynamic, and rheological parameters. The displacement efficiency was determined through image processing in order to identify the formation of fingers or plugs. Unlike the Newtonian case, the transition does not occur when the viscosity ratio is roughly equal to one, but nevertheless, it was observed that the stability of the interface depends on the viscosity ratio. Specifically, more branches are observed at low viscosity ratios. Furthermore, a higher stability is observed when the Newtonian liquid displaces the shear thinning liquid, especially when the polymer is more rigid. When the Newtonian liquid is being displaced, elastic effects favor the displacing efficiency.

### Acoustic streaming outside and inside a fluid particle undergoing monopole and dipole oscillations

Author(s): Thierry Baasch, Alexander A. Doinikov, and Jürg Dual

An analytical theory is developed for acoustic streaming induced by an acoustic wave field inside and outside a spherical fluid particle, which can be a liquid droplet or a gas bubble. The particle is assumed to undergo the monopole (pulsation) and the dipole (translation) oscillation modes. The dis...

[Phys. Rev. E 101, 013108] Published Wed Jan 15, 2020

### Hidden prompt splashing by corona splashing at drop impact on a smooth dry surface

Author(s): Taku Ashida, Masao Watanabe, Kazumichi Kobayashi, Hiroyuki Fujii, and Toshiyuki Sanada

Using a high-speed camera, three types of splashing are identified as drops impact on a surface; the types of splashing depend on the surface roughness and on the ambient gas pressure.

[Phys. Rev. Fluids 5, 011601(R)] Published Wed Jan 15, 2020

### Thixotropic pumping in a cylindrical pipe

Author(s): David Pritchard, Andrew I. Croudace, and Stephen K. Wilson

The response of thixotropic fluids to applied forces depends not just on the instantaneous forces but on how they change over time. A model of thixotropic flow in a pipe illustrates how this can lead to the net transport of fluid under oscillatory forcing at intermediate Deborah numbers and that the effect vanishes in the limit of either a small or a large Deborah number (i.e., very slow or very fast forcing).

[Phys. Rev. Fluids 5, 013303] Published Wed Jan 15, 2020

### Inertial migration of neutrally buoyant particles in superhydrophobic channels

Author(s): Tatiana V. Nizkaya, Evgeny S. Asmolov, Jens Harting, and Olga I. Vinogradova

The effective anisotropic hydrodynamic slip of a channel wall decorated by superhydrophobic grooves is shown to alter the equilibrium positions of neutrally buoyant particles and to generate their motion transverse to the pressure gradient.

[Phys. Rev. Fluids 5, 014201] Published Wed Jan 15, 2020

### Two regime cooling in flow induced by a spark discharge

Author(s): Bhavini Singh, Lalit K. Rajendran, Pavlos P. Vlachos, and Sally P. M. Bane

Cooling of the flow induced by a spark plasma discharge is found to occur at two different rates: an initially fast cooling regime followed by a slow cooling regime. Convective cooling in the fast regime contributes to 30–50% of the total cooling and occurs within the first millisecond of the induced flow.

[Phys. Rev. Fluids 5, 014501] Published Tue Jan 14, 2020

### Vacuum suction unit based on the zero pressure difference method

Vacuum suction units are widely used in various manufacturing lines, climbing robots, etc. Their most difficult problem is vacuum leakage, which leads to suction failure. Vacuum leakage is traditionally prevented by blocking the flow path between the atmosphere and the vacuum zone, which is difficult for a suction unit working on a rough surface. This paper proposes using the zero pressure difference (ZPD) method, which is based on a completely different mechanism. The ZPD method eliminates the pressure difference at the boundary of the vacuum zone, so vacuum leakage can be prevented regardless of the roughness of the working surface. A new vacuum suction unit based on the ZPD method was designed, fabricated, and tested. The ZPD suction unit forms a rotating water layer on the periphery of the vacuum zone, and the resulting inertial force generates a steep pressure gradient so that a high vacuum is maintained at the center of the vacuum zone while the pressure at the boundary remains equal to the atmospheric pressure. Experiments showed that a 0.8-kg ZPD suction unit generated a suction force of over 245 N on rough surfaces with a power consumption of less than 400 W. In contrast, a traditional suction unit of the same size would need a vacuum pump consuming several kilowatts and weighing dozens of kilograms to generate a similar suction force because of severe vacuum leakage. The ZPD suction unit was then successfully applied to a robotic arm, wall-climbing robot, and spider-man wall-climbing device.

### Experimental study on the slip velocity of turbulent flow over and within porous media

The phenomenon of coupled flow between free flow and porous media is characteristic of fluid flowing across porous media, but the slip characteristics at the coupling interface need to be further studied. The purpose of this work is to investigate the velocity distribution of turbulence with a high Reynolds number above and in porous media. In this paper, a visual flume test bench is built to simulate porous media as an accumulation of spherical glass beads with a diameter of 10 mm. The free flow velocity of fluid crossing the porous media and the velocity inside the porous media are measured by ultrasonic Doppler velocimetry. The effects of Reynolds number, relative water depth, and porosity parameters on the slip velocity and momentum transfer near the interface are studied. The results show that the slip coefficient of a porous-media bed with 0.331 porosity ranges from 0.000 082 to 0.000 594, while that of a porous-media bed with 0.476 porosity ranges from 0.000 034 to 0.001 068. The slip velocity increases with the increase in Reynolds number but decreases with the increase in relative water depth and porosity. The thickness of the transition layer in the porous-media region is insensitive to the Reynolds number and relative depth, but sensitive to porosity and increases with the increase in porosity. In this study, the influence of effective parameters on turbulent velocity is studied by experiments, which provides an important reference value for the development of a theoretical model in turbulent flow.

### An immersed boundary-lattice Boltzmann method for gaseous slip flow

An immersed boundary (IB)-lattice Boltzmann (LB) method is proposed for microchannel slip flow encountered in microfluidics applications such as microelectromechanical Systems, filtration applications with nanofibers, polymer processing, and unconventional shale gas and coal seam gas applications. The LB method is theoretically analyzed to have an intrinsic ability to model velocity discontinuities at finite Knudsen numbers (Kn) when a sufficiently fine grid spacing and an external continuous perturbation, e.g., the body force of an IB method, are applied. Based on this analysis, an IB method coupled with a LB framework without ghost grids in nonfluid areas is proposed to study gaseous slip flow at finite Kn. In addition, an improved treatment to the suspending grids in nonfluid areas is proposed to assist the IB-LB method. In the simulations of two-dimensional Poiseuille and Couette flows for 0.01 ≤ Kn ≤ 1, the slip flow predicted by the proposed nonghost-grid IB-LB method achieves good agreement with that predicted by the linearized Boltzmann and/or Direct Simulation Monte Carlo methods up to Kn = 0.2. Since the proposed IB-LB method is free of adjustable parameters and slip velocity models, it provides a simple and promising pathway for modeling microscale flow applications for the validated regime, i.e., Kn < = 0.2.

### Drop dynamics of viscoelastic filaments

Author(s): Hrishikesh Pingulkar, Jorge Peixinho, and Olivier Crumeyrolle

As a capillary bridge of a viscoelastic fluid breaks to form beads-on-a-string, diameter-space-time diagrams are used to reproduce the position of the minimum diameter on the filament, the asymmetric satellite drop distribution and the movement of the filament in the direction of drop coalescence. Further, the size of the largest drop and the number of drops formed are quantified as a function of polymer concentration.

[Phys. Rev. Fluids 5, 011301(R)] Published Mon Jan 13, 2020

### Experimental evidence of settling retardation in a turbulence column

Author(s): Y. Akutina, T. Revil-Baudard, J. Chauchat, and O. Eiff

An experimental investigation of the settling velocity of solid particles in homogeneous isotropic turbulence finds that for different shapes of particles, the settling is slowed down by the turbulence. A relationship between modified settling velocity and turbulence intensity is obtained.

[Phys. Rev. Fluids 5, 014303] Published Mon Jan 13, 2020

### Formation of power-law scalings of spectra and multiscale coherent structures in the near-field of grid-generated turbulence

Author(s): Tatsuya Yasuda, Susumu Goto, and John Christos Vassilicos

An investigation shows that 5/3 and -7/3 frequency spectra of turbulent energy and pressure, respectively, appear along shear layers in the very near-field of grid turbulence via interactions between vortices due to shedding and shear-layer instability.

[Phys. Rev. Fluids 5, 014601] Published Mon Jan 13, 2020