# Latest papers in fluid mechanics

### Rigid fiber motion in slightly non-Newtonian viscoelastic fluids

The perturbation technique based on the retardation-motion expansion is a simple method to obtain flow solutions at low Weissenberg number. In this context, this perturbation analysis is used to develop simple expressions for the motion of fibers suspended in viscoelastic fluids. In particular, the suspending fluid is characterized by a second-order fluid, Giesekus and PPT (Phan–Thien–Tanner) models, and their derivatives, such as the upper and lower convected Maxwell models. The first-order perturbation results in a similar effective velocity gradient that is exploited to express the translation and rotational motion of a single fiber and the associated extra stress tensor. In terms of a parameter related to the various viscoelastic fluid models, it is found that a fiber aligns along the vorticity direction when subjected to a shear flow. However, when a lower convected Maxwell model is considered, the elongated particle orients in the flow direction, as basically predicted by the Jeffery solution for a Newtonian suspending fluid. Furthermore, the conservation equation for particle concentration leads to particle migration in a pressure-driven flow channel and good agreement is observed with experimental data.

### Diffusive instabilities of baroclinic lenticular vortices

We consider a model of a circular lenticular vortex immersed into a deep and vertically stratified viscous fluid in the presence of gravity and rotation. The vortex is assumed to be baroclinic with a Gaussian profile of angular velocity both in the radial and axial directions. Assuming the base state to be in cyclogeostrophic balance, we derive linearized equations of motion and seek for their solution in a geometric optics approximation to find amplitude transport equations that yield a comprehensive dispersion relation. Applying the algebraic Bilharz criterion to the latter, we establish that the stability conditions are reduced to three inequalities that define the stability domain in the space of parameters. The main destabilization mechanism is either monotonic or oscillatory axisymmetric instability depending on the Schmidt number (Sc), vortex Rossby number, and the difference between radial and axial density gradients as well as the difference between epicyclic and vertical oscillation frequencies. We discover that the boundaries of the regions of monotonic and oscillatory axisymmetric instabilities meet at a codimension-2 point, forming a singularity of the neutral stability curve. We give an exhaustive classification of the geometry of the stability boundary, depending on the values of the Schmidt number. Although we demonstrate that the centrifugally stable (unstable) Gaussian lens can be destabilized (stabilized) by the differential diffusion of mass and momentum and that destabilization can happen even in the limit of vanishing diffusion, we also describe explicitly a set of parameters in which the Gaussian lens is stable for all Sc > 0.

### The effects of roughness levels on the instability of the boundary-layer flow over a rotating disk with an enforced axial flow

This paper investigates the effects of surface roughness on the convective stability behavior of boundary-layer flow over a rotating disk. An enforced axial flow and the Miklavčič and Wang (MW) model of roughness are applied to this flow. The effects of both anisotropic and isotropic surface roughness on the distinct instability properties of the boundary-layer flow over a rotating disk will also be examined for this model. It is possible to implement these types of roughness on this geometric shape while considering an axial flow. This approach requires a modification for the no-slip condition and that the current boundary conditions are partial-slip conditions. The Navier–Stokes equations are used to obtain the steady mean-flow system, and linear stability equations are then formulated to obtain neutral stability curves while investigating the convective instability behavior for stationary modes. The stability analysis results are then confirmed by the linear convective growth rates for stationary disturbances and the energy analysis. The stability characteristics of the inviscid type I (or cross-flow) instability and the viscous type II instability are examined over a rough, rotating disk within the boundary layer at all axial flow rates considered. Our findings indicate that the radial grooves have a strong destabilizing effect on the type II mode as the axial flow is increased, whereas the concentric grooves and isotropic surface roughness stabilize the boundary-layer flow for the type I mode. It is worth noting that the flows over a concentrically grooved disk with increasing enforced axial flow strength are the most stable for the inviscid type I instability.

### Electric-field induced phase transitions in capillary electrophoretic systems

The movement of particles in a capillary electrophoretic system under electroosmotic flow was modeled using Monte Carlo simulation with the Metropolis algorithm. Two different cases with repulsive and attractive interactions between molecules were taken into consideration. Simulation was done using a spin-like system, where the interactions between the nearest and second closest neighbors were considered in two separate steps of the modeling study. A total of 20 different cases with different rates of interactions for both repulsive and attractive interactions were modeled. The movement of the particles through the capillary is defined as current. At a low interaction level between molecules, a regular electroosmotic flow is obtained; on the other hand, with increasing interactions between molecules, the current shows a phase transition behavior. The results also show that a modular electroosmotic flow can be obtained for separations by tuning the ratio between molecular interactions and electric field strength.

### Pore-resolved volume-of-fluid simulations of two-phase flow in porous media: Pore-scale flow mechanisms and regime map

Two-phase flow through porous media is important to the development of secondary and tertiary oil recovery. In the present work, we have simulated oil recovery through a pore-resolved three-dimensional medium using volume-of-fluid method. The effects of wettability and interfacial tension (IFT) on two-phase flow mechanisms are investigated using pore-scale events, oil-phase morphology, forces acting on oil ganglia surfaces, and oil recovery curves, for Capillary numbers (Ca) in the range of 1.2 × 10−3 to 6 × 10−1. We found that the two-phase flow through oil-wet medium is governed by pore-by-pore filling mechanism dominated by the Haines-jumps. At low Ca values, a change in the wettability from oil- to neutrally wet resulted into the change of pore-by-pore filling mechanism to co-operative pore filling and as the medium wettability changes from the neutrally to the weakly water-wet, the corner flow events begin to emerge. At low Ca values, the invasion through weakly water-wet porous medium is dominated by co-operative filling and results into an increased oil recovery, whereas the two-phase flow through strongly water-wet medium is governed by corner flow events resulting in a low oil recovery. The corner flow events are found to be a function of not only the medium wettability, but also of Ca and are a characteristic of controlled imbibition. Further, we show that a substantial decrease in the IFT results in a fingerlike invasion at pore-scale, irrespective of the medium wettability. Finally, a two-phase flow regime map is proposed in terms of Ca and contact angle based on the two-phase interface morphology.

### Hydrodynamics of active particles in viscosity gradients

Author(s): Vaseem A. Shaik and Gwynn J. Elfring

The introduction of a particle into a preexisting nonuniform viscosity field will generally modify the viscosity field in order to satisfy boundary conditions on the particle surface. Here we discuss the effect of this disturbance viscosity on the dynamics of active particles, as well as characterize the relative importance of the local changes in stress versus the nonlocal flow changes due to nonuniform viscosity.

[Phys. Rev. Fluids 6, 103103] Published Wed Oct 20, 2021

### Collision dynamics of binary liquid metal droplets under horizontal magnetic field

Author(s): Xiao Jia, Juan-Cheng Yang, Jie Zhang, Long Chen, and Ming-Jiu Ni

We conduct experimental research on binary liquid metal droplet collisions under the influence of a horizontal magnetic field. For magnetic intensity smaller than 1.5 T, only reflexive separation is obviously facilitated, but other collision regimes show little difference with zero magnetic intensity. We infer that when magnetic intensity is larger than a critical value of 4 T, remarkable influences on all regimes would be observed.

[Phys. Rev. Fluids 6, 103702] Published Wed Oct 20, 2021

### Electrohydrodynamic instabilities in freely suspended viscous films under normal electric fields

Author(s): Mohammadhossein Firouznia and David Saintillan

We study electrohydrodynamic instabilities in a freely suspended liquid film subject to a normal electric field. The behavior of the system is characterized as a function of the relevant dimensionless groups during the linear and nonlinear regimes of growth. We demonstrate how the coupling of flow and surface charge transport in different modes of instability can give rise to manifold nonlinear phenomena such as tip streaming or pinching of the film into droplets.

[Phys. Rev. Fluids 6, 103703] Published Wed Oct 20, 2021

### Toward autonomous large eddy simulations of turbulence based on interscale energy transfer among resolved scales

Author(s): J. Andrzej Domaradzki

Is an autonomous large eddy simulation (LES) possible where a subgrid-scale (SGS) model is extracted in a bootstrapping way from LES fields? We show how the SGS energy transfer among resolved scales and its wave number distribution can be obtained from evolving LES fields. This information, supplemented by known asymptotic properties of energy flux in the inertial range, allows self-contained LES without prescribing extraneous SGS models. The method is tested in LES of isotropic turbulence at high Reynolds number (Re) where inertial range dynamics is expected and for lower Re decaying turbulence under conditions of the classical Comte-Bellot and Corrsin experiments (energy spectra in figure).

[Phys. Rev. Fluids 6, 104606] Published Wed Oct 20, 2021

### Experimental investigation of single bubbles rising in stagnant liquid: Statistical analysis and image processing

Despite the large effort devoted to the study of single bubbles rising in a stagnant liquid, the complex phenomena involved have resulted in a large scatter in the terminal velocity. Providing new experimental data where the statistical uncertainty is thoroughly evaluated is therefore necessary. Single bubble experiments were conducted in a tall vertical column containing stagnant liquid at ambient conditions. To track the bubbles over the spatial range, high-speed cameras were mounted on a linear unit drive. The tall column allowed us to study the effect of hydrostatic pressure and late developed bubble dynamics on the bubble motion. The bubble properties, i.e., the bubble velocity, size, shape, and trajectory, were evaluated using an image analysis processing method. The analysis includes a quantitative evaluation of important parameters involved in the handling of the raw data. Several of the existing correlations for the terminal velocity were validated against the experimental data. The data are well predicted by the correlation proposed by Tomiyama et al. [“Terminal velocity of single bubbles in surface tension force dominant regime,” Int. J. Multiphase Flow 28, 1497–1519 (2002)]. The uncertainty in the experimental data has been emphasized, providing a quantitative evaluation based on several statistical methods. The number of experimental events necessary to obtain statistical significance was evaluated using a 95% confidence interval. Satisfying precision is found to be fulfilled for 10–15 bubble rise events. For bubbles of comparable size, the statistically significant terminal velocity data were found to exhibit a small scatter.

### A numerical model for the simulation of oil–ice interaction

Accurate modeling of the interaction between oil and sea ice is essential for predicting oil spill fate and transport in ice-infested waters. A three-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) method is incorporated to model such interactions. The effects from air and water are well captured using suitable force components and without explicit inclusion of air and water phases. This reduces the four-phase SPH model into a two-phase model, significantly reducing computational costs and potentially enabling the use of this model for large-scale simulations. We validate the model against experimental data recently available in the literature on oil–ice interactions. The experiments studied the interaction in a flume between an ice floe and oil slick for different types of crude oils. The current velocities were varied and the thicknesses of the oil slicks were measured. The validation results show that our SPH model can adequately simulate the interaction between oil slicks and ice floes. The simulated average thicknesses fit well with the measured thicknesses despite the considerable difference in the viscosity of the tested crude oil. Moreover, the effects of oil density, surface tension, viscosity, and current velocity on oil slick accumulation in front of the ice floe are studied. The higher current velocities and higher oil density lead to thicker oil slick thickness next to the ice floe. The surface tension effect on oil slick thickness is not significant. Finally, we provide estimates for the minimum oil slick thickness for a finite range of oil viscosities.

### High-speed NMR imaging of capillary action in thin nontransparent porous media

Author(s): R. Nicasy, H. P. Huinink, S. J. F. Erich, and O. C. G. Adan

An improved high-speed NMR profiling method is introduced that enables us to measure capillary action in thin, nontransparent porous media. Liquid profiles can be measured as fast as 10 ms with a spatial resolution of 14.5μm. Capillary absorption of microliter-sized droplets into nontransparent nylo...

[Phys. Rev. E 104, L043101] Published Tue Oct 19, 2021

### Two-body transient viscous interactions in free space

Author(s): Bo Liu and Sukalyan Bhattacharya

A generalization of Stokesian dynamics is formulated to describe hydrodynamic interactions between two spheres in a viscous fluid. The analysis quantifies transient mutual interactions in terms of frequency-dependent friction coefficients of both spheres as well as their temporally varying mobility response to an impulsive force. The analysis also contributes to work on many-body unsteady Brownian motions.

[Phys. Rev. Fluids 6, 104305] Published Tue Oct 19, 2021

### Spectral condensation in laboratory two-dimensional turbulence

Author(s): Lei Fang and Nicholas T. Ouellette

Due to the inverse energy cascade, when the energy dissipation length scale in two-dimensional turbulence is larger than the domain size, energy is expected to condense into the lowest allowed mode. Thus, the appearance of large-scale structures is often taken as a proxy for spectral condensation, particularly in laboratory realizations of two-dimensional turbulence. We show that large-scale flows alone, however, are not robust indicators of spectral condensation, because small domains may both weaken the inverse cascade and introduce new dissipation mechanisms.

[Phys. Rev. Fluids 6, 104605] Published Tue Oct 19, 2021

### Three-dimensional measurements of an inclined vortex ring interacting with a density stratification

Author(s): Johan Pinaud, Julie Albagnac, Sébastien Cazin, Zeinab Rida, Dominique Anne-Archard, and Pierre Brancher

Vortex rings are self-propagating structures that can transport mass and momentum to locations remote from the ring creation. We focus on the reorganization of a light vortex ring impinging, at a given angle to the vertical, a layer of fluid stably stratified in density, as in many environmental applications. We also examine the stratified layer response with regard to baroclinic vorticity and internal gravity wave generation. The symmetry of both the flow and wave field is preserved over time for normal impacts. For inclined impacts, the flow reorganizes into a vertically flattened dipolar structure and internal gravity waves radiate from two sources that match with the dipole cores.

[Phys. Rev. Fluids 6, 104701] Published Tue Oct 19, 2021

### Stability of a horizontal vortex in weakly stratified flow

Author(s): John P. McHugh

A horizontal vortex in a moving stratified flow will have the density field overturn along the axis of the vortex. Gravity distorts this steady vortex, ultimately leading to three instabilities. The twirling and rolling instabilities are strong for small Froude number and small pitch. The streaming instability is strong for large pitch and is independent of Froude number.

[Phys. Rev. Fluids 6, 104802] Published Tue Oct 19, 2021

### Social distancing slows down steady dynamics in pedestrian flows

Amidst the ongoing pandemic, social distancing has been broadly adopted as an effective front-line defense strategy for mitigating disease transmission. Viewed through the lens of particle-based simulations of flow, the practice of social distancing corresponds to a (significant) increase in an internal length scale of the flow, namely, the radius within which particles (pedestrians) strongly repel fellow particles. In this study, we report the results of two-dimensional pedestrian dynamics simulations modeling pedestrian counter-flows under confinement, in which individual pedestrians are described as active particles that aim to maintain a target speed while avoiding collisions. By systematically varying two quantities—the pedestrian density and the degree of social distancing—we compute fundamental diagrams for confined and socially distanced pedestrian flows, which show average pedestrian speed as a function of density and social distancing. These results reveal the sensitive dependence of average velocity on both independent variables, including a social distancing-induced jamming transition. These results highlight the need for both deliberate planning and careful public-health messaging regarding social distancing as shared indoor spaces return to appreciable levels of occupation.

### Gust mitigation with an oscillating airfoil at low Reynolds number

The encounter between micro-aerial vehicles (MAVs) and gusts is often detrimental and mitigating the effects of the gust is important for operating MAVs under severe environmental conditions. This study investigates the impact of vertical gusts on stationary and oscillating NACA0012 (National Advisory Committee for Aeronautics) airfoils at low Reynolds numbers using high-order computational fluid dynamics methods, and identifies key dynamics that dominate gust mitigation. The interaction of the gusts with the stationary airfoil generates large unsteady forces, which exceed the peak static lift coefficient. A simple pitch-down maneuver and oscillating airfoil motion were tested as methods for mitigating the effects of the gusts. A rapid and significant pitch-down maneuver is observed to inadvertently cause a stall event by exceeding the negative stall angle. A stepwise change in the angle of attack (AoA), as the gust develops, is shown to be more effective at mitigating the gust effect. However, this gust mitigation strategy is still not effective if the gust continues to grow in magnitude. Low amplitude wing oscillations were then tested as a novel method for gust mitigation. Increasing the reduced frequency of the oscillating airfoil is shown to dominate the gust and results in a predictable oscillatory lift and drag/thrust behavior. Results also show that this effect is relatively insensitive to variations in the Strouhal number. These results suggest there may be gust mitigation strategies leveraging oscillating wing behaviors on MAVs.

### Lax–Wendroff type solver for two-phase system to restrain parasitic currents

In this paper, a Lax–Wendroff type solver is developed to solve the governing equations for two-phase flows. By incorporating the source term into the numerical flux and approximating the cell volume force by the interfacial forces, the proposed scheme is able to restrain parasitic currents in two-phase systems. Numerical results suggest that the magnitude of the parasitic currents is considerably reduced, and the stability is also improved. Particularly, for a one-dimensional flat interface and a two-dimensional (2D) stationary droplet, the velocity fields drop to machine zero even with a large density ratio (1:1000). It is also found that the viscosity plays an important role in the suppression of parasitic currents when the density ratio is large.

### Spatial deterministic wave forecasting for nonlinear sea–states

We derive a simple algebraic form of the nonlinear wavenumber correction of unidirectional surface gravity waves in deep water, based on temporal measurements of the water surface and the spatial Zakharov equation. This allows us to formulate an improvement over linear deterministic wave forecasting with no additional computational cost. Our new formulation is used to forecast both synthetically generated as well as experimentally measured seas and shows marked improvements over the linear theory.