# Latest papers in fluid mechanics

### A fundamental rule: Determining the importance of flow prior to polymer crystallization

A continuum-level model for nonisothermal polymer crystallization following a complex flow is presented, along with a fundamental rule that may be employed to determine if the flow will influence the ensuing crystallization dynamics. This rule is based on two dimensionless parameters: the (Rouse) Weissenberg number and an inverse Deborah number defined by the ratio between the time taken to cool and the melting point vs the stretch relaxation time, which determines the time available for flow-enhanced crystallization. Moreover, we show how the time to reach the melting point can be derived semianalytically and expressed in terms of the processing conditions in the case of pipe flow—ubiquitous in polymer processing. While the full numerical model is required to quantitatively predict induction times and spherulite-size distributions, the proposed fundamental rule may be used practically to ensure, or eliminate, flow-enhanced structures by controlling the processing conditions or material properties. We discuss how flow-enhanced structures may be revealed only after postprocessing annealing and finally examine previous works that have successfully applied the model to extrusion-based three-dimensional printing.

### Refining the connection between the logarithmic velocity profile and energy spectrum based on eddy's inclination angle

Author(s): Hao-Jie Huang

It has long been surmised that the “log” law of the mean-velocity profile (MVP) is closely related to the “−5/3 or −1” power law of the energy spectrum in wall-bounded turbulence. A refined model for the connection between MVP and the energy spectrum based on eddy’s inclination angle is proposed.

[Phys. Rev. Fluids 4, 114702] Published Wed Nov 20, 2019

### Harmonic and subharmonic waves on the surface of a vibrated liquid drop

Author(s): Ivan S. Maksymov and Andrey Pototsky

Liquid drops and vibrations are ubiquitous in both everyday life and technology, and their combination can often result in fascinating physical phenomena opening up intriguing opportunities for practical applications in biology, medicine, chemistry, and photonics. Here we study, theoretically and ex...

[Phys. Rev. E 100, 053106] Published Wed Nov 20, 2019

### Effect of bolus viscosity on carbohydrate digestion and glucose absorption processes: An in vitro study

Digestion is the process of breaking down food into smaller nutrient components which can be easily absorbed in the intestinal tract. The aim of this study was to experimentally investigate the influence of bolus (gastric content) viscosity on digestion and nutrient absorption processes, using an in vitro gastrointestinal model, the TIM-1 system. Two types of simple carbohydrates, namely, glucose and maltodextrin, were used as model foods. The initial bolus viscosity was varied (∼1 mPa·s, ∼15 mPa·s, and ∼100 mPa·s) using different glycerol-water proportions. A fluorescent molecular rotor compound (Fast Green For Coloring Food) was used to monitor viscosity changing patterns of the gastrointestinal content during digestion in the in vitro stomach and small intestinal sections. The digested-nutrient absorption data indicated that the initial bolus viscosity did not significantly affect the glucose absorption process in the small intestine. However, an increase in the initial bolus viscosity from ∼1 mPa·s to ∼15 mPa·s reduced the maltodextrin to glucose conversion by 35%. A further increase in the initial bolus viscosity from ∼15 mPa·s to ∼100 mPa·s did not significantly reduce the maltodextrin to glucose conversion.

### Numerical study on wide gap Taylor Couette flow with flow transition

This study aims to investigate the possible sources of nonaxisymmetric disturbances and their propagation mechanism in Taylor Couette flow for wide gap problems using a direct numerical simulation with a radius ratio of 0.5 and the Reynolds number (Re) ranging from 60 to 650. Here, attention is focused on the viscous layer (VL) thickness in near-wall regions and its spatial distribution along the axial direction to gain an insight into the origin and propagation of nonaxisymmetric disturbances. The results show that an axisymmetric Taylor-vortex flow occurs when Re is between 68 and 425. Above Re = 425, transition from axisymmetric to nonaxisymmetric flow is observed up to Re = 575 before the emergence of wavy-vortex flow. From the variation of VL thickness with Re, the VL does not experience any significant changes in the flow separation region of the inner wall, as well as jet impingement region of both the inner and outer walls. However, a sudden increase in VL thickness in the flow separation region of the outer wall reveals possible sources of nonaxisymmetric disturbances in the flow separation region of the outer wall. These disturbances develop into the periodic secondary flow as the axisymmetric flow transforms into nonaxisymmetric flow, and this leads to the emergence of the azimuthal wave. The periodic secondary flow contributes to a sudden increase in the natural wavelength and rapid reduction in the strength of two counter-rotating Taylor vortices. This in turn leads to a substantial reduction of torque in the transition flow vis-à-vis axisymmetric Taylor-vortex flow.

### Allotropic transformation instigated thermal diffusivity of soot nanofluid: Thermal lens study

This paper employs the sensitive single-beam thermal lens technique for analyzing the thermal behavior of gasoline soot containing allotropes of carbon by preparing its nanofluid (NF). The soot, annealed at different temperatures up to 400 °C (the samples), used for preparing the NF, is found to enhance the thermal diffusivity (α) up to 95% without changing the solid volume fraction, suggesting its possible use in coolants. The thermal induced modifications are understood from the field emission scanning electron microscopic, X-ray diffraction (XRD), thermogravimetric, and Raman spectroscopic analyses. The variation of α of the sample is found to exhibit similar variations observed in XRD and Raman spectroscopic analyses. The study stresses the significance of the optimum temperature (300 °C) for the soot NF above which morphological and structural modifications may lead to thermal energy trapping rather than dissipation or cooling.

### Numerical study of total temperature effect on hypersonic boundary layer transition

The total temperature in the hypersonic wind tunnel test can be significantly different from that in real flight conditions, and this leads to a large discrepancy in the measurement of the boundary layer transition between ground experiment measurements and flight tests. Even at the same Mach number and Reynolds number, different wind tunnels may yield different transition data for the same model due to the total temperature effect. In this paper, the boundary layer transition on a 7° half-angle sharp cone (at a 0° angle of attack) with four freestream total temperatures is investigated using both the simulations of a local correlation-based transition model and linear stability analysis. The results show that as the freestream total temperature increases, the starting point of the transition on the sharp cone gradually moves backward and the length of the transition region decreases. The N factor of the unstable wave gradually decreases with increasing freestream total temperature, causing the transition onset to move backward. The total temperature effects on boundary transition as determined by both methods of analysis were in good agreement.

### Quantitative analysis for the effects of internal flow on mass transfer processes inside rising bubbles

The mass transfer process inside bubbles is an important, but easily overlooked, component of the global mass transfer process. Bubble deformation influences the internal flow pattern and the mass transfer area. Furthermore, the internal flow impacts on the concentration distribution. This paper presents the results of a study on the mass transfer process inside bubbles and the interactions among the above factors using a computational fluid dynamics model. The accuracy of the model is verified by an experiment with a chromogenic reaction. Gas–interface mass transfer processes with and without internal flow are compared to show the positive effects of the shape change and the flow. A mass transfer enhancement factor, which is related to the concentration gradient and the mass transfer area, is presented to quantitatively analyze the effects. The results show that various internal flow patterns and concentration distributions can occur in different bubbles. The change in the average mass fraction and the average mass transfer coefficient of the process including internal flow are 2.8 times and 28.0% higher than those of the process without any internal flow. The enhancement factors are greater than 1.0, which indicates that a stronger internal flow intensifies the mass transfer process.

### Retention and infiltration of bacteria on a plant leaf driven by surface water evaporation

Evaporation-driven internal flows within a sessile droplet can transport microorganisms close to the leaf surface and facilitate their infiltration into the available openings, such as stomata. Here, using microfabricated surfaces out of polydimethylsiloxane, the sole effects of evaporation of sessile droplets in contamination of plant leaves was studied. These surfaces were patterned with stomata, trichomes, and grooves that are common surface microstructures on plant leaves. Evaporation of sessile droplets, containing bacterial suspensions, on real leaves and fabricated surfaces was studied using confocal microscopy. To provide insight about the effects of leaf hydrophobicity and surface roughness on the bacterial retention and infiltration, variations of contact angle of sessile droplets at these surfaces were measured during evaporation. The results showed that evaporation-driven flow transported bacteria close to the surface of spinach leaves and fabricated surfaces, leading to distinct infiltration into the stomata. Larger size and wider spacing of the micropores, and a more hydrophilic surface, led bacteria to spread more at the droplet base area and infiltrate into more stomata. Evaporation-driven movement of contact line, which can sweep bacteria over the leaf surface, was shown to lead to bacterial infiltration into the stomatal pores. Findings should help improve microbial safety of leafy greens.

### Extended Reynolds lubrication model for incompressible Newtonian fluid

Author(s): Shintaro Takeuchi and Jingchen Gu

An extended lubrication model is proposed by taking into account a larger surface-to-surface distance than that for the Reynolds lubrication theory, and the wall-normal variation of the pressure is related to the longitudinal derivative of the local velocity of the Couette-Poiseuille flow.

[Phys. Rev. Fluids 4, 114101] Published Tue Nov 19, 2019

### Nonlinear Darcy flow dynamics during ganglia stranding and mobilization in heterogeneous porous domains

Author(s): A. G. Yiotis, A. Dollari, M. E. Kainourgiakis, D. Salin, and L. Talon

Development of “tortuous” mean ganglia flux paths during immiscible two-phase flow through a disordered and periodic 2D porous domain is studied. Results reveal that such paths are related to the gradual mobilization of stranded ganglia due to the pore-scale interplay between capillary, gravity, and viscous forces.

[Phys. Rev. Fluids 4, 114302] Published Tue Nov 19, 2019

### Self-propulsion of a sticky sphere partially covered with a surface slip velocity

Microorganisms follow various strategies to swim in a viscous medium. In an attempt to understand the swimming of ciliated microorganisms, we study low Reynolds number locomotion of a rigid slip-stick swimmer where the propulsive slip velocity is concentrated around an annular patch, which imitates the distinctive surface activity of the microorganisms. In addition, we assume the Navier slip condition at the rigid-fluid interface, which contributes to the hydrodynamic slip or stickiness across the surface. We solve for the locomotion speed and the corresponding flow fields of the swimmer in an axisymmetric unbounded medium. Our analysis reveals insights into how the choice of active slip influences the swimming velocity and the other relevant swimming characteristics. Interestingly, we find that for an optimal active slip in the annular range [π/4, 3π/4], the locomotion speed of the partially covered swimmer is enhanced by a factor of [math] compared to the standard fully covered squirmer. In addition, the corresponding swimming efficiency is enhanced by ∼2.4 times. We independently treat the influence of stickiness of the swimmer on the swimming characteristics. We find that the stickiness reduces the hydrodynamic resistance for the partially covered swimmer and further enhances the swimming speed and efficiency. These findings will be helpful to design efficient artificial swimmers in terms of higher mobility and lower power dissipation.

### Effect of the magnetic field on the ferrofluid flow in a curved cylindrical annular duct

The laminar fully developed ferrofluid flow of an otherwise magnetic fluid into a curved annular duct of circular cross section, subjected to a transverse external magnetic field, is studied in the present work. The specific geometry is chosen as it is encountered in heat exchangers and mixers where compactness is a priority. Results are obtained for different values of curvature, field strength, and particles’ volumetric concentration. A computational algorithm is used which couples the continuity, Navier Stokes, and magnetization equations using a nonuniform grid. The velocity–pressure coupling is achieved using the so-called continuity-vorticity-pressure variational equation method, adapted to the toroidal-poloidal coordinate system. The results confirm the ability of the method to produce accurate results in curvilinear coordinates and stretched grids, which is important for the standardization of the method’s application to generalized coordinate systems. Concerning the micropolar flow characteristics, the results reveal the effect of the magnetic field on the ferrofluid flow. It is shown that the axial velocity distribution is highly affected by the field strength and the volumetric concentration, that the axial pressure drop depends almost linearly on the field strength, and that a secondary flow is generated due to the combined effect of the external magnetic field and the curvature. The present analysis provides important insight into the effect of the three main parameters, revealing cases where a straight annular pipe might be preferable to a curved one and specific parts of the pipe that could be susceptible to enhanced loads, giving information that is crucial for design optimization.

### A new liquid transport model considering complex influencing factors for nano- to micro-sized circular tubes and porous media

A new liquid transport model in wetted nano- to microsized circular tubes is proposed using basic dynamical analyses that comprehensively consider the Lifshitz–van der Waals force (LWF), the electroviscous force, the weak liquid compressibility, and the Bingham-plastic behavior. The model predicts that the average velocity is initially zero and increases nonlinearly with a concave shape before increasing linearly with the pressure gradient (ΔP/L) and is validated using the experimental data. The threshold pressure gradient (TPG) and the lower limit of the movable-fluid radius (Rm) are calculated based on the proposed model, which are mainly determined by the yield stresses from the Bingham plastic behavior and are also affected by the compressibility and LWF. Considering the microstructural complexity of real porous media, the average velocity model is also applicable for tight porous media with a capillary equivalent radius from the permeability. The calculated average velocity is non-Darcy with TPG. The TPG decreases as the permeability increases, and the Rm decreases with the pressure gradient in the low range and remains constant at the higher ranges, which is primarily between 10 and 30 nm. All these results for porous media are compared with the experimental data of core seepage and show good agreement in general. The proposed model has a clear parametric representation compared with previous nonlinear models. It explains the underlying reasons for the nonlinear, low-velocity flow mechanism in nano- to microsized tubes and pores and provides theoretical guidance for liquid transport in porous media and oil recovery from tight oil reservoirs.

### A self-similarity mathematical model of carbon isotopic flow fractionation during shale gas desorption

The existence of nanosized pore systems differentiates isotopic gas transport inside a shale matrix from conventional continuum flow. In this study, a novel self-similarity mathematical model was developed to investigate the effects of gas flow transport (both slip flow and free molecular diffusion flow) on isotopic gas fractionation for four different shale samples (S1 and S2 from north Germany and S3 and S4 from Xiashiwan Field, Ordos Basin, China). In this model, the nonlinear permeability and diffusion coefficients were developed for the isotopologues (12CH4 and 13CH4), respectively. By selecting appropriate exponents of the pressure gradient for 12CH4 and 13CH4, respectively, the estimated isotopic methane concentration and production rate showed a good agreement with experimental data. The developed model shows that the gas concentration of the isotopologues in samples S1 and S2 increases with time following a power law. Similarly, the gas production rates of the isotopologues in samples S3 and S4 decay with time following a power law. Moreover, the exponents of the pressure gradient for the isotopologues are close to 4 for samples S1 and S2, indicating that the effect of slip flow on isotopic gas fractionation cannot be ignored. For samples S3 and S4, the exponents of the pressure gradient for the isotopologues increase with temperature rising, which shows the promotion of isotopic gas fractionation under higher heating temperatures. The slight difference between the exponents of the pressure gradient for the isotopologues for the same shale sample reveals that the isotopic gas fractionation of carbon is a slow process.

### Landmarks and frontiers in biological fluid dynamics

Author(s): John O. Dabiri

The broad relevance of fluid mechanics to biology has been increasingly appreciated by engineers and biologists alike, leading to continued expansion of research in the field of biological fluid dynamics. A selection of classic and recent work that can guide future research is highlighted.

[Phys. Rev. Fluids 4, 110501] Published Mon Nov 18, 2019

### Singularities in fluid mechanics

Author(s): H. K. Moffatt

A dynamical system is described that captures the near-singular character of vortex reconnection, thus indicating how enstrophy in turbulent flow can become infinite in the zero-viscosity limit. Similarities with the near-singular behavior in the problem of cusp-formation at a free surface are identified.

[Phys. Rev. Fluids 4, 110502] Published Mon Nov 18, 2019

### Flight of the fruit fly

Author(s): Itai Cohen

Professor Itai Cohen describes the challenge of studying insect flight and, in the accompanying video recording of his invited lecture from the 71st annual APS DFD meeting, illustrates the mechanisms used by insects to control this behavior and achieve spellbinding acrobatic feats.

[Phys. Rev. Fluids 4, 110503] Published Mon Nov 18, 2019

### Horizontal axis wind turbine testing at high Reynolds numbers

Author(s): Mark A. Miller, Janik Kiefer, Carsten Westergaard, Martin O. L. Hansen, and Marcus Hultmark

The flow conditions of a full-scale wind turbine are reproduced in a laboratory with dynamic similarity, using a pressurized wind tunnel. Aerodynamic scale-effects persist at higher Re than previously believed, and it is shown that the boundary layer state is critical for turbine performance.

[Phys. Rev. Fluids 4, 110504] Published Mon Nov 18, 2019

### Coherent structure-based approach to modeling wall turbulence

Author(s): Dennice F. Gayme and Benjamin A. Minnick

A restricted nonlinear representation of the flow as a streamwise constant large-scale interacting with dynamically restricted perturbations faithfully reproduces low order statistics, cross-stream structures and energy transport in turbulent channels, at vastly reduced computational costs.

[Phys. Rev. Fluids 4, 110505] Published Mon Nov 18, 2019