# Physics of Fluids

Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.

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### Stability of slip channel flow revisited

Physics of Fluids, Volume 31, Issue 8, August 2019.

In this work, we revisit the temporal stability of slip channel flow. Lauga and Cossu [“A note on the stability of slip channel flows,” Phys. Fluids 17, 088106 (2005)] and Min and Kim [“Effects of hydrophobic surface on stability and transition,” Phys. Fluids 17, 108106 (2005)] have investigated both modal stability and non-normality of slip channel flow and concluded that the velocity slip greatly suppresses linear instability and only modestly affects the non-normality. Here, we study the stability of channel flow with streamwise and spanwise slip separately as two limiting cases of anisotropic slip and explore a broader range of slip length than previous studies did. We find that, with a sufficiently large slip, both streamwise and spanwise slip trigger three-dimensional leading instabilities. Overall, the critical Reynolds number is only slightly increased by streamwise slip, whereas it can be greatly decreased by spanwise slip. Streamwise slip suppresses the nonmodal transient growth, whereas the spanwise slip enlarges the nonmodal growth, although it does not affect the base flow. Interestingly, as the spanwise slip length increases, the optimal perturbations exhibit flow structures different from the well-known streamwise rolls. However, in the presence of equal slip in both directions, the three-dimensional leading instabilities disappear and the flow is greatly stabilized. The results suggest that earlier instability and larger transient growth can be triggered by introducing anisotropy in the velocity slip.

In this work, we revisit the temporal stability of slip channel flow. Lauga and Cossu [“A note on the stability of slip channel flows,” Phys. Fluids 17, 088106 (2005)] and Min and Kim [“Effects of hydrophobic surface on stability and transition,” Phys. Fluids 17, 108106 (2005)] have investigated both modal stability and non-normality of slip channel flow and concluded that the velocity slip greatly suppresses linear instability and only modestly affects the non-normality. Here, we study the stability of channel flow with streamwise and spanwise slip separately as two limiting cases of anisotropic slip and explore a broader range of slip length than previous studies did. We find that, with a sufficiently large slip, both streamwise and spanwise slip trigger three-dimensional leading instabilities. Overall, the critical Reynolds number is only slightly increased by streamwise slip, whereas it can be greatly decreased by spanwise slip. Streamwise slip suppresses the nonmodal transient growth, whereas the spanwise slip enlarges the nonmodal growth, although it does not affect the base flow. Interestingly, as the spanwise slip length increases, the optimal perturbations exhibit flow structures different from the well-known streamwise rolls. However, in the presence of equal slip in both directions, the three-dimensional leading instabilities disappear and the flow is greatly stabilized. The results suggest that earlier instability and larger transient growth can be triggered by introducing anisotropy in the velocity slip.

Categories: Latest papers in fluid mechanics

### A computational study of droplet-based bioprinting: Effects of viscoelasticity

Physics of Fluids, Volume 31, Issue 8, August 2019.

Despite significant progress, cell viability continues to be a central issue in droplet-based bioprinting applications. Common bioinks exhibit viscoelastic behavior owing to the presence of long-chain molecules in their mixture. We computationally study effects of viscoelasticity of bioinks on cell viability during deposition of cell-loaded droplets on a substrate using a compound droplet model. The inner droplet, which represents the cell, and the encapsulating droplet are modeled as viscoelastic liquids with different material properties, while the ambient fluid is Newtonian. The model proposed by Takamatsu and Rubinsky [“Viability of deformed cells,” Cryobiology 39(3), 243–251 (1999)] is used to relate cell deformation to cell viability. We demonstrate that adding viscoelasticity to the encapsulating droplet fluid can significantly enhance the cell viability, suggesting that viscoelastic properties of bioinks can be tailored to achieve high cell viability in droplet-based bioprinting systems. The effects of the cell viscoelasticity are also examined, and it is shown that the Newtonian cell models may significantly overpredict the cell viability.

Despite significant progress, cell viability continues to be a central issue in droplet-based bioprinting applications. Common bioinks exhibit viscoelastic behavior owing to the presence of long-chain molecules in their mixture. We computationally study effects of viscoelasticity of bioinks on cell viability during deposition of cell-loaded droplets on a substrate using a compound droplet model. The inner droplet, which represents the cell, and the encapsulating droplet are modeled as viscoelastic liquids with different material properties, while the ambient fluid is Newtonian. The model proposed by Takamatsu and Rubinsky [“Viability of deformed cells,” Cryobiology 39(3), 243–251 (1999)] is used to relate cell deformation to cell viability. We demonstrate that adding viscoelasticity to the encapsulating droplet fluid can significantly enhance the cell viability, suggesting that viscoelastic properties of bioinks can be tailored to achieve high cell viability in droplet-based bioprinting systems. The effects of the cell viscoelasticity are also examined, and it is shown that the Newtonian cell models may significantly overpredict the cell viability.

Categories: Latest papers in fluid mechanics

### Numerical and experimental study of the motion of a sphere in a communicating vessel system subject to sloshing

Physics of Fluids, Volume 31, Issue 8, August 2019.

The purpose of this work is twofold: to present a computational strategy to simulate the dynamics of a rigid sphere during water sloshing and to validate the model with original experimental data. The numerical solution is obtained through the coupling between a two-fluid Navier-Stokes solver and a rigid solid dynamics solver, based on a Newton scheme. A settling sphere case reported in the literature is first analyzed to validate the numerical strategy by ascertaining the settling velocity. In addition, an experiment is carried out based on a sphere submerged into a communicating vessel subjected to sloshing. Experimental data are captured using image processing and statistically treated to provide sphere dynamics quantitative information. The effects of different classical models used to describe drag coefficients, added mass, and wall effects are considered in the study to evaluate their influence on the results. The numerical model provides results that are consistent with the physical data, and the trajectory analysis shows good agreement between the simulations and the experiments.

The purpose of this work is twofold: to present a computational strategy to simulate the dynamics of a rigid sphere during water sloshing and to validate the model with original experimental data. The numerical solution is obtained through the coupling between a two-fluid Navier-Stokes solver and a rigid solid dynamics solver, based on a Newton scheme. A settling sphere case reported in the literature is first analyzed to validate the numerical strategy by ascertaining the settling velocity. In addition, an experiment is carried out based on a sphere submerged into a communicating vessel subjected to sloshing. Experimental data are captured using image processing and statistically treated to provide sphere dynamics quantitative information. The effects of different classical models used to describe drag coefficients, added mass, and wall effects are considered in the study to evaluate their influence on the results. The numerical model provides results that are consistent with the physical data, and the trajectory analysis shows good agreement between the simulations and the experiments.

Categories: Latest papers in fluid mechanics

### Statistical analysis of vortical structures in turbulent boundary layer over directional grooved surface pattern with spanwise heterogeneity

Physics of Fluids, Volume 31, Issue 8, August 2019.

We examine the turbulent boundary layers developing over convergent-divergent riblets (C-D riblets) with three different heights (h+ = 8, 14, and 20) at Reθ = 723 using particle image velocimetry. It is observed that although a logarithmic region presents in the velocity profiles over the converging and diverging line, Townsend’s outer-layer similarity hypothesis is invalid. Compared to the smooth-wall case, C-D riblets with a height of 2.4% of the smooth-wall boundary layer thickness can cause a significant increase in the turbulence production activities over the converging region, as evidenced by a more than 50% increase in the turbulent shear stress and in the population of prograde and retrograde spanwise vortices. In contrast, the impact of riblets on the diverging region is much smaller. The slope of vortex packets becomes steeper, and they are more streamwise stretched in the outer layer over the diverging region, whereas their shape and orientation is less affected over the converging region. Furthermore, the number of uniform momentum zones across the boundary layer increases over the converging region, causing a reduction in the thickness of uniform momentum zones in the outer part of the boundary layer. Overall, while an increased riblet height affects a large portion of the boundary layer away from the wall over the converging region, the impact on the diverging region is largely confined within the near-wall region. Such distinct differences in the response of the boundary layer over the diverging and converging region are attributed to the opposite local secondary flow motion induced by C-D riblets.

We examine the turbulent boundary layers developing over convergent-divergent riblets (C-D riblets) with three different heights (h+ = 8, 14, and 20) at Reθ = 723 using particle image velocimetry. It is observed that although a logarithmic region presents in the velocity profiles over the converging and diverging line, Townsend’s outer-layer similarity hypothesis is invalid. Compared to the smooth-wall case, C-D riblets with a height of 2.4% of the smooth-wall boundary layer thickness can cause a significant increase in the turbulence production activities over the converging region, as evidenced by a more than 50% increase in the turbulent shear stress and in the population of prograde and retrograde spanwise vortices. In contrast, the impact of riblets on the diverging region is much smaller. The slope of vortex packets becomes steeper, and they are more streamwise stretched in the outer layer over the diverging region, whereas their shape and orientation is less affected over the converging region. Furthermore, the number of uniform momentum zones across the boundary layer increases over the converging region, causing a reduction in the thickness of uniform momentum zones in the outer part of the boundary layer. Overall, while an increased riblet height affects a large portion of the boundary layer away from the wall over the converging region, the impact on the diverging region is largely confined within the near-wall region. Such distinct differences in the response of the boundary layer over the diverging and converging region are attributed to the opposite local secondary flow motion induced by C-D riblets.

Categories: Latest papers in fluid mechanics

### Comparison of simulation and experiments for multimode aerodynamic breakup of a liquid metal column in a shock-induced cross-flow

Physics of Fluids, Volume 31, Issue 8, August 2019.

While the mechanisms that drive breakup and aerodynamic dispersion of traditional liquids such as water have been extensively studied, it is not yet clear if models for traditional liquids can be used to accurately describe the behavior of molten metals. In this paper, multiphase simulations with the interface-capturing combined level-set volume-of-fluid approach are used to provide time-resolved morphology and breakup data for a liquid column subject to a shock-induced cross-flow. For the first time, numerical simulation of the behavior of a liquid metal (Galinstan alloy composed of gallium, indium, and tin) is compared to the well-documented behavior of water. Simulations consider a gas cross-flow Weber number between 10 and 12, which produces a multimode breakup morphology consisting of multiple baglike structures. Up to bag breakup, we confirm that the deformation rate of Galinstan follows the same dependence on the gas cross-flow Weber number as ordinary liquids when time is nondimensionalized by including the liquid-gas density ratio. Moreover, we determine that the appearance of a central stem along the column upstream surface in multimode bag breakup is consistent with the occurrence of Rayleigh-Taylor instability. We also resolve bag stretching and fragmentation, to the full extent allowed by our computational resources, and carry out a direct comparison with the measurements of size and velocity of secondary droplets from high-speed digital inline holography. For Galinstan, we illustrate the differences between simulation and experiment that emerge because of the modification of the surface properties of the metal exposed to air.

While the mechanisms that drive breakup and aerodynamic dispersion of traditional liquids such as water have been extensively studied, it is not yet clear if models for traditional liquids can be used to accurately describe the behavior of molten metals. In this paper, multiphase simulations with the interface-capturing combined level-set volume-of-fluid approach are used to provide time-resolved morphology and breakup data for a liquid column subject to a shock-induced cross-flow. For the first time, numerical simulation of the behavior of a liquid metal (Galinstan alloy composed of gallium, indium, and tin) is compared to the well-documented behavior of water. Simulations consider a gas cross-flow Weber number between 10 and 12, which produces a multimode breakup morphology consisting of multiple baglike structures. Up to bag breakup, we confirm that the deformation rate of Galinstan follows the same dependence on the gas cross-flow Weber number as ordinary liquids when time is nondimensionalized by including the liquid-gas density ratio. Moreover, we determine that the appearance of a central stem along the column upstream surface in multimode bag breakup is consistent with the occurrence of Rayleigh-Taylor instability. We also resolve bag stretching and fragmentation, to the full extent allowed by our computational resources, and carry out a direct comparison with the measurements of size and velocity of secondary droplets from high-speed digital inline holography. For Galinstan, we illustrate the differences between simulation and experiment that emerge because of the modification of the surface properties of the metal exposed to air.

Categories: Latest papers in fluid mechanics

### Development of an impulsive model of dissociation in direct simulation Monte Carlo

Physics of Fluids, Volume 31, Issue 8, August 2019.

A previously proposed classical impulsive model for dissociation of diatomic molecules in direct simulation Monte Carlo (DSMC), the Macheret-Fridman for direct simulation Monte Carlo (MF-DSMC) model [Luo et al., “Classical impulsive model for dissociation of diatomic molecules in direct simulation Monte Carlo,” Phys. Rev. Fluids 3, 113401 (2018)], is extended in this work. To improve the prediction of state-specific rates at high vibrational energy, the anharmonic vibrational phase angle distribution function is first incorporated into the model. Then, to improve the prediction of thermal equilibrium dissociation rates, the general concept of calculating total collision cross sections with the MF-DSMC model is discussed and the framework of implementing a collision model based on exponential potential is constructed. The improved model is validated by comparisons with quasiclassical trajectory calculations, empirical estimations, and experimental measurements. In general, better agreement compared with the original version of the model is obtained. The improved model is also evaluated by simulating O2 reacting shock experiment.

A previously proposed classical impulsive model for dissociation of diatomic molecules in direct simulation Monte Carlo (DSMC), the Macheret-Fridman for direct simulation Monte Carlo (MF-DSMC) model [Luo et al., “Classical impulsive model for dissociation of diatomic molecules in direct simulation Monte Carlo,” Phys. Rev. Fluids 3, 113401 (2018)], is extended in this work. To improve the prediction of state-specific rates at high vibrational energy, the anharmonic vibrational phase angle distribution function is first incorporated into the model. Then, to improve the prediction of thermal equilibrium dissociation rates, the general concept of calculating total collision cross sections with the MF-DSMC model is discussed and the framework of implementing a collision model based on exponential potential is constructed. The improved model is validated by comparisons with quasiclassical trajectory calculations, empirical estimations, and experimental measurements. In general, better agreement compared with the original version of the model is obtained. The improved model is also evaluated by simulating O2 reacting shock experiment.

Categories: Latest papers in fluid mechanics

### Axial conduction and dissipation in oscillatory laminar pipe flow at low and high frequencies

Physics of Fluids, Volume 31, Issue 8, August 2019.

The problem of fully developed laminar fluid flow in pipes, driven by an oscillatory pressure gradient, can be solved exactly for the time-dependent velocity field and related quantities such as flow rate and tidal displacement. When dissipation is neglected and the momentary axial variation of temperature is assumed to be linear, the corresponding thermal energy equation describing heat transfer along a pipe connecting two reservoirs at different temperatures can also be solved to yield exact solutions for the time-dependent temperature field, axial heat flux, and effective axial conductivity. In this paper, it is shown that these exact solutions for the unsteady temperature field are invalid at low Womersley numbers because the momentary axial variation of temperature is not linear. When the thermal energy equation is written in quasisteady form, approximate quasisteady analytical solutions can be found for the temperature field, which yield effective axial conductivities several orders of magnitude greater than those given by the low-Womersley-number, unsteady-flow solution. It is also shown that the conditions under which effects of dissipation on axial heat transfer become significant, at high Womersley numbers, can be determined by a simple criterion. When dissipation is significant, exact solutions for the unsteady temperature field are invalid at high Womersley numbers because the momentary axial variation of temperature is also nonlinear.

The problem of fully developed laminar fluid flow in pipes, driven by an oscillatory pressure gradient, can be solved exactly for the time-dependent velocity field and related quantities such as flow rate and tidal displacement. When dissipation is neglected and the momentary axial variation of temperature is assumed to be linear, the corresponding thermal energy equation describing heat transfer along a pipe connecting two reservoirs at different temperatures can also be solved to yield exact solutions for the time-dependent temperature field, axial heat flux, and effective axial conductivity. In this paper, it is shown that these exact solutions for the unsteady temperature field are invalid at low Womersley numbers because the momentary axial variation of temperature is not linear. When the thermal energy equation is written in quasisteady form, approximate quasisteady analytical solutions can be found for the temperature field, which yield effective axial conductivities several orders of magnitude greater than those given by the low-Womersley-number, unsteady-flow solution. It is also shown that the conditions under which effects of dissipation on axial heat transfer become significant, at high Womersley numbers, can be determined by a simple criterion. When dissipation is significant, exact solutions for the unsteady temperature field are invalid at high Womersley numbers because the momentary axial variation of temperature is also nonlinear.

Categories: Latest papers in fluid mechanics

### Erratum: “Numerical simulation of the interaction of two shear layers in double backward-facing steps” [Phys. Fluids 31, 056106 (2019)]

Physics of Fluids, Volume 31, Issue 8, August 2019.

Categories: Latest papers in fluid mechanics

### Macromolecular architecture and complex viscosity

Physics of Fluids, Volume 31, Issue 8, August 2019.

General rigid bead-rod theory [O. Hassager, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60(10), 4001–4008 (1974)] explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead-rod theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric macromolecules. In this work, we explore the zero-shear and complex viscosities of 24 different axisymmetric polymer configurations. When nondimensionalized with the zero-shear viscosity, the complex viscosity depends on the dimensionless frequency and the sole dimensionless architectural parameter, the macromolecular lopsidedness. In this work, in this way, we compare and contrast the elastic and viscous components of the complex viscosities of macromolecular chains that are straight, branched, ringed, or star-branched. We explore the effects of branch position along a straight chain, branched-chain backbone length, branched-chain branch-functionality, branch spacing along a straight chain (including pom-poms), the number of branches along a straight chain, ringed polymer perimeter, branch-functionality in planar stars, and branch dimensionality.

General rigid bead-rod theory [O. Hassager, “Kinetic theory and rheology of bead-rod models for macromolecular solutions. II. Linear unsteady flow properties,” J. Chem. Phys. 60(10), 4001–4008 (1974)] explains polymer viscoelasticity from macromolecular orientation. By means of general rigid bead-rod theory, we relate the complex viscosity of polymeric liquids to the architecture of axisymmetric macromolecules. In this work, we explore the zero-shear and complex viscosities of 24 different axisymmetric polymer configurations. When nondimensionalized with the zero-shear viscosity, the complex viscosity depends on the dimensionless frequency and the sole dimensionless architectural parameter, the macromolecular lopsidedness. In this work, in this way, we compare and contrast the elastic and viscous components of the complex viscosities of macromolecular chains that are straight, branched, ringed, or star-branched. We explore the effects of branch position along a straight chain, branched-chain backbone length, branched-chain branch-functionality, branch spacing along a straight chain (including pom-poms), the number of branches along a straight chain, ringed polymer perimeter, branch-functionality in planar stars, and branch dimensionality.

Categories: Latest papers in fluid mechanics

### Saturated film boiling over a circular cylinder subjected to horizontal cross-flow in the mixed regime

Physics of Fluids, Volume 31, Issue 8, August 2019.

Film boiling over a circular cylinder in a horizontal cross-flow of saturated liquid is studied in the mixed regime that is characterized by a combined influence of buoyancy and flow inertia at low magnitudes of the Froude number (Fr). Liquid-vapor interface evolution and the ensuing vapor wake dynamics together with heat transfer have been determined through a computational framework developed for phase change problems on two-dimensional unstructured grids using a coupled level set and volume of fluid interface capturing method. While the quasisteady nature of ebullition cycle is gradually lost as Fr increases, the effect of cross-flow orientation with respect to gravity is shown to be nontrivial in the mixed regime. A direct consequence of the orthogonal gravity and flow fields is an anomalous impairment of heat transfer with an increase in cross-flow velocity under certain conditions, which is discussed in detail. Simultaneously, the film boiling behavior as influenced by several other hydrodynamic and thermal parameters is also ascertained. The interplay between buoyancy and inertia is further highlighted while discussing the interdependent liquid and vapor wake characteristics in the mixed regime with horizontal cross-flow. The liquid wake behavior is shown to result not only from the bluff body geometry but also the instantaneous vapor wake profiles, with the wall superheat affecting the time scale of wake interaction. Finally, a reduction factor (ξ) is proposed and determined as a function of the Froude number, which is used in conjunction with a correlation for upward cross-flow film boiling to predict the heat transfer.

Film boiling over a circular cylinder in a horizontal cross-flow of saturated liquid is studied in the mixed regime that is characterized by a combined influence of buoyancy and flow inertia at low magnitudes of the Froude number (Fr). Liquid-vapor interface evolution and the ensuing vapor wake dynamics together with heat transfer have been determined through a computational framework developed for phase change problems on two-dimensional unstructured grids using a coupled level set and volume of fluid interface capturing method. While the quasisteady nature of ebullition cycle is gradually lost as Fr increases, the effect of cross-flow orientation with respect to gravity is shown to be nontrivial in the mixed regime. A direct consequence of the orthogonal gravity and flow fields is an anomalous impairment of heat transfer with an increase in cross-flow velocity under certain conditions, which is discussed in detail. Simultaneously, the film boiling behavior as influenced by several other hydrodynamic and thermal parameters is also ascertained. The interplay between buoyancy and inertia is further highlighted while discussing the interdependent liquid and vapor wake characteristics in the mixed regime with horizontal cross-flow. The liquid wake behavior is shown to result not only from the bluff body geometry but also the instantaneous vapor wake profiles, with the wall superheat affecting the time scale of wake interaction. Finally, a reduction factor (ξ) is proposed and determined as a function of the Froude number, which is used in conjunction with a correlation for upward cross-flow film boiling to predict the heat transfer.

Categories: Latest papers in fluid mechanics

### Impact of the Lewis number on finger flame acceleration at the early stage of burning in channels and tubes

Physics of Fluids, Volume 31, Issue 8, August 2019.

For premixed combustion in channels and tubes with one end open, when a flame is ignited at the centerline at the closed end of the pipe and it propagates toward the open one, significant flame acceleration occurs at an early stage of the combustion process due to formation of a finger-shaped flame front. This scenario is tagged “finger flame acceleration” (FFA), involving an initially hemispherical flame kernel, which subsequently acquires a finger shape with increasing surface area of the flame front. Previous analytical and computational studies of FFA employed a conventional assumption of equidiffusivity when the thermal-to-mass-diffusivity ratio (the Lewis number) is unity (Le = 1). However, combustion is oftentimes nonequidiffusive (Le ≠ 1) in practice such that there has been a need to identify the role of Le in FFA. This demand is addressed in the present work. Specifically, the dynamics and morphology of the Le ≠ 1 flames in two-dimensional (2D) channels and cylindrical tubes are scrutinized by means of the computational simulations of the fully compressible reacting flow equations, and the role of Le is identified. Specifically, the Le > 1 flames accelerate slower as compared with the equidiffusive ones. In contrast, the Le < 1 flames acquire stronger distortion of the front, experience the diffusional-thermal combustion instability, and thereby accelerate much faster than the Le = 1 flames. In addition, combustion in a cylindrical configuration shows stronger FFA than that under the same burning conditions in a 2D planar geometry.

For premixed combustion in channels and tubes with one end open, when a flame is ignited at the centerline at the closed end of the pipe and it propagates toward the open one, significant flame acceleration occurs at an early stage of the combustion process due to formation of a finger-shaped flame front. This scenario is tagged “finger flame acceleration” (FFA), involving an initially hemispherical flame kernel, which subsequently acquires a finger shape with increasing surface area of the flame front. Previous analytical and computational studies of FFA employed a conventional assumption of equidiffusivity when the thermal-to-mass-diffusivity ratio (the Lewis number) is unity (Le = 1). However, combustion is oftentimes nonequidiffusive (Le ≠ 1) in practice such that there has been a need to identify the role of Le in FFA. This demand is addressed in the present work. Specifically, the dynamics and morphology of the Le ≠ 1 flames in two-dimensional (2D) channels and cylindrical tubes are scrutinized by means of the computational simulations of the fully compressible reacting flow equations, and the role of Le is identified. Specifically, the Le > 1 flames accelerate slower as compared with the equidiffusive ones. In contrast, the Le < 1 flames acquire stronger distortion of the front, experience the diffusional-thermal combustion instability, and thereby accelerate much faster than the Le = 1 flames. In addition, combustion in a cylindrical configuration shows stronger FFA than that under the same burning conditions in a 2D planar geometry.

Categories: Latest papers in fluid mechanics

### Surface parametric instability of star-shaped oscillating liquid drops

Physics of Fluids, Volume 31, Issue 8, August 2019.

The star-shaped oscillation of water drops has been observed in various physical situations under vertical excitation with different sources. In the past, the motion of such drops was simplified to two dimensions and only the azimuthal oscillation modes were considered. The parametric instability mechanism explained with the 2D (two-dimensional) model and the corresponding dispersion relation are not satisfactory. In this paper, we show that the external excitation induces a Faraday-wave-like parametric instability on the upper surface of the drop, and the surface patterns and azimuthal oscillations are coupled to produce star-shaped oscillations, which induces a significant softening to oscillation frequencies. We build a 3D (three-dimensional) theoretical model, in which the surface patterns and azimuthal oscillations are connected via kinematical boundary conditions and vary at the same frequency. Given the surface and azimuthal mode numbers, we propose a quasi-3D dispersion relation, which shows better consistency with the experimental data compared with the previous quasi-2D dispersion relation. Our theoretical model provides a more accurate description of the dynamics of liquid drops and will motivate a wide range of applications.

The star-shaped oscillation of water drops has been observed in various physical situations under vertical excitation with different sources. In the past, the motion of such drops was simplified to two dimensions and only the azimuthal oscillation modes were considered. The parametric instability mechanism explained with the 2D (two-dimensional) model and the corresponding dispersion relation are not satisfactory. In this paper, we show that the external excitation induces a Faraday-wave-like parametric instability on the upper surface of the drop, and the surface patterns and azimuthal oscillations are coupled to produce star-shaped oscillations, which induces a significant softening to oscillation frequencies. We build a 3D (three-dimensional) theoretical model, in which the surface patterns and azimuthal oscillations are connected via kinematical boundary conditions and vary at the same frequency. Given the surface and azimuthal mode numbers, we propose a quasi-3D dispersion relation, which shows better consistency with the experimental data compared with the previous quasi-2D dispersion relation. Our theoretical model provides a more accurate description of the dynamics of liquid drops and will motivate a wide range of applications.

Categories: Latest papers in fluid mechanics

### Spatiotemporal linear stability of viscoelastic free shear flows: Dilute regime

Physics of Fluids, Volume 31, Issue 8, August 2019.

We report the temporal and spatiotemporal stability analyses of antisymmetric, free shear, viscoelastic flows obeying the Oldroyd-B constitutive equation in the limit of low to moderate Reynolds number (Re) and Weissenberg number (We). The resulting fourth-order Orr-Sommerfeld equation is reduced to a set of six auxiliary equations that are numerically integrated starting from the rescaled far-field conditions, i.e., via Compound Matrix Method. The temporal stability analysis indicates that with increasing We, (a) the entire range of the most unstable mode is shifted toward longer waves (i.e., the entire region of temporal instability is gradually concentrated near zero wavenumber), (b) the vorticity structure contours are dilated, and (c) the residual Reynolds stresses are diminished. All these analogous observations previously reported in the inertial limit [J. Azaiez and G. M. Homsy, “Linear stability of free shear flow of viscoelastic liquids,” J. Fluid Mech. 268, 37–69 (1994).] suggest a viscoelastic destabilization mechanism operating at low and moderate Re. The Briggs idea of analytic continuation is deployed to classify regions of temporal stability, absolute and convective instabilities, as well as evanescent modes. The main result is that the free shear flow of dilute polymeric liquids is either (absolutely/convectively) unstable for all Re or the transition to instability occurs at comparatively low Re, a finding attributed to the fact that viscoelasticity aggravates instabilities via shear-induced anisotropy and the slow relaxation effects.

We report the temporal and spatiotemporal stability analyses of antisymmetric, free shear, viscoelastic flows obeying the Oldroyd-B constitutive equation in the limit of low to moderate Reynolds number (Re) and Weissenberg number (We). The resulting fourth-order Orr-Sommerfeld equation is reduced to a set of six auxiliary equations that are numerically integrated starting from the rescaled far-field conditions, i.e., via Compound Matrix Method. The temporal stability analysis indicates that with increasing We, (a) the entire range of the most unstable mode is shifted toward longer waves (i.e., the entire region of temporal instability is gradually concentrated near zero wavenumber), (b) the vorticity structure contours are dilated, and (c) the residual Reynolds stresses are diminished. All these analogous observations previously reported in the inertial limit [J. Azaiez and G. M. Homsy, “Linear stability of free shear flow of viscoelastic liquids,” J. Fluid Mech. 268, 37–69 (1994).] suggest a viscoelastic destabilization mechanism operating at low and moderate Re. The Briggs idea of analytic continuation is deployed to classify regions of temporal stability, absolute and convective instabilities, as well as evanescent modes. The main result is that the free shear flow of dilute polymeric liquids is either (absolutely/convectively) unstable for all Re or the transition to instability occurs at comparatively low Re, a finding attributed to the fact that viscoelasticity aggravates instabilities via shear-induced anisotropy and the slow relaxation effects.

Categories: Latest papers in fluid mechanics

### Rheological signatures of aging in hard sphere colloidal glasses

Physics of Fluids, Volume 31, Issue 8, August 2019.

Colloidal glasses are out-of-equilibrium in nature. When such materials are quenched from a shear-melted state into a quiescent one, their structure freezes due to entropic caging of the constituents. However, thermal fluctuations allow slow structural evolution, a process known as aging, in favor of minimizing free energy. Here, we examine the rheological signatures of aging, in a model system of nearly hard sphere colloidal glass. Subtle changes in the linear viscoelastic properties are detected with the age of the colloidal glass where viscous modulus shows a decrease with aging whereas the elastic modulus remains unaffected. This is associated with the slowing-down of long-time out-of-cage dynamics as the glass ages. On the contrary, nonlinear rheological measurements such as start-up shear flow, stress relaxation, and creep experiments show a strong dependence on sample age. Moreover, creep and stress relaxation experiments show ample evidence of avalanche type processes that occur during aging of colloidal glasses. Finally, comparison of creep and start-up shear flow measurements indicate that the latter is more energy efficient in inducing flow in colloidal glasses irrespective of aging dynamics.

Colloidal glasses are out-of-equilibrium in nature. When such materials are quenched from a shear-melted state into a quiescent one, their structure freezes due to entropic caging of the constituents. However, thermal fluctuations allow slow structural evolution, a process known as aging, in favor of minimizing free energy. Here, we examine the rheological signatures of aging, in a model system of nearly hard sphere colloidal glass. Subtle changes in the linear viscoelastic properties are detected with the age of the colloidal glass where viscous modulus shows a decrease with aging whereas the elastic modulus remains unaffected. This is associated with the slowing-down of long-time out-of-cage dynamics as the glass ages. On the contrary, nonlinear rheological measurements such as start-up shear flow, stress relaxation, and creep experiments show a strong dependence on sample age. Moreover, creep and stress relaxation experiments show ample evidence of avalanche type processes that occur during aging of colloidal glasses. Finally, comparison of creep and start-up shear flow measurements indicate that the latter is more energy efficient in inducing flow in colloidal glasses irrespective of aging dynamics.

Categories: Latest papers in fluid mechanics

### Reynolds number effect on drag control via spanwise wall oscillation in turbulent channel flows

Physics of Fluids, Volume 31, Issue 8, August 2019.

The effect of Reynolds number (Reτ) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Reτ ranging from 200 to 2000. For the nondimensional oscillation period T+ = 100 with maximum velocity amplitude A+ = 12, the drag reduction ([math]) decreases from 35.3% ± 0.5% at Reτ = 200 to 22.3% ± 0.7% at Reτ = 2000. The oscillation frequency ω+ for maximum [math] slightly increases with Reτ, i.e., from ω+ ≈ 0.06 at Reτ = 200 to 0.08 at Reτ = 2000, with [math]. These results show that [math] progressively decreases with increasing Reτ. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Reτ. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Reτ is due to the weakened effectiveness in suppressing the near-wall large-scale turbulence, whose contribution continuously increases due to the enhanced modulation and penetration effect of the large-scale and very large-scale motions in the log and outer regions. Both the power-law model ([math]) and the log-law model [DR = f(Reτ, ΔB), where ΔB is the vertical shift of the log-law intercept under control] are examined here by comparing them with our simulation data, from these two models we predict more than 10% drag reduction at very high Reynolds numbers, say, Reτ = 105.

The effect of Reynolds number (Reτ) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Reτ ranging from 200 to 2000. For the nondimensional oscillation period T+ = 100 with maximum velocity amplitude A+ = 12, the drag reduction ([math]) decreases from 35.3% ± 0.5% at Reτ = 200 to 22.3% ± 0.7% at Reτ = 2000. The oscillation frequency ω+ for maximum [math] slightly increases with Reτ, i.e., from ω+ ≈ 0.06 at Reτ = 200 to 0.08 at Reτ = 2000, with [math]. These results show that [math] progressively decreases with increasing Reτ. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Reτ. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Reτ is due to the weakened effectiveness in suppressing the near-wall large-scale turbulence, whose contribution continuously increases due to the enhanced modulation and penetration effect of the large-scale and very large-scale motions in the log and outer regions. Both the power-law model ([math]) and the log-law model [DR = f(Reτ, ΔB), where ΔB is the vertical shift of the log-law intercept under control] are examined here by comparing them with our simulation data, from these two models we predict more than 10% drag reduction at very high Reynolds numbers, say, Reτ = 105.

Categories: Latest papers in fluid mechanics

### Vortex dynamics during acoustic-mode transition in channel branches

Physics of Fluids, Volume 31, Issue 8, August 2019.

The vortex dynamics during acoustic mode transition in channel branches were experimentally investigated with phase-locking particle image velocimetry (PIV) measurements. Particularly, a real-time waveform recognition approach, based on an offline pressure analysis by dynamic mode decomposition (DMD) and a real-time computation by field programmable gate array, was established. In the offline DMD analysis, energetic pressure DMD modes during acoustic mode transition were extracted from pressure data measured by a pressure transducer array and found to agree well with the natural acoustic standing-wave modes numerically determined from an acoustic modal analysis. The acoustic mode transition process was classified into three successive phases: Phase-I: hybrid acoustic modulations, Phase-II: no acoustic modulation, and Phase-III: third-order acoustic modulation. Subsequently, the vortex dynamics corresponding to Phase-I and Phase-III were determined by phase-locking PIV measurements with the real-time waveform recognition approach. The results are summarized as follows. (1) The vortex dynamics coupled with the first acoustic standing-wave mode in Phase-I were related to the first shear layer hydrodynamic mode in channel branches. (2) The vortex dynamics coupled with the second acoustic standing-wave mode in Phase-I were recognized as the signatures of the second shear layer hydrodynamic mode. (3) However, in Phase-III of the acoustic mode transition, modulated by the third acoustic standing-wave mode, the corresponding vortex dynamics fully developed into a second shear layer hydrodynamic mode. This work provides a better understanding of the complex vortex dynamics of channel flows with broad implications for industrial piping systems.

The vortex dynamics during acoustic mode transition in channel branches were experimentally investigated with phase-locking particle image velocimetry (PIV) measurements. Particularly, a real-time waveform recognition approach, based on an offline pressure analysis by dynamic mode decomposition (DMD) and a real-time computation by field programmable gate array, was established. In the offline DMD analysis, energetic pressure DMD modes during acoustic mode transition were extracted from pressure data measured by a pressure transducer array and found to agree well with the natural acoustic standing-wave modes numerically determined from an acoustic modal analysis. The acoustic mode transition process was classified into three successive phases: Phase-I: hybrid acoustic modulations, Phase-II: no acoustic modulation, and Phase-III: third-order acoustic modulation. Subsequently, the vortex dynamics corresponding to Phase-I and Phase-III were determined by phase-locking PIV measurements with the real-time waveform recognition approach. The results are summarized as follows. (1) The vortex dynamics coupled with the first acoustic standing-wave mode in Phase-I were related to the first shear layer hydrodynamic mode in channel branches. (2) The vortex dynamics coupled with the second acoustic standing-wave mode in Phase-I were recognized as the signatures of the second shear layer hydrodynamic mode. (3) However, in Phase-III of the acoustic mode transition, modulated by the third acoustic standing-wave mode, the corresponding vortex dynamics fully developed into a second shear layer hydrodynamic mode. This work provides a better understanding of the complex vortex dynamics of channel flows with broad implications for industrial piping systems.

Categories: Latest papers in fluid mechanics

### On the generation of vorticity and hydrodynamics of vortex ring during liquid drop impingement

Physics of Fluids, Volume 31, Issue 8, August 2019.

In this work, we investigate the phenomenon of vortex generation and formation of a vortex ring when a liquid drop impinges on a miscible liquid surface. Although the formation of a vortex ring for this system has been studied for more than a century, little is known about its exact mechanism of generation and how its hydrodynamics is related to the shape of the drop. This is due to the complexity involved in the conversion of the initially generated vorticity into a vortex ring. To cast light on this intriguing phenomenon, time-resolved high-speed imaging with high magnification is used. This allows us to probe deeper into the vortex generation process and study the formation of the ring. We make a comprehensive study of the effect of drop impingement height and drop shape at the time of impact on the vortex generation and the hydrodynamics of the ring. The effect of crater evolution on the hydrodynamics of the vortex ring is studied in terms of its diameter and translational velocity. By examining the role of the shape of the crater on vortex ring penetration, we answer the question why the most penetrating vortex rings are generated by a prolate shaped drop.

In this work, we investigate the phenomenon of vortex generation and formation of a vortex ring when a liquid drop impinges on a miscible liquid surface. Although the formation of a vortex ring for this system has been studied for more than a century, little is known about its exact mechanism of generation and how its hydrodynamics is related to the shape of the drop. This is due to the complexity involved in the conversion of the initially generated vorticity into a vortex ring. To cast light on this intriguing phenomenon, time-resolved high-speed imaging with high magnification is used. This allows us to probe deeper into the vortex generation process and study the formation of the ring. We make a comprehensive study of the effect of drop impingement height and drop shape at the time of impact on the vortex generation and the hydrodynamics of the ring. The effect of crater evolution on the hydrodynamics of the vortex ring is studied in terms of its diameter and translational velocity. By examining the role of the shape of the crater on vortex ring penetration, we answer the question why the most penetrating vortex rings are generated by a prolate shaped drop.

Categories: Latest papers in fluid mechanics

### Flow and heat transfer characteristics of a nanofluid between a square enclosure and a wavy wall obstacle

Physics of Fluids, Volume 31, Issue 8, August 2019.

A mathematical model for the natural convection flow and heat transfer of a nanofluid in an annulus enclosed by a square cylinder and a wavy wall cylinder is developed. Using vorticity-stream function formulation, we first derive governing equations in the Cartesian coordinates. Then, these equations are transformed utilizing coordinate transformations into a system of equations valid for the present physical domain. The problem is solved using the finite difference method. It is found that for higher values of the volume fraction of nanoparticles, the number of undulations of the wavy wall of the inner cylinder and Rayleigh number, the strength of streamlines significantly increases. However, the amplitude of undulations diminishes the intensity of streamlines. The isotherms are also strongly influenced by these parameters. Contrary to this, the Nusselt number at the inner and outer cylinders is remarkably increased due to the increase of the volume fraction of nanoparticles, amplitude of undulations, and Rayleigh number. For the higher volume fraction of nanoparticles and Rayleigh number, the average Nusselt number at the inner and outer cylinders is higher. The maximum and minimum values of the velocity profile increase with the higher Rayleigh number. Nevertheless, the converse scenario is observed for the larger amplitude of undulation and volume fraction of nanoparticles. The temperature near the inner cylinder noticeably decreases with the increase of the Rayleigh number, whereas it slowly reduces for higher amplitude of undulations. Above all, this investigation might be helpful for the researchers in regard to the approach of making a more complex geometry by using coordinate transformations. Furthermore, the results could provide vital information about the problems in current technological applications.

A mathematical model for the natural convection flow and heat transfer of a nanofluid in an annulus enclosed by a square cylinder and a wavy wall cylinder is developed. Using vorticity-stream function formulation, we first derive governing equations in the Cartesian coordinates. Then, these equations are transformed utilizing coordinate transformations into a system of equations valid for the present physical domain. The problem is solved using the finite difference method. It is found that for higher values of the volume fraction of nanoparticles, the number of undulations of the wavy wall of the inner cylinder and Rayleigh number, the strength of streamlines significantly increases. However, the amplitude of undulations diminishes the intensity of streamlines. The isotherms are also strongly influenced by these parameters. Contrary to this, the Nusselt number at the inner and outer cylinders is remarkably increased due to the increase of the volume fraction of nanoparticles, amplitude of undulations, and Rayleigh number. For the higher volume fraction of nanoparticles and Rayleigh number, the average Nusselt number at the inner and outer cylinders is higher. The maximum and minimum values of the velocity profile increase with the higher Rayleigh number. Nevertheless, the converse scenario is observed for the larger amplitude of undulation and volume fraction of nanoparticles. The temperature near the inner cylinder noticeably decreases with the increase of the Rayleigh number, whereas it slowly reduces for higher amplitude of undulations. Above all, this investigation might be helpful for the researchers in regard to the approach of making a more complex geometry by using coordinate transformations. Furthermore, the results could provide vital information about the problems in current technological applications.

Categories: Latest papers in fluid mechanics

### The role of surface wettability on the heat transfer in liquid-liquid two-phase flow in a microtube

Physics of Fluids, Volume 31, Issue 8, August 2019.

Liquid-liquid two-phase flow is capable of boosting heat transfer in microdevices compared to the single-phase and gas-liquid flows. A thorough investigation is performed here to characterize the heat transfer in water-oil flow in a microtube. Finite element method along with the level-set model is employed for numerical simulation. A main part of this paper is devoted to studying the effect of wettability on the heat transfer performance. Four contact angles of 0°, 30°, 150°, and 180° are investigated, which revealed that the contact angle of 150° produces the highest Nusselt number (Nu). Triple points form at this contact angle, and the slugs slide on the wall, which results in more significant wall shear and slip velocity on the wall. Based on the observed flow configuration, a novel idea is developed to use the nonuniform distribution of contact angle to augment the local Nu. It is observed that changing the wall from hydrophobic to hydrophilic will locally increase Nu around the transition point. In addition to the contact angle, the slug length, frequency of slug generation, and the film thickness around the slugs affect Nu. Three Weber numbers (We) at four contact angles are examined by varying the flow rate of the oil phase in the next part of the paper. We affects Nu by changing the frequency of slug generation and consequently its length. Finally, the effect of film thickness is scrutinized at various capillary numbers (Ca). The film thickness increases with Ca which reduces the heat removal rate.

Liquid-liquid two-phase flow is capable of boosting heat transfer in microdevices compared to the single-phase and gas-liquid flows. A thorough investigation is performed here to characterize the heat transfer in water-oil flow in a microtube. Finite element method along with the level-set model is employed for numerical simulation. A main part of this paper is devoted to studying the effect of wettability on the heat transfer performance. Four contact angles of 0°, 30°, 150°, and 180° are investigated, which revealed that the contact angle of 150° produces the highest Nusselt number (Nu). Triple points form at this contact angle, and the slugs slide on the wall, which results in more significant wall shear and slip velocity on the wall. Based on the observed flow configuration, a novel idea is developed to use the nonuniform distribution of contact angle to augment the local Nu. It is observed that changing the wall from hydrophobic to hydrophilic will locally increase Nu around the transition point. In addition to the contact angle, the slug length, frequency of slug generation, and the film thickness around the slugs affect Nu. Three Weber numbers (We) at four contact angles are examined by varying the flow rate of the oil phase in the next part of the paper. We affects Nu by changing the frequency of slug generation and consequently its length. Finally, the effect of film thickness is scrutinized at various capillary numbers (Ca). The film thickness increases with Ca which reduces the heat removal rate.

Categories: Latest papers in fluid mechanics

### Turbulent structures of shock-wave diffraction over 90° convex corner

Physics of Fluids, Volume 31, Issue 8, August 2019.

The turbulent structures and long-time flow dynamics of shock diffraction over 90° convex corner associated with an incident shock Mach number Ms = 1.5 are investigated by large eddy simulation (LES). The average evolution of the core of the primary vortex is in agreement with the previous two dimensional studies. The Type-N wall shock structure is found to be in excellent agreement with the previous experimental data. The turbulent structures are well resolved and resemble those observed in the experimental findings. Subgrid scale dissipation and subgrid scale activity parameter are quantified to demonstrate the effectiveness of the LES. An analysis based on turbulent-nonturbulent interface reveals that locally incompressible regions exhibit the universal teardrop shape of the joint probability density function of the second and third invariants of the velocity gradient tensor. Stable focus stretching (SFS) structures dominate throughout the evolution in these regions. Stable node/saddle/saddle structures are found to be predominant at the early stage in locally compressed regions, and the flow structures evolve to more SFS structures at later stages. On the other hand, the locally expanded regions show a mostly unstable nature. From the turbulent kinetic energy, we found that the pressure dilatation remains important at the early stage, while turbulent diffusion becomes important at the later stage. Furthermore, the analysis of the resolved vorticity transport equation reveals that the stretching of vorticity due to compressibility and stretching of vorticity due to velocity gradients plays an important role compared to diffusion of vorticity due to viscosity as well as the baroclinic term.

The turbulent structures and long-time flow dynamics of shock diffraction over 90° convex corner associated with an incident shock Mach number Ms = 1.5 are investigated by large eddy simulation (LES). The average evolution of the core of the primary vortex is in agreement with the previous two dimensional studies. The Type-N wall shock structure is found to be in excellent agreement with the previous experimental data. The turbulent structures are well resolved and resemble those observed in the experimental findings. Subgrid scale dissipation and subgrid scale activity parameter are quantified to demonstrate the effectiveness of the LES. An analysis based on turbulent-nonturbulent interface reveals that locally incompressible regions exhibit the universal teardrop shape of the joint probability density function of the second and third invariants of the velocity gradient tensor. Stable focus stretching (SFS) structures dominate throughout the evolution in these regions. Stable node/saddle/saddle structures are found to be predominant at the early stage in locally compressed regions, and the flow structures evolve to more SFS structures at later stages. On the other hand, the locally expanded regions show a mostly unstable nature. From the turbulent kinetic energy, we found that the pressure dilatation remains important at the early stage, while turbulent diffusion becomes important at the later stage. Furthermore, the analysis of the resolved vorticity transport equation reveals that the stretching of vorticity due to compressibility and stretching of vorticity due to velocity gradients plays an important role compared to diffusion of vorticity due to viscosity as well as the baroclinic term.

Categories: Latest papers in fluid mechanics