# Latest papers in fluid mechanics

### Colloidal hydrodynamics of biological cells: A frontier spanning two fields

Author(s): Akshay J. Maheshwari, Alp M. Sunol, Emma Gonzalez, Drew Endy, and Roseanna N. Zia

Colloidal biology is a frontier of exploration in biological cells bridging the operational gap between structural biology (atomistic resolution over nanoseconds) and systems biology (minutes of operation, no spatial resolution). Colloid physics bridges this gap where much of cell machinery operates.

[Phys. Rev. Fluids 4, 110506] Published Mon Nov 18, 2019

### Some fluid mechanical aspects of artistic painting

Author(s): Roberto Zenit

Artistic painting is analyzed with fluid mechanics. We identify hydrodynamic instabilities which are either prevented or induced to create textures of aesthetic value. In watercolor painting the ‘coffee stain’ instability can be induced or prevented by varying pigment type and amount and paper wetness.

[Phys. Rev. Fluids 4, 110507] Published Mon Nov 18, 2019

### Corrsin lecture on hairy hydrodynamics

Author(s): A. E. Hosoi

Simple models for hairy surfaces interacting with flows are derived, and used to extract optimization and design principles in idealized contexts. Reconfiguration, in which flow couples to the hairs geometric configuration, is investigated along with drainage of thin films through beds of hairs.

[Phys. Rev. Fluids 4, 110508] Published Mon Nov 18, 2019

### Orientation control and nonlinear trajectory tracking of colloidal particles using microfluidics

Author(s): Dinesh Kumar, Anish Shenoy, Songsong Li, and Charles M. Schroeder

A new flow-based technique for precisely manipulating the orientation and trajectory of anisotropic Brownian particles using path-following control, without the need for optical or electric fields, is presented.

[Phys. Rev. Fluids 4, 114203] Published Mon Nov 18, 2019

### Influence of wall-attached structures on the boundary of the quiescent core region in turbulent pipe flow

Author(s): Jongmin Yang, Jinyul Hwang, and Hyung Jin Sung

The entrainment phenomena of the quiescent core region in a turbulent pipe flow are examined by characterizing the tall wall-attached structures of the streamwise velocity fluctuations. The quiescent core region is the uniform momentum zone with the highest streamwise velocity magnitude.

[Phys. Rev. Fluids 4, 114606] Published Mon Nov 18, 2019

### Stability of a jet moving in a rectangular microchannel

Author(s): M. G. Cabezas, M. A. Herrada, and José M. Montanero

We study numerically the basic flow and linear stability of a capillary jet confined in a rectangular microchannel. We consider both the case where the interface does not touch the solid surfaces and that in which the jet adheres to them with a contact angle slightly smaller than 180∘. Given an arbi...

[Phys. Rev. E 100, 053104] Published Mon Nov 18, 2019

### Determination of energy flux rate in homogeneous ferrohydrodynamic turbulence using two-point statistics

Author(s): Sukhdev Mouraya and Supratik Banerjee

Under the influence of an external magnetic field **H**, the suspended ferromagnetic particles of a laminar ferrofluid flow try to be oriented along **H** through a relaxation mechanism. Turbulence affects the interaction between the magnetization of each suspended particle and the external field thereby le...

[Phys. Rev. E 100, 053105] Published Mon Nov 18, 2019

### Vortex shedding patterns in flow past a streamwise oscillating square cylinder at low Reynolds number using dynamic meshing

We present a two-dimensional numerical study for uniform flow past a streamwise oscillating square cylinder at a Reynolds number of 200. To overcome the limitations with an oscillating inlet flow as used in earlier studies, a dynamic meshing feature is used to oscillate the cylinder. A parametric study is carried out by varying amplitude and frequency of cylinder oscillation. Two symmetric modes, named here as S-II-I and S-IV-D, have been found. In S-II-I mode, a pair of vortices are shed symmetrically on each side of the cylinder in one cycle (S-II mode), and in S-IV-D mode, two pairs of vortices of opposite sense are shed on each side of the cylinder. A vortex flapping mode has also been obtained for low to moderate amplitude and frequency ratios. A new mode of vortex shedding termed the “vortex dipole” mode is found and involves the alternate arrangement of vortex pairs unlike the zigzag arrangement of single vortices in a Kármán vortex street. As in most nonlinear oscillators, vortex shedding becomes chaotic when forced sufficiently strongly and is usually associated with nonlinear interactions between competing frequencies. Many modes observed in the current study become chaotic when the peak cylinder velocity becomes comparable with the inlet velocity. The 0-1 test for chaos is applied to the time series of lift coefficient to show that the signals are truly chaotic. We also observe chaos due to mode competition when shedding transitions from an antisymmetric to symmetric modes.

### Experimental and theoretical study of swept-wing boundary-layer instabilities. Three-dimensional Tollmien-Schlichting instability

Extensive combined experimental and theoretical investigations of the linear evolution of three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. The flow under consideration is the boundary layer over an airfoil at 35° sweep and an angle of attack of +1.5°. At these conditions, TS instability is found to be the predominant one. Perturbations with different frequencies and spanwise wavenumbers are generated in a controlled way using a row of elastic membranes. All experimental results are deeply processed and compared with results of calculations based on theoretical approaches. Very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved.

### Flow structures in transitional and turbulent boundary layers

The basic problems of transition in both incompressible and compressible boundary layers are reviewed. Flow structures in low-speed transitional and developed turbulent boundary layers are presented, together with almost all of the physical mechanisms that have been proposed for their formation. Comparisons of different descriptions of the same flow structures are discussed as objectively as possible. The importance of basic structure such as solitonlike coherent structure is addressed. For compressible flows, the receptivity and instability of boundary layer are reviewed, including the effect of different parameters on the transition. Finally, the principle of aerodynamic heating of hypersonic boundary layer is presented.

### Complex viscosity of helical and doubly helical polymeric liquids from general rigid bead-rod theory

With general rigid bead-rod modeling, we recreate shapes of complex macromolecular structures with beads, by rigidly fixing bead positions relative to one another. General rigid-bead rod theory then attributes the elasticity of polymeric liquids to the orientation that their macromolecules develop during flow. For linear viscoelastic behaviors, this theory has been evaluated for just a few very simple structures: rigid rings, the rigid tridumbbell, and three quadrafunctional branched structures. For oscillatory shear flow, the frequency dependencies of both parts of the complex viscosity are, at least qualitatively, predicted correctly. In this paper, we use general rigid-bead rod theory for the most complex macromolecular architectures to date. We thus explore the role of helix geometry on the complex viscosity of a helical polymeric liquid. Specifically, for both singly and doubly helical structures, we investigate the effects of helix radius, flight length, helix length, and the number of beads per flight on the complex viscosity function, the fluid relaxation time, and the zero-shear values of the steady shear viscosity and of the first normal stress coefficient. As a worked example, we examine specifically deoxyribonucleic acid (DNA). Using general rigid bead-rod theory, we dissect the DNA to see how the first helix, second helix, and then the base pairs each contribute to the complex viscosity. We next explore the rheological implications of gene replication to find that the unzipping of DNA into a pair of single strands is viscostatic.

### Characteristics of swimming shelled Antarctic pteropods (<i>Limacina helicina antarctica</i>) at intermediate Reynolds number regime

Author(s): Mohammad Mohaghar, Deepak Adhikari, and Donald R. Webster

Shelled Antarctic pteropods (aquatic snails nicknamed “sea butterflies”) swim with a pair of parapodia (or “wings”) in a high efficiency propulsion regime when the Reynolds number based on the flapping exceeds 35.

[Phys. Rev. Fluids 4, 111101(R)] Published Fri Nov 15, 2019

### Active control of dispersion within a channel with flow and pulsating walls

Author(s): Sophie Marbach and Karen Alim

The effect of pulsating channel walls on transport and dispersion of solutes along a channel is investigated. Hands-on analytic expressions to model dispersion in this setting using a versatile method are derived. Different scenarios where dispersion may be enhanced or suppressed are found.

[Phys. Rev. Fluids 4, 114202] Published Fri Nov 15, 2019

### Three-dimensional simulation of tracer transport dynamics in formations with high-permeability channels or fractures: Estimation of oil saturation

We simulate flow and dispersion of tracers in three-dimensional fractured geometries obtained with Voronoi tessellations. “Fractures” are generated and discretized using a parallel in-house code. These “fractures” can also be regarded as the high-permeability flow paths through the rock or a network of the “super-k” channels. The generated geometry contains multiply-connected matrix and fracture regions. The matrix region represents a porous rock filled with solid, water, and oil. Tracers diffuse in both regions, but advection is limited only to the fractures. The lattice-Boltzmann and random-walk particle-tracking methods are employed in flow and transport simulations. Mass-transfer across the matrix–fracture interface is implemented using the specular reflection boundary condition. Tracer partitioning coefficients can vary among the tracer compounds and in space. We use our model to match a field tracer injection test designed to determine remaining oil saturation. By analyzing the time-dependent behavior of the fully resolved, three-dimensional “fracture”–matrix geometry, we show that the industry-standard approach may consistently overestimate remaining oil saturation. For a highly heterogeneous reservoir system, the relative error of the field-based remaining oil estimates may exceed 50%.

### Onset of transition in the flow of polymer solutions through deformable tubes

Experiments are performed to investigate laminar-turbulent transition in the flow of Newtonian and viscoelastic fluids in soft-walled microtubes of diameter ∼400 μm by using the micro-particle image velocimetry technique. The Newtonian fluids used are water and water-glycerine mixtures, while the polymer solutions used are prepared by dissolving polyacrylamide in water. Using different tube diameters, elastic moduli of the tube wall, and polymer concentrations, we probe a wide range of dimensionless wall elasticity parameter Σ and dimensionless fluid elasticity number E. Here, Σ = (ρGR2)/η2, where ρ is the fluid density, G is the shear modulus of the soft wall, R is the radius of the tube, and η is the solution viscosity. The elasticity of the polymer solution is characterized by E = (λη0)/R2ρ, where λ is the zero-shear relaxation time, η0 is the zero-shear viscosity, ρ is the solution density, and R is the tube radius. The onset of transition is detected by a shift in the ratio of centerline peak to average velocity. A jump in the normalized centerline velocity fluctuations and the flattening of the velocity profile are also used to corroborate the onset of instability. Transition for the flow of Newtonian fluid through deformable tubes (of shear modulus ∼50 kPa) is observed at a transition Reynolds number of Ret ∼ 700, which is much lower than Ret ∼ 2000 for a rigid tube. For tubes of lowest shear modulus ∼30 kPa, Ret for Newtonian fluid is as low as 250. For the flow of polymer solutions in a deformable tube (of shear modulus ∼50 kPa), Ret ∼ 100, which is much lower than that for Newtonian flow in a deformable tube with the same shear modulus, indicating a destabilizing effect of polymer elasticity on the transition already present for Newtonian fluids. Conversely, we also find instances where flow of a polymer solution in a rigid tube is stable, but wall elasticity destabilizes the flow in a deformable tube. The jump in normalized velocity fluctuations for the flow of both Newtonian and polymer solutions in soft-walled tubes is much gentler compared to that for Newtonian transition in rigid tubes. Hence, the mechanism underlying the soft-wall transition for the flow of both Newtonian fluids and polymer solutions could be very different as compared to the transition of Newtonian flows in rigid pipes. When Ret is plotted with the wall elasticity parameter Σ for different moduli of the tube wall, by taking Newtonian fluids of different viscosities and polymer solutions of different concentrations, we observed a data collapse, with Ret following a scaling relation of Ret ∼ Σ0.7. Thus, both fluid elasticity and wall elasticity combine to trigger a transition at Re as low as 100 in the flow of polymer solutions through deformable tubes.

### Space-time correlations of velocity in a Mach 0.9 turbulent round jet

In a turbulent jet, the numerical investigation of space-time correlations C(r, τ) at two-point and two-time of streamwise fluctuating velocities is presented along the nozzle lipline. Large-eddy simulation (LES) is performed for a Mach 0.9 turbulent jet issuing from a round nozzle. The turbulent boundary layer is well developed at the nozzle outlet, upon the inner wall, by adopting synthetic turbulent inlet boundary conditions. We study the cross correlations of streamwise fluctuating velocities at three particular streamwise positions, i.e., x = 0.71, 7.03, and 34.47r0, corresponding to different stages of jet development, where r0 is the radius of the nozzle. Present results show that the classical Taylor’s frozen-flow model is unable to predict C(r, τ) accurately in this strongly spatially developing shear flow since the distortion of the flow pattern is missing. The isocorrelation contours of C(r, τ) show a clearly elliptical feature, which is found to be well predicted by the elliptic approximation (EA) model [G.-W. He and J.-B. Zhang, “Elliptic model for space-time correlations in turbulent shear flows,” Phys. Rev. E 73, 055303 (2006)]. According to the EA model, C(r, τ) has a scaling form of C(rE, 0) with two characteristic velocities U and V, i.e., rE = (r − Uτ)2 + V2τ2. By examining LES data, it is found that the characteristic velocity U determined in LES is in general consistent with the theoretical Ut in the EA model, while the trend of V in LES also matches with that of the theoretical Vt. Additionally, it is interesting that the ratio of V to Vt is approximately a constant V/Vt ≃ 1.3 in the turbulent jet.

### Statistical behaviors of conditioned two-point second-order structure functions in turbulent premixed flames in different combustion regimes

The second-order structure functions and their components conditioned upon various events have been analyzed for unweighted and density-weighted velocities using a Direct Numerical Simulation database. The heat release due to combustion has been shown to have significant influences on the structure functions and their components conditioned on different mixture states. The use of density-weighted velocities changes the relative magnitudes of differently conditioned structure functions but does not reduce the scatter of these magnitudes. The structure functions conditioned to constant-density unburned reactants at both points and normalized using the root-mean-square velocity conditioned to the reactants are larger at higher values of mean reaction progress variables [math] (deeper within the flame brush), with this trend being not weakened with increasing turbulence intensity u′/SL. These results indicate that, contrary to a common belief, combustion-induced thermal expansion can significantly affect the incoming constant-density turbulent flow of unburned reactants even at u′/SL and Karlovitz number Ka as large as 10 and 18, respectively. The statistical behaviors of the structure functions reveal that the magnitude of the flame normal gradient of the velocity component tangential to the local flame can be significant, and it increases with increasing turbulence intensity. Moreover, the structure functions conditioned on both points in the heat release zone bear the signature of the anisotropic effects induced by the baroclinic torque for the flames belonging to the wrinkled flamelet and corrugated flamelet regimes. These anisotropic effects weaken with increasing turbulence intensity in the thin reaction zone regime.

### Role of gravity and capillary waves in the origin of circular hydraulic jumps

Author(s): Hossein Askarizadeh, Hossein Ahmadikia, Claas Ehrenpreis, Reinhold Kneer, Ahmadreza Pishevar, and Wilko Rohlfs

A study shows that hydraulic jumps are governed by both gravitational and capillary forces. The jump location results from a competition of supercritical flow with gravity-capillary waves traveling in the upstream direction. Fluid properties, flow conditions, and the state of development scale the respective forces.

[Phys. Rev. Fluids 4, 114002] Published Thu Nov 14, 2019

### Vortex-induced vibration and galloping of a circular cylinder in presence of cross-flow thermal buoyancy

The effect of cross-flow thermal buoyancy on vortex-induced vibration (VIV) of a circular cylinder is numerically investigated. An in-house fluid-structure solver based on the sharp-interface immersed boundary method is employed. The cylinder is kept in the uniform flow stream and is mounted elastically such that it is constrained to move in the transverse direction to the flow. The surface of the cylinder is heated at a prescribed temperature, and the thermal buoyancy is imposed in the transverse direction to the flow. Simulations are performed for the following parameters: Reynolds number Re = (50, 150), Prandtl number Pr = 7.1, mass ratio m = 2, reduced velocity UR = [4–15], and Richardson number Ri = [0–4]. We found that the thermal buoyancy could suppress or agitate the VIV. At lower Re (=50) and Ri = (1, 2), we observe the suppression in the VIV; however, there is no suppression for higher Re (=150) for these values of Ri. Galloping is observed for higher values of Ri = (3, 4) for Re = (50, 150). The galloping has been reported for rotationally asymmetric bluff bodies (e.g., D-section cylinder) in previous studies in isothermal flows. We show that a circular cylinder, a rotationally symmetric body, exhibits galloping due to the transversely acting thermal buoyancy at higher Ri.

### Formation, growth, and saturation of dry holes in thick liquid films under vapor-mediated Marangoni effect

Films and drops of liquids can change their shapes and move under the spatial gradient of surface tension. A remote volatile liquid of relatively low surface tension can induce such flows because its vapor locally lowers the surface tension of the films and drops. Here, we show that aqueous liquid films thicker than approximately 100 µm can be punctured to immediately expose a dry hole by an overhanging isopropyl alcohol drop, which is attributed to the vapor-mediated Marangoni effect. We construct and corroborate scaling laws to predict the film dynamics, considering the balance of the driving capillary force and resisting viscous and hydrostatic forces as well as the contact angle of the alcohol-adsorbed solid surface. This remote scheme to induce and sustain changes of liquid morphology can be applied for fluid sculpture and patterning for industrial and artistic practices.