# Latest papers in fluid mechanics

### Numerical study of Taylor–Couette flow with longitudinal corrugated surface

This study investigates the Taylor–Couette flow (TCF) with a longitudinal corrugated surface on a stationary outer cylinder and a rotating smooth inner cylinder using large eddy simulation for three values of amplitude to wavelength ratios (A*) (0.1875, 0.2149, and 0.25) to explore the influence of the corrugated surface on the flow structures and the variation of torque for a wider range of Reynolds numbers (Re) (60–650). From the results, four flow regimes are observed. At Re = 60, initially, a pair of secondary vortices appears at the inner wall of the minimum gap region and it evolves to a pair of axisymmetric stationary wall induced vortices (ASSWIVs) in the maximum gap region. As Re increases to 80, 85, and 103 for the three values of A* (0.1875, 0.2149, and 0.25), respectively, another pair of axisymmetric stationary secondary vortices is seen at the minimum gap region of the inner wall. A further increase in Re (Re > 125, 130, and 138 for the three values of A*, respectively) results in the appearance of axisymmetric periodic secondary axial flow. Increasing Re further (Re > 225, 240, and 260 for A* = 0.25, 0.2149, and 0.1875, respectively) leads to the emergence of non-axisymmetric and non-periodic secondary axial flow (NANPSAF) with an azimuthal wave. Generally, the torque in TCF with the corrugated surface is found to be lower than TCF with a smooth surface except for the occurrence of the ASSWIV flow regime and weak axial secondary flow in the NANPSAF regime.

### An atomic-level study of the N2–N2 collision process at temperatures up to 2000 K

This article studies the mechanics of the N2–N2 collision process at temperatures up to 2000 K through an extensive set of classical trajectory calculations of binary collisions. It is found that key postcollision characteristics, namely, the deflection angle and the rotational–translational energy exchange rate, are significantly affected by precollision values of the rotational energies of the molecules, which is not addressed in commonly used collision models. On the macroscopic scale, such a behavior will lead to viscosity collision cross section and relaxation rate becoming dependent on both translational and rotational temperatures, as well as on the form of the nonequilibrium rotational energy distribution.

### Characteristics of wall-attached motions in open channel flows

Time-resolved particle image velocimetry measurements with sufficient spatial resolutions combined with coherence spectrum analysis were adopted to investigate the geometric and kinematic features of wall-attached motions in open channel flows. Results indicate that the diagnosed streamwise wavelength of wall-attached motions λxWA based on a given near zero coherence spectrum threshold exhibits a constant streamwise wavelength/wall-normal distance ratio accompanied with a roughly constant inclination angle within y+ > ∼100 and y/h ≤ 0.7 [y+ is the inner-scale normalized distance to the wall y with y+ = y/(ν/uτ) (ν is the kinematic viscosity and uτ is the friction velocity) and h is the water depth], meaning that they are geometrically self-similar. However, in the free-surface region, where y/h > 0.7, the diagnosed wall-attached motions are non-self-similar with λxWA increasing more dramatically and reaching up to ∼20h at the free surface, which is comparable to the typical scales of very-large-scale motions therein. The wall-attached motions are demonstrated to be both energetic and stress active. Within y/h < 0.7, the wall-attached motions with the streamwise wavelength greater than λxWA (including both the self-similar and non-self-similar wavelength range portions) carry more than 40% of the streamwise turbulent kinetic energy (TKE) and 30% of Reynolds shear stress. Beyond y/h = 0.7, where the self-similar portions vanish, all the wall-attached motions are non-self-similar wall-attached motions, which themselves still maintain considerable strength even at the free surface and contribute to 25% of the streamwise TKE and 10% of the Reynolds shear stress therein.

### Effect of slip on the contact-line instability of a thin liquid film flowing down a cylinder

Author(s): Chicheng Ma, Jianlin Liu, Mingyu Shao, Bo Li, Lei Li, and Zhangna Xue

Liquid coating films on solid surfaces exist widely in a plethora of industrial processes. In this study, we focus on the falling of a liquid film on the side surface of a vertical cylinder, where the surface is viewed as slippery, such as a liquid-infused surface. The evolution profiles and flow in...

[Phys. Rev. E 101, 053108] Published Fri May 22, 2020

### Bundled slender-body theory for elongated geometries in swimming bacteria

Author(s): Bin Liu and Jeremias Gonzalez

An elongated but finite body is represented by a bundle of thin filaments for redeeming the theoretical treatment of the slender-body theory, validated by comparing its predictions with known solutions. As an immediate application, this bundled slender-body theory is used to model swimming microorganisms that consist of both thin motile organelles and cell bodies with finite aspect ratios.

[Phys. Rev. Fluids 5, 053102] Published Fri May 22, 2020

### Suspension rheology of adhesive particles at high shear-rates

Author(s): J. J. J. Gillissen, A. Papadopoulou, S. Balabani, M. K. Tiwari, and H. J. Wilson

An experimentally verification of a novel theoretical relationship between the suspension viscosity and the interparticle adhesion force F is presented.

[Phys. Rev. Fluids 5, 053302] Published Fri May 22, 2020

### Oblique collisions of two wetted spheres

Author(s): Robert H. Davis and Jacob W. Sitison

When a pair of wetted particles undergoes an oblique collision their liquid layers overlap and cause lubrication and capillary forces. The relative motion in the direction normal to sphere surfaces in the contact region is then arrested, and the pair of particles can either remain agglomerated, experience rapid rebound, or rotate and slowly separate as a result of centrifugal forces. Collision laws for wet particles are presented, and the conditions leading to the different outcomes are determined.

[Phys. Rev. Fluids 5, 054305] Published Fri May 22, 2020

### Using braids to quantify interface growth and coherence in a rotor-oscillator flow

Author(s): Margaux Filippi, Marko Budišić, Michael R. Allshouse, Séverine Atis, Jean-Luc Thiffeault, and Thomas Peacock

The growth rate of material interfaces is an important proxy for mixing and reaction rates in fluid dynamics. Within experimental limits, mathematical braids can be used to identify regions of coherence within the flow that are distinct from regions of high mixing and to estimate growth rates of material interfaces.

[Phys. Rev. Fluids 5, 054504] Published Fri May 22, 2020

### Control of unsteady partial cavitation and cloud cavitation in marine engineering and hydraulic systems

Cavitation is a process of liquid evaporation, bubble or vapor sheet formation, and further collapse of vapor structures, which plays a destructive role in many industrial applications. In marine transport and hydraulic machinery, cavitation usually occurs nearby the surface of a ship propeller and rudder, impeller blades in a pump, and distributor vanes and runner blades in a hydroturbine and causes various undesirable effects such as vibrations of frameworks and/or moving parts, material erosion, and noise enhancement. Based on an extensive literature review, this research is aimed at an experimental investigation of a passive approach to control cavitation on a benchmark hydrofoil using a wedge-type vortex generator in different flow regimes with a high Reynolds number. In this study, we employed a high-speed imaging method to explore the spatial patterns and time evolutions of cavitation structures and utilized a hydroacoustic pressure transducer to record and analyze local pressure pulsations due to the collapse of the cavities in the hydrofoil wake region. The results show that the examined control technique is quite effective and capable of hindering the formation of cloud cavities and reducing the amplitude of pressure pulsations associated with unsteady cavitation dynamics. This study provides important experimental information, which can be useful for improving industrial technologies and for promoting new developments in this particular research field.

### Study on the transient characteristics of pulsation bubble near a free surface based on finite volume method and front tracking method

The pulsation bubble dynamics near a free surface have significant engineering applications. Based on the finite volume method, a front tracking method coupled with an extrapolation technique is applied to study the transient characteristics of the pulsation bubble near the free surface with the different stand-off distance parameter γ and buoyancy parameter δ (the parameters are defined in Sec. II D). By comparison, the numerical results agree well with the results from the spark-generated bubble experiment. For the cases with small δ, (i) the phenomenon that the bubble top is elongated is no longer obvious while γ > 2.0, (ii) with the decrease in γ, the bubble centroid at the minimum volume is gradually away from the free surface except for migrating upward while 0.85 < γ < 1.0, and (iii) while γ > 1.2, the free surface begins to fall with the bubble collapse after rising during the expansion stage and almost falls back to its original position while γ > 2.4. For the cases with γ = 1.0–1.13, (i) while δ > 0.2293, the jet penetrates the bubble before the bubble reaches its minimum volume, and both are contrary while δ < 0.2293, (ii) while δ > 0.4636, the free surface begins to fall with the bubble collapse after rising during the expansion stage, and (iii) the bubble is always migrating toward the free surface while δ > 0.4109. Meanwhile, the phenomena such as the inward jet formed inside the toroidal bubble, the toroidal bubble split, and the water skirt are also analyzed.

### A microfluidic rectifier for Newtonian fluids using asymmetric converging–diverging microchannels

Flow rectification for Newtonian fluids remains challenging compared with that for non-Newtonian fluids because the physical properties of Newtonian fluids are independent of the structure of flow channels, and flow rectification can only be achieved through direction-dependent flow scenarios. In this work, we fabricate a microfluidic rectifier for Newtonian fluids using asymmetric converging–diverging microchannels. The highest diodicity measured for the rectifier is 1.77, which is 15%–54% higher than previous microfluidic rectifiers for Newtonian fluids. An expression for the diodicity is developed based on two scaling laws for the flow resistances in the forward and backward directions. Numerical simulations are also performed to confirm the experiments.

### Coarse-graining, compressibility, and thermal fluctuation scaling in dissipative particle dynamics employed with pre-determined input parameters

In this study, a Dissipative Particle Dynamics (DPD) method is employed with its input parameters directly determined from the fluid properties, such as the fluid mass density, water compressibility, and viscosity. The investigation of thermal fluctuation scaling requires constant fluid properties, and this proposed DPD version meets this requirement. Its numerical verifications in simple or complex fluids under viscometric or non-viscometric flows indicate that (i) the level of thermal fluctuations in the DPD model for both types of fluids is consistently reduced with an increase in the coarse-graining level and (ii) viscometric or non-viscometric flows of a model fluid at different coarse-graining levels have a similar behavior. Furthermore, to reduce the compressibility effect of the DPD fluid in simulating incompressible flows, a new simple treatment is presented and shown to be very effective.

### Influence of dielectrical heating on convective flow in a radial force field

Author(s): Vadim Travnikov, Florian Zaussinger, Peter Haun, and Christoph Egbers

We present results of numerical and experimental investigations of thermal convection induced by internal heating in both a nonrotating and a rotating spherical gap filled with dielectric fluid. The inner and outer surfaces are maintained at constant temperatures Tin and Tout, respectively. A radial...

[Phys. Rev. E 101, 053106] Published Thu May 21, 2020

### Numerical study of droplet impact on a flexible substrate

Author(s): Yongfeng Xiong, Haibo Huang, and Xi-Yun Lu

Droplets interacting with deformable moving boundaries is ubiquitous. The flexible boundaries may dramatically affect the hydrodynamic behavior of droplets. A numerical method for simulating droplet impact on flexible substrates is developed. The effect of flexibility is investigated. To reduce the ...

[Phys. Rev. E 101, 053107] Published Thu May 21, 2020

### Surface heat loss and chemical kinetic response in deflagration-to-detonation transition in microchannels

Author(s): Wenhu Han, Jin Huang, Gongtian Gu, Cheng Wang, and Chung K. Law

We examine how heat loss at walls affects the deflagration-to-detonation transition. We find that in the adiabatic case, autoignition near the wall produces fast flames in the boundary layer, while autoignition does not occur in the boundary layer for the case with heat loss at the walls.

[Phys. Rev. Fluids 5, 053201] Published Thu May 21, 2020

### Hydrodynamic influence on the aggregation of colloids with short-range depletion potential in dilute suspensions

Author(s): Adolfo Vázquez-Quesada and Rafael Delgado-Buscalioni

We numerically study the effect of hydrodynamics on colloid aggregation in dilute suspensions using inertial coupling, a type of immersed boundary method. Some previous studies found that hydrodynamics affects the equilibrium cluster shape. Comparing to Langevin dynamics and Monte Carlo simulations we find instead no statistically relevant difference in the formed cluster structure due to hydrodynamic effects, only a slowing down. Time correlation studies find two timescales: a short one faster than the single particle diffusion time, and a longer exponential decay of several diffusion times.

[Phys. Rev. Fluids 5, 053301] Published Thu May 21, 2020

### Application of the Lambert W function to steady shearing Newtonian flows with logarithmic wall slip

We consider various viscometric flows of a Newtonian fluid, i.e., plane, annular, and circular Couette flows and planar and axisymmetric Poiseuille flows, in the presence of wall slip that follows a logarithmic slip law. We derive analytical solutions in terms of the Lambert W function. The effects of logarithmic slip on these flows are discussed, and comparisons of the results with their Navier-slip counterparts are made.

### Solid-flow interactions of a large aspect ratio cylinder in a shallow open channel

The complex wake created by an emergent slender circular cylinder in a shallow open channel flow is studied at a cylinder Reynolds number (ReD) of 3300 and at a subcritical Froude number of 0.58 in water. Methodical laser Doppler velocimetry measurements were taken in a very fine grid in three horizontal planes at near bed, mid-depth, and near free surface both upstream and downstream of the cylinder. Demarcation of the entire wake region starting from the first point of the onset of disturbed flow upstream to undisturbed flow downstream entirely based on experiments successfully added a novel contribution to the research on wake flow over a single cylinder. The proximity of the bed and free surface has a significant effect on the structure of the wake compared to the mid-depth. The size, shape, and development of the recirculation region behind the cylinder vary in the vertical direction from the bed to free surface. The longest wake closure point was found in the near bed region and the shortest was found near the free surface. The new model developed pertinent to longitudinal velocity deficit can be used as a velocity deficit scale for the entire far wake region for shallow wakes at mid-depth and near free surface. Urms/Us profiles along the transverse direction initially show a double peak behavior for all three levels, and well away from the cylinder downstream, the double peak becomes broader and less distinct, which is attributed to the effect of the separating shear layers. It is also noted that the wake characteristics of slender cylinders are significantly different from those of wakes generated by cylinders with small aspect ratios.

### Coalescence of vertically aligned drops over a superhydrophobic surface

The coalescence process of two liquid droplets where one is placed initially over the other is investigated. The lower drop is placed over a horizontal surface in a sessile configuration. The liquids of interest selected are water, glycerin, and Cs-alloy. The two liquid drops merge under atmospheric conditions. The substrate is superhydrophobic with respect to the three liquids, the equilibrium contact angle being 150°. For the combined drop, the Bond number is ∼0.2. Numerical simulations have been performed in an axisymmetric coordinate system along with supporting experiments. A variety of contact line models reported in the literature have been adopted and compared. Experiments are carried out for validation against simulation with water as the liquid medium. The coalescence phenomenon is recorded by a high-speed camera. The two drops coalesce spontaneously and generate interfacial shapes, velocity fields, footprint, and wall shear stress in time. In water, the combined drop recoils from the surface before spreading over the surface and approaching equilibrium. This trend, including the instant and height of recoil, is correctly realized in the contact line models. Additionally, two distinct timescales originate during the coalescence process. These are associated with inertia and surface tension at small times and inertia–viscosity for longer durations. The instantaneous footprint radius and the average wall shear stress fall to zero during recoil, increase then to a maximum, and diminish to zero with damped oscillations over the longer timescale. Recoil is seen in water as well as Cs-alloy, but not in glycerin. Despite differences in the instantaneous data, these predictions are broadly reproduced by each of the contact line models.

### Flow topology and its transformation inside droplets traveling in rectangular microchannels

The flow topology inside a droplet acts directly on the cells or substances enclosed therein and is, therefore, of great significance in controlling the living environment of cells and the biochemical reaction process. In this paper, the flow characteristics inside droplets moving in rectangular microchannels are studied experimentally by particle image velocimetry for capillary numbers ranging from 10−5 to 10−2. In order to decouple the effects of total flow, droplet spacing, viscosity ratio, droplet size, and the depth-to-width ratio of the channel on the flow field, the droplet trains with a designed initial state are first produced by controlling the two-phase flow rate and setting up an auxiliary inlet, which is used to adjust the droplet size and spacing, and then run at a set flow rate. As the total flow increases, the flow topologies inside the plunger droplet gradually change from four eddies to two at relatively high viscosity ratios, whereas the opposite transition direction is observed in the low-viscosity-ratio system. The flow topology inside spherical droplets is unaffected by the total flow or capillary number, invariably producing double vortices. The effect of the channel wall on the droplet boundary decreases as the droplet spacing increases or the droplet size decreases. Assuming the continuity of the fluid mass, the competition between the gutter-flow driving stress and the oil-film resistance determines the boundary velocity of the droplet. The oil-film resistance dominates the motion of the droplet boundary in high-aspect-ratio channels, resulting in the negative rotation of the boundary velocity vectors and six vortices in the interior of the droplet. The results are conducive to the further development of microfluidic flow cytometry, particle concentration control, and droplet micromixers.