# 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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### Effect of density of a sphere launched vertically in water on the water-surface behavior and sphere motion in air

Physics of Fluids, Volume 32, Issue 11, November 2020.

Submerged solid spheres with specific gravities relative to water ranging from 1.36 to 7.93 were launched vertically upward toward the free surface of calm water. The motion of each sphere and the behavior of the water surface were investigated from the time the sphere passed through the calm water surface until it attained its maximum displacement position. The energy lost in the interaction between the sphere and the water surface (i.e., the interfacial containing energy Eo) was estimated from energy conservation. A larger Eo at the maximum displacement position of the sphere led to a larger increase in the height and width of the interfacial water sheet where the upper side of the sphere intersected with the free surface of calm water. This result corresponded to the result obtained by changing the submergence depth, as reported by Takamure and Uchiyama [“Air–water interface dynamics and energy transition in air of a sphere passed vertically upward through the interface,” Exp. Therm. Fluid Sci. 118, 110167 (2020)]. This aspect suggests that the characteristics of the interfacial water sheet are the dominant parameters influencing Eo. The presented findings can facilitate the determination of parameters to model the water exit problem.

Submerged solid spheres with specific gravities relative to water ranging from 1.36 to 7.93 were launched vertically upward toward the free surface of calm water. The motion of each sphere and the behavior of the water surface were investigated from the time the sphere passed through the calm water surface until it attained its maximum displacement position. The energy lost in the interaction between the sphere and the water surface (i.e., the interfacial containing energy Eo) was estimated from energy conservation. A larger Eo at the maximum displacement position of the sphere led to a larger increase in the height and width of the interfacial water sheet where the upper side of the sphere intersected with the free surface of calm water. This result corresponded to the result obtained by changing the submergence depth, as reported by Takamure and Uchiyama [“Air–water interface dynamics and energy transition in air of a sphere passed vertically upward through the interface,” Exp. Therm. Fluid Sci. 118, 110167 (2020)]. This aspect suggests that the characteristics of the interfacial water sheet are the dominant parameters influencing Eo. The presented findings can facilitate the determination of parameters to model the water exit problem.

Categories: Latest papers in fluid mechanics

### Leidenfrost drop impact on inclined superheated substrates

Physics of Fluids, Volume 32, Issue 11, November 2020.

In real applications, drops always impact on solid walls with various inclinations. For the oblique impact of a Leidenfrost drop, which has a vapor layer under its bottom surface to prevent its direct contact with the superheated substrate, the drop can nearly frictionlessly slide along the substrate accompanied by spreading and retracting. To individually study these processes, we experimentally observe the impact of ethanol drops on superheated inclined substrates using high-speed imaging from two different views synchronously. We first study the dynamic Leidenfrost temperature, which mainly depends on the normal Weber number We⊥. Then, the substrate temperature is set to be high enough to study the Leidenfrost drop behavior. During the spreading process, drops are always kept uniform, and the maximum spreading factor Dm/D0 follows a power-law dependence on the large normal Weber number We⊥ as [math] for We⊥ ≥ 30. During the retracting process, drops with low impact velocities become non-uniform due to the gravity effect. For the sliding process, the residence time of all studied drops is nearly a constant, which is not affected by the inclination and the We number. The frictionless vapor layer resulting in the dimensionless sliding distance L/D0 follows a power-law dependence on the parallel Weber number We|| as [math]. Without direct contact with the substrate, the behaviors of drops can be separately determined by We⊥ and We||. When the impact velocity is too high, the drop fragments into many tiny droplets, which is called the splashing phenomenon. The critical splashing criterion is found to be [math] 120 or [math] 5300 in the current parameter regime.

In real applications, drops always impact on solid walls with various inclinations. For the oblique impact of a Leidenfrost drop, which has a vapor layer under its bottom surface to prevent its direct contact with the superheated substrate, the drop can nearly frictionlessly slide along the substrate accompanied by spreading and retracting. To individually study these processes, we experimentally observe the impact of ethanol drops on superheated inclined substrates using high-speed imaging from two different views synchronously. We first study the dynamic Leidenfrost temperature, which mainly depends on the normal Weber number We⊥. Then, the substrate temperature is set to be high enough to study the Leidenfrost drop behavior. During the spreading process, drops are always kept uniform, and the maximum spreading factor Dm/D0 follows a power-law dependence on the large normal Weber number We⊥ as [math] for We⊥ ≥ 30. During the retracting process, drops with low impact velocities become non-uniform due to the gravity effect. For the sliding process, the residence time of all studied drops is nearly a constant, which is not affected by the inclination and the We number. The frictionless vapor layer resulting in the dimensionless sliding distance L/D0 follows a power-law dependence on the parallel Weber number We|| as [math]. Without direct contact with the substrate, the behaviors of drops can be separately determined by We⊥ and We||. When the impact velocity is too high, the drop fragments into many tiny droplets, which is called the splashing phenomenon. The critical splashing criterion is found to be [math] 120 or [math] 5300 in the current parameter regime.

Categories: Latest papers in fluid mechanics

### A study on bubble nuclei population dynamics under reduced pressure

Physics of Fluids, Volume 32, Issue 11, November 2020.

The existence of cavitation nuclei is one of the necessary conditions for liquid cavitation. Bubble nucleus is the most basic cavitation nucleus, and bubble nuclei size distribution is a parameter describing the population of gas nuclei. To study the dynamics of bubble nuclei population after artificial seeding under reduced pressure, a decompression chamber was built, combined with the artificial seeding system and the acoustic nuclei measurement system. After the nuclei seeding, the experimental study of the nuclei population dynamics with pressure and time was carried out. It is found that as the pressure decreases, the number density of larger size nuclei decreases, while the number density of smaller size nuclei increases. In the measured size range, the maximum value of number density of the nuclei size distribution increases. In addition, based on the theory of bubble dynamics, the growth process of the nucleus under reduced pressure is calculated and analyzed, which can realize the preliminary prediction of the nuclei population dynamics under reduced pressure.

The existence of cavitation nuclei is one of the necessary conditions for liquid cavitation. Bubble nucleus is the most basic cavitation nucleus, and bubble nuclei size distribution is a parameter describing the population of gas nuclei. To study the dynamics of bubble nuclei population after artificial seeding under reduced pressure, a decompression chamber was built, combined with the artificial seeding system and the acoustic nuclei measurement system. After the nuclei seeding, the experimental study of the nuclei population dynamics with pressure and time was carried out. It is found that as the pressure decreases, the number density of larger size nuclei decreases, while the number density of smaller size nuclei increases. In the measured size range, the maximum value of number density of the nuclei size distribution increases. In addition, based on the theory of bubble dynamics, the growth process of the nucleus under reduced pressure is calculated and analyzed, which can realize the preliminary prediction of the nuclei population dynamics under reduced pressure.

Categories: Latest papers in fluid mechanics

### Fluid–particle drag and particle–particle drag in low-Reynolds-number bidisperse gas–solid suspensions

Physics of Fluids, Volume 32, Issue 11, November 2020.

Particle-resolved direct numerical simulations (PR-DNSs) of dynamic bidisperse gas–solid suspensions are performed at low particle Reynolds numbers. Unlike the fixed-bed suspensions, the mobility of particles allows particles of different size types to develop different slip velocities relative to the fluid phase. The scaled slip velocity, defined as the ratio of the slip velocity of one particle type to the mean slip velocity of the mixture, varies profoundly depending on the specific properties of the bidisperse mixture. For large particles, the drag force, scaled by the mean drag force of the mixture, is reasonably predicted by the models obtained from fixed-bed suspensions, while for small particles, these models tend to underestimate the scaled drag force as the scaled slip velocity decreases. By introducing the scaled slip velocity, a new model for the fluid–particle drag on each particle type is proposed and agrees well with the PR-DNS data. For the situation where the monodisperse drag models are employed to predict the mixture mean drag force, a new mean diameter that is variant with the total solid volume fraction is suggested. This diameter increases as the total solid volume fraction decreases and approaches the Sauter mean diameter in the close-packed volume fraction. In dilute suspensions, due to the strong influence of surrounding fluids on the particle phase, the simulated particle–particle drag is significantly smaller than the predictions of models based on kinetic theory of granular flow. Based on the PR-DNS results, new relations for particle–particle drag are also proposed.

Particle-resolved direct numerical simulations (PR-DNSs) of dynamic bidisperse gas–solid suspensions are performed at low particle Reynolds numbers. Unlike the fixed-bed suspensions, the mobility of particles allows particles of different size types to develop different slip velocities relative to the fluid phase. The scaled slip velocity, defined as the ratio of the slip velocity of one particle type to the mean slip velocity of the mixture, varies profoundly depending on the specific properties of the bidisperse mixture. For large particles, the drag force, scaled by the mean drag force of the mixture, is reasonably predicted by the models obtained from fixed-bed suspensions, while for small particles, these models tend to underestimate the scaled drag force as the scaled slip velocity decreases. By introducing the scaled slip velocity, a new model for the fluid–particle drag on each particle type is proposed and agrees well with the PR-DNS data. For the situation where the monodisperse drag models are employed to predict the mixture mean drag force, a new mean diameter that is variant with the total solid volume fraction is suggested. This diameter increases as the total solid volume fraction decreases and approaches the Sauter mean diameter in the close-packed volume fraction. In dilute suspensions, due to the strong influence of surrounding fluids on the particle phase, the simulated particle–particle drag is significantly smaller than the predictions of models based on kinetic theory of granular flow. Based on the PR-DNS results, new relations for particle–particle drag are also proposed.

Categories: Latest papers in fluid mechanics

### Generalized friction and dilatancy laws for immersed granular flows consisting of large and small particles

Physics of Fluids, Volume 32, Issue 11, November 2020.

The motion of fully immersed granular materials, composed of two distinct particle sizes, flowing down rough inclined planes is studied through fluid–particle numerical simulations. We focus on the effect of ambient fluids, as well as their interplay with particle size segregation, on the steady-state kinematic and rheological profiles of the granular-fluid mixture flow. Simulation results are analyzed in the framework of a visco-inertial rheological model, which is first validated in monodisperse flows with a wide range of the ambient fluid viscosity (i.e., from air to water and slurry) and then generalized for size-bidisperse mixtures. It is found that the local effective friction and volume fraction of mixtures with different particle sizes can be approximated from the rheology of single-component flows. While the presence of viscous ambient fluids slows down size segregation (perpendicular to the flow) depending on the mixture composition and flow viscosity, the effective bulk friction is shown to be independent of the state and progress of segregation.

The motion of fully immersed granular materials, composed of two distinct particle sizes, flowing down rough inclined planes is studied through fluid–particle numerical simulations. We focus on the effect of ambient fluids, as well as their interplay with particle size segregation, on the steady-state kinematic and rheological profiles of the granular-fluid mixture flow. Simulation results are analyzed in the framework of a visco-inertial rheological model, which is first validated in monodisperse flows with a wide range of the ambient fluid viscosity (i.e., from air to water and slurry) and then generalized for size-bidisperse mixtures. It is found that the local effective friction and volume fraction of mixtures with different particle sizes can be approximated from the rheology of single-component flows. While the presence of viscous ambient fluids slows down size segregation (perpendicular to the flow) depending on the mixture composition and flow viscosity, the effective bulk friction is shown to be independent of the state and progress of segregation.

Categories: Latest papers in fluid mechanics

### Dynamics of spheroids in an unbound quadratic flow of a general second-order fluid

Physics of Fluids, Volume 32, Issue 11, November 2020.

This work employs the second-order fluid model to investigate the effect of first and second normal stresses on the motion of spheroidal particles in unbound parabolic flows, where particles migrate toward the flow center. We specifically examine the effects of fluid Weissenberg number Wi and the ratio of normal stress coefficients α = ψ2/ψ1. Previous works have considered the motion of spheroidal particles in the co-rotational limit (α = −0.5), where the effect of fluid viscoelasticity is to modify the fluid pressure but not the shear stresses. Here, we examine all ranges of α that are found for functional complex fluids such as dilute polymer solutions, emulsions, and particulate suspensions and determine how viscoelastic shear stresses alter particle migration. We use perturbation theory and the Lorentz reciprocal theorem to derive the O(Wi) corrections to the translational and rotational velocities of a freely suspended spheroid in an unbound tube or slit flow. Our results show that for both prolate and oblate particles, the viscoelasticity characterized by α significantly affects the particle cross-stream migration, but does not qualitatively change the trends seen in the co-rotational limit (α = −0.5). For a range of α (−0.9 ≤ α ≤ 0) investigated in this work, particles possess the largest mobility when α = −0.9 and smallest mobility when α = 0. Although α does not alter particle rotation at a given shear rate, we observe significant changes in particle orientation during migration toward the flow center because changes in migration speed give rise to particles experiencing different shear histories.

This work employs the second-order fluid model to investigate the effect of first and second normal stresses on the motion of spheroidal particles in unbound parabolic flows, where particles migrate toward the flow center. We specifically examine the effects of fluid Weissenberg number Wi and the ratio of normal stress coefficients α = ψ2/ψ1. Previous works have considered the motion of spheroidal particles in the co-rotational limit (α = −0.5), where the effect of fluid viscoelasticity is to modify the fluid pressure but not the shear stresses. Here, we examine all ranges of α that are found for functional complex fluids such as dilute polymer solutions, emulsions, and particulate suspensions and determine how viscoelastic shear stresses alter particle migration. We use perturbation theory and the Lorentz reciprocal theorem to derive the O(Wi) corrections to the translational and rotational velocities of a freely suspended spheroid in an unbound tube or slit flow. Our results show that for both prolate and oblate particles, the viscoelasticity characterized by α significantly affects the particle cross-stream migration, but does not qualitatively change the trends seen in the co-rotational limit (α = −0.5). For a range of α (−0.9 ≤ α ≤ 0) investigated in this work, particles possess the largest mobility when α = −0.9 and smallest mobility when α = 0. Although α does not alter particle rotation at a given shear rate, we observe significant changes in particle orientation during migration toward the flow center because changes in migration speed give rise to particles experiencing different shear histories.

Categories: Latest papers in fluid mechanics

### Fingering instability in Marangoni spreading on a deep layer of polymer solution

Physics of Fluids, Volume 32, Issue 11, November 2020.

Spreading on the free surface of a complex fluid is ubiquitous in nature and industry, such as drug delivery, oil spill, and surface treatment with patterns. Here, we report on a fingering instability that develops during Marangoni spreading on a deep layer of the polymer solution. In particular, the wavelength depends on the molecular weight and concentration of the polymer solution. We use the transmission lattice method to characterize the free surface morphology during spreading and the finger height at the micron scale. We use the Maxwell model to explain the spreading radius, which is dominated by elasticity at small time scales and by viscous dissipation at large time scales. In a viscous regime, with consideration of shear thinning, the spreading radius follows the universal 3/4 power law. Our model suggests a more generalized law of the spreading radius than the previous laws for Newtonian fluids. Furthermore, we give a physical explanation on the origin of the fingering instability as due to normal stresses at high shear rates generating a high contact angle, providing a necessary condition for the fingering instability. The normal stress also generates the elastic deformation at the leading edge and so selects the wavelength of the fingering instability. Understanding the spreading mechanism on a layer of viscoelastic fluid has a particular implication in airway drug delivery and surface coating.

Spreading on the free surface of a complex fluid is ubiquitous in nature and industry, such as drug delivery, oil spill, and surface treatment with patterns. Here, we report on a fingering instability that develops during Marangoni spreading on a deep layer of the polymer solution. In particular, the wavelength depends on the molecular weight and concentration of the polymer solution. We use the transmission lattice method to characterize the free surface morphology during spreading and the finger height at the micron scale. We use the Maxwell model to explain the spreading radius, which is dominated by elasticity at small time scales and by viscous dissipation at large time scales. In a viscous regime, with consideration of shear thinning, the spreading radius follows the universal 3/4 power law. Our model suggests a more generalized law of the spreading radius than the previous laws for Newtonian fluids. Furthermore, we give a physical explanation on the origin of the fingering instability as due to normal stresses at high shear rates generating a high contact angle, providing a necessary condition for the fingering instability. The normal stress also generates the elastic deformation at the leading edge and so selects the wavelength of the fingering instability. Understanding the spreading mechanism on a layer of viscoelastic fluid has a particular implication in airway drug delivery and surface coating.

Categories: Latest papers in fluid mechanics

### Vortex formation in starting buoyant jets at moderate Richardson numbers

Physics of Fluids, Volume 32, Issue 11, November 2020.

In this paper, the formation process of the leading vortex ring in positively and negatively buoyant starting jets with moderate Richardson number in the range of 0.06 < |Ri| ≤ 0.321 has been investigated numerically and theoretically. Using the similarity variables |Ri| and |Ri|2/5 for the positively and negatively buoyant starting jets, respectively, fitting equations can be obtained to predict the buoyant jet penetration rate. Based on these fitting equations, a revised circulation model is proposed by incorporating the effects of both over-pressure and buoyancy. The revised model is well consistent with the numerical results for all positively buoyant starting jets. However, for the negatively buoyant starting jets, this model can predict well only during the initial period. The over-pressure has little influence on the vortex ring characteristics of the starting jets with positive buoyancy, whereas it can significantly affect the vortex ring formation of the negatively buoyant starting jets at moderate Richardson numbers. As the positive Richardson number increases, the instabilities of the trailing shear layer occur earlier. At moderately negative Richardson numbers, a “double plume” structure (an inner sinking circular forced plume and an outer rising annular plume) can be observed. The outer negative vorticity layers develop gradually due to the baroclinic effect. Consequently, the size and strength of the leading vortex progressively decrease. As the negative Richardson number decreases, the negative vorticity layers occur earlier and grow faster.

In this paper, the formation process of the leading vortex ring in positively and negatively buoyant starting jets with moderate Richardson number in the range of 0.06 < |Ri| ≤ 0.321 has been investigated numerically and theoretically. Using the similarity variables |Ri| and |Ri|2/5 for the positively and negatively buoyant starting jets, respectively, fitting equations can be obtained to predict the buoyant jet penetration rate. Based on these fitting equations, a revised circulation model is proposed by incorporating the effects of both over-pressure and buoyancy. The revised model is well consistent with the numerical results for all positively buoyant starting jets. However, for the negatively buoyant starting jets, this model can predict well only during the initial period. The over-pressure has little influence on the vortex ring characteristics of the starting jets with positive buoyancy, whereas it can significantly affect the vortex ring formation of the negatively buoyant starting jets at moderate Richardson numbers. As the positive Richardson number increases, the instabilities of the trailing shear layer occur earlier. At moderately negative Richardson numbers, a “double plume” structure (an inner sinking circular forced plume and an outer rising annular plume) can be observed. The outer negative vorticity layers develop gradually due to the baroclinic effect. Consequently, the size and strength of the leading vortex progressively decrease. As the negative Richardson number decreases, the negative vorticity layers occur earlier and grow faster.

Categories: Latest papers in fluid mechanics

### Experimental visualization of sneezing and efficacy of face masks and shields

Physics of Fluids, Volume 32, Issue 11, November 2020.

In the present work, we propose and demonstrate a simple experimental visualization to simulate sneezing by maintaining dynamic similarity to actual sneezing. A pulsed jet with Reynolds number Re = 30 000 is created using compressed air and a solenoid valve. Tracer particles are introduced in the flow to capture the emulated turbulent jet formed due to a sneeze. The visualization is accomplished using a camera and laser illumination. It is observed that a typical sneeze can travel up to 25 ft in ∼22 s in a quiescent environment. This highlights that the present widely accepted safe distance of 6 ft is highly underestimated, especially under the act of a sneeze. Our study demonstrates that a three-layer homemade mask is just adequate to impede the penetration of fine-sized particles, which may cause the spreading of the infectious pathogen responsible for COVID-19. However, a surgical mask cannot block the sneeze, and the sneeze particle can travel up to 2.5 ft. We strongly recommend using at least a three-layer homemade mask with a social distancing of 6 ft to combat the transmission of COVID-19 virus. In offices, we recommend the use of face masks and shields to prevent the spreading of droplets carrying the infectious pathogen. Interestingly, an N-95 mask blocks the sneeze in the forward direction; however, the leakage from the sides and top spreads the sneeze in the backward direction up to 2 ft. We strongly recommend using the elbow or hands to prevent droplet leakage even after wearing a mask during sneezing and coughing.

In the present work, we propose and demonstrate a simple experimental visualization to simulate sneezing by maintaining dynamic similarity to actual sneezing. A pulsed jet with Reynolds number Re = 30 000 is created using compressed air and a solenoid valve. Tracer particles are introduced in the flow to capture the emulated turbulent jet formed due to a sneeze. The visualization is accomplished using a camera and laser illumination. It is observed that a typical sneeze can travel up to 25 ft in ∼22 s in a quiescent environment. This highlights that the present widely accepted safe distance of 6 ft is highly underestimated, especially under the act of a sneeze. Our study demonstrates that a three-layer homemade mask is just adequate to impede the penetration of fine-sized particles, which may cause the spreading of the infectious pathogen responsible for COVID-19. However, a surgical mask cannot block the sneeze, and the sneeze particle can travel up to 2.5 ft. We strongly recommend using at least a three-layer homemade mask with a social distancing of 6 ft to combat the transmission of COVID-19 virus. In offices, we recommend the use of face masks and shields to prevent the spreading of droplets carrying the infectious pathogen. Interestingly, an N-95 mask blocks the sneeze in the forward direction; however, the leakage from the sides and top spreads the sneeze in the backward direction up to 2 ft. We strongly recommend using the elbow or hands to prevent droplet leakage even after wearing a mask during sneezing and coughing.

Categories: Latest papers in fluid mechanics

### Speed–direction description of turbulent flows

Physics of Fluids, Volume 32, Issue 11, November 2020.

In this note, we introduce speed and direction variables to describe the motion of incompressible viscous fluid. Fluid velocity u is decomposed into u = ur, with u = |u| and r = u/|u|. We consider a directional split of the Navier–Stokes equations into a coupled system of equations for u and for r. The equation for u is particularly simple but solely maintains the energy balance of the system. Under the assumption of a weak correlation between fluctuations in speed and direction in a developed turbulent flow, we further illustrate the application of u–r variables to describe mean statistics of a shear turbulence. The standard (full) Reynolds stress tensor does not appear in a resulting equation for the mean flow profile.

In this note, we introduce speed and direction variables to describe the motion of incompressible viscous fluid. Fluid velocity u is decomposed into u = ur, with u = |u| and r = u/|u|. We consider a directional split of the Navier–Stokes equations into a coupled system of equations for u and for r. The equation for u is particularly simple but solely maintains the energy balance of the system. Under the assumption of a weak correlation between fluctuations in speed and direction in a developed turbulent flow, we further illustrate the application of u–r variables to describe mean statistics of a shear turbulence. The standard (full) Reynolds stress tensor does not appear in a resulting equation for the mean flow profile.

Categories: Latest papers in fluid mechanics

### A computational study on osmotic chemotaxis of a reactive Janusbot

Physics of Fluids, Volume 32, Issue 11, November 2020.

We explore the chemotaxis of an elliptical double-faced Janus motor (Janusbot) stimulated by a second-order chemical reaction on the surfaces, aA + bB → cC + dD, inside a microfluidic channel. The self-propulsions are modeled considering the full descriptions of hydrodynamic governing equations coupled with reaction–diffusion equations and fluid–structure interaction. The simulations, employing a finite element framework, uncover that the differential rate kinetics of the reactions on the dissimilar faces of the Janusbot help in building up enough osmotic pressure gradient for the motion as a result of non-uniform spatiotemporal variations in the concentrations of the reactants and products around the particle. The simulations uncover that the mass diffusivities of the reactants and products along with the rates of forward and backward reactions play crucial roles in determining the speed and direction of the propulsions. Importantly, we observe that the motor can move even when there is no difference in the total stoichiometry of the reactants and products, (a + b) = (c + d). In such a scenario, while the reaction triggers the motion, the difference in net-diffusivities of the reactants and products develops adequate osmotic thrust for the propulsion. In contrast, for the situations with a + b ≠ c + d, the particle can exhibit propulsion even without any difference in net-diffusivities of the reactants and products. The direction and speed of the motion are dependent on difference in mass diffusivities and reaction rate constants at different surfaces.

We explore the chemotaxis of an elliptical double-faced Janus motor (Janusbot) stimulated by a second-order chemical reaction on the surfaces, aA + bB → cC + dD, inside a microfluidic channel. The self-propulsions are modeled considering the full descriptions of hydrodynamic governing equations coupled with reaction–diffusion equations and fluid–structure interaction. The simulations, employing a finite element framework, uncover that the differential rate kinetics of the reactions on the dissimilar faces of the Janusbot help in building up enough osmotic pressure gradient for the motion as a result of non-uniform spatiotemporal variations in the concentrations of the reactants and products around the particle. The simulations uncover that the mass diffusivities of the reactants and products along with the rates of forward and backward reactions play crucial roles in determining the speed and direction of the propulsions. Importantly, we observe that the motor can move even when there is no difference in the total stoichiometry of the reactants and products, (a + b) = (c + d). In such a scenario, while the reaction triggers the motion, the difference in net-diffusivities of the reactants and products develops adequate osmotic thrust for the propulsion. In contrast, for the situations with a + b ≠ c + d, the particle can exhibit propulsion even without any difference in net-diffusivities of the reactants and products. The direction and speed of the motion are dependent on difference in mass diffusivities and reaction rate constants at different surfaces.

Categories: Latest papers in fluid mechanics

### Modeling of sub-grid conditional mixing statistics in turbulent sprays using machine learning methods

Physics of Fluids, Volume 32, Issue 11, November 2020.

Deep artificial neural networks (ANNs) are used for modeling sub-grid scale mixing quantities such as the filtered density function (FDF) of the mixture fraction and the conditional scalar dissipation rate. A deep ANN with four hidden layers is trained with carrier-phase direct numerical simulations (CP-DNS) of turbulent spray combustion. A priori validation corroborates that ANN predictions of the mixture fraction FDF and the conditional scalar dissipation rate are in very good agreement with CP-DNS data. ANN modeled solutions show much better performance with a mean error of around 1%, which is one order of magnitude smaller than that of standard modeling approaches such as the β-FDF and its modified version. The predicted conditional scalar dissipation rate agrees very well with CP-DNS data over the entire mixture fraction space, whereas conventional models derived for pure gas phase combustion fail to describe ⟨N|ξ = η⟩ in regions with higher mixture fraction and low probability. In the second part of this paper, uncertainties associated with ANN predictions are analyzed. It is shown that a suitable selection of training sets can reduce the size of the necessary test database by ∼50% without compromising the accuracy. Feature importance analysis is used to analyze the importance of different combustion model parameters. While the droplet evaporating rate, the droplet number density, and the mixture fraction remain the dominant features, the influence of turbulence related parameters only becomes important if turbulence levels are sufficiently high.

Deep artificial neural networks (ANNs) are used for modeling sub-grid scale mixing quantities such as the filtered density function (FDF) of the mixture fraction and the conditional scalar dissipation rate. A deep ANN with four hidden layers is trained with carrier-phase direct numerical simulations (CP-DNS) of turbulent spray combustion. A priori validation corroborates that ANN predictions of the mixture fraction FDF and the conditional scalar dissipation rate are in very good agreement with CP-DNS data. ANN modeled solutions show much better performance with a mean error of around 1%, which is one order of magnitude smaller than that of standard modeling approaches such as the β-FDF and its modified version. The predicted conditional scalar dissipation rate agrees very well with CP-DNS data over the entire mixture fraction space, whereas conventional models derived for pure gas phase combustion fail to describe ⟨N|ξ = η⟩ in regions with higher mixture fraction and low probability. In the second part of this paper, uncertainties associated with ANN predictions are analyzed. It is shown that a suitable selection of training sets can reduce the size of the necessary test database by ∼50% without compromising the accuracy. Feature importance analysis is used to analyze the importance of different combustion model parameters. While the droplet evaporating rate, the droplet number density, and the mixture fraction remain the dominant features, the influence of turbulence related parameters only becomes important if turbulence levels are sufficiently high.

Categories: Latest papers in fluid mechanics

### Turbulence anisotropy and intermittency in open-channel flows on rough beds

Physics of Fluids, Volume 32, Issue 11, November 2020.

An experimental campaign, based on Particle Image Velocimetry measurements in a laboratory flume with different median sediment sizes in the no-motion condition, has been carried out aiming at investigating the effects of bed roughness on turbulence anisotropy in two different vertical zones of the turbulent open-channel flow. An analysis of turbulence anisotropy, which relies on second-order structure functions and anisotropy angle, has been performed. The scale-dependent anisotropy level has been quantified, verifying the tendency of the system to span from large-scale anisotropy, due to the main shear of the boundary layer, to small-scale isotropy. Isotropy is well-established for the largest sediment sizes. High-order structure function analysis reveals that intermittency is more pronounced in the near-bed layers, where the flow is more populated by coherent vortices. Spectral anisotropy and intermittency strongly characterize the transport properties of turbulence and are, therefore, important phenomena for natural bed rivers.

An experimental campaign, based on Particle Image Velocimetry measurements in a laboratory flume with different median sediment sizes in the no-motion condition, has been carried out aiming at investigating the effects of bed roughness on turbulence anisotropy in two different vertical zones of the turbulent open-channel flow. An analysis of turbulence anisotropy, which relies on second-order structure functions and anisotropy angle, has been performed. The scale-dependent anisotropy level has been quantified, verifying the tendency of the system to span from large-scale anisotropy, due to the main shear of the boundary layer, to small-scale isotropy. Isotropy is well-established for the largest sediment sizes. High-order structure function analysis reveals that intermittency is more pronounced in the near-bed layers, where the flow is more populated by coherent vortices. Spectral anisotropy and intermittency strongly characterize the transport properties of turbulence and are, therefore, important phenomena for natural bed rivers.

Categories: Latest papers in fluid mechanics

### A reactive molecular dynamics study of hyperthermal atomic oxygen erosion mechanisms for graphene sheets

Physics of Fluids, Volume 32, Issue 11, November 2020.

Carbon-based composite materials are widely used in the aerospace field due to their light weight and excellent physical/chemical properties. The mechanisms of the erosion process, e.g., surface catalysis and ablation, during the impact of oxygen atoms, however, remain unclear. In this study, the surface catalysis and ablation behavior during the erosion process of hyperthermal atomic oxygens were achieved through the molecular dynamics method with the reactive force field potential. The concomitant impacts of energy flux density of energetic oxygen atoms, the presence of multiple layers beneath the graphene sheet, and the morphology of graphite surfaces, i.e., graphite basal plane, armchair (AC) edge surface, and zigzag edge surface, respectively, were discussed. The results show that the adsorption of oxygen atoms dominates at the beginning by generating O2 molecules, suggesting the importance of surface catalytic for any ablation study. A unique “layer-by-layer” ablation phenomenon by hyperthermal atomic oxygen is observed for multi-layered graphite slab, and the ablation rate reduces as the number of graphene layers increases. The morphology/structure of the surface shows significant effects on the ablation rate, with AC surfaces showing the largest etching rate and the basal one showing the lowest. The low binding energies of the AC edge are responsible for the difficulty in the formation of stable functional group structures to resist the etching of high-enthalpy oxygen atoms. Such revelation of the detailed surface catalysis and ablation mechanism at the atomistic scale provides insight into design of future materials for the augmentation of the thermal protection effect.

Carbon-based composite materials are widely used in the aerospace field due to their light weight and excellent physical/chemical properties. The mechanisms of the erosion process, e.g., surface catalysis and ablation, during the impact of oxygen atoms, however, remain unclear. In this study, the surface catalysis and ablation behavior during the erosion process of hyperthermal atomic oxygens were achieved through the molecular dynamics method with the reactive force field potential. The concomitant impacts of energy flux density of energetic oxygen atoms, the presence of multiple layers beneath the graphene sheet, and the morphology of graphite surfaces, i.e., graphite basal plane, armchair (AC) edge surface, and zigzag edge surface, respectively, were discussed. The results show that the adsorption of oxygen atoms dominates at the beginning by generating O2 molecules, suggesting the importance of surface catalytic for any ablation study. A unique “layer-by-layer” ablation phenomenon by hyperthermal atomic oxygen is observed for multi-layered graphite slab, and the ablation rate reduces as the number of graphene layers increases. The morphology/structure of the surface shows significant effects on the ablation rate, with AC surfaces showing the largest etching rate and the basal one showing the lowest. The low binding energies of the AC edge are responsible for the difficulty in the formation of stable functional group structures to resist the etching of high-enthalpy oxygen atoms. Such revelation of the detailed surface catalysis and ablation mechanism at the atomistic scale provides insight into design of future materials for the augmentation of the thermal protection effect.

Categories: Latest papers in fluid mechanics

### A vapor–liquid equilibrium induced Lewis number effect in real-gas shear layers: A theoretical study

Physics of Fluids, Volume 32, Issue 11, November 2020.

In this work, the relevance of the multi-phase thermodynamic model based on the vapor–liquid equilibrium (VLE) assumption over the single-phase model is discussed. An emphasis on the importance of the non-linear coupling between thermodynamic, transport, and governing equations is given from a macroscopic point of view by analyzing the mixing effects on a spatial mixing layer in real-gas (non-ideal) conditions. The goal is to prove the existence of an important difference between the two thermodynamic models and, therefore, establish the foundations on the effects that VLE induces in a fluid flow. The results indicate that differences in micro-mixing, ultimately changing the vortex dynamics, are directly related to the imbalance between the heat and mass transfer that occurs within the VLE mixing region of a shear layer.

In this work, the relevance of the multi-phase thermodynamic model based on the vapor–liquid equilibrium (VLE) assumption over the single-phase model is discussed. An emphasis on the importance of the non-linear coupling between thermodynamic, transport, and governing equations is given from a macroscopic point of view by analyzing the mixing effects on a spatial mixing layer in real-gas (non-ideal) conditions. The goal is to prove the existence of an important difference between the two thermodynamic models and, therefore, establish the foundations on the effects that VLE induces in a fluid flow. The results indicate that differences in micro-mixing, ultimately changing the vortex dynamics, are directly related to the imbalance between the heat and mass transfer that occurs within the VLE mixing region of a shear layer.

Categories: Latest papers in fluid mechanics

### Correction and improvement of a widely used droplet–droplet collision outcome model

Physics of Fluids, Volume 32, Issue 11, November 2020.

The widely used droplet–droplet collision outcome model distinguishing stretching separation (SS) and fast coalescence (FC) (named SS/FC model) proposed by Jiang et al. [J. Fluid Mech. 234, 171 (1992)] is corrected and improved in this study. By re-deriving the momentum conservation, the correct mathematical expression of the tangential velocity along the sliding direction is obtained. Moreover, to reduce the uncertainties of model applications, the model is improved by expressing the constants as a function of the Ohnesorge number and droplet size ratio. The validation results demonstrate the effectiveness of the improved SS/FC model.

The widely used droplet–droplet collision outcome model distinguishing stretching separation (SS) and fast coalescence (FC) (named SS/FC model) proposed by Jiang et al. [J. Fluid Mech. 234, 171 (1992)] is corrected and improved in this study. By re-deriving the momentum conservation, the correct mathematical expression of the tangential velocity along the sliding direction is obtained. Moreover, to reduce the uncertainties of model applications, the model is improved by expressing the constants as a function of the Ohnesorge number and droplet size ratio. The validation results demonstrate the effectiveness of the improved SS/FC model.

Categories: Latest papers in fluid mechanics

### A note on a swirling squirmer in a shear-thinning fluid

Physics of Fluids, Volume 32, Issue 11, November 2020.

Micro-organisms and artificial microswimmers often move in biological fluids displaying complex rheological behaviors, including viscoelasticity and shear-thinning viscosity. A comprehensive understanding of the effectiveness of different swimming gaits in various types of complex fluids remains elusive. The squirmer model has been commonly used to represent different types of swimmers and probe the effects of different types of complex rheology on locomotion. While many studies focused only on squirmers with surface velocities in the polar direction, a recent study has revealed that a squirmer with swirling motion can swim faster in a viscoelastic fluid than in Newtonian fluids [Binagia et al., J. Fluid Mech. 900, A4, (2020)]. Here, we consider a similar setup but focus on the sole effect due to shear-thinning viscosity. We use asymptotic analysis and numerical simulations to examine how the swirling flow affects the swimming performance of a squirmer in a shear-thinning but inelastic fluid described by the Carreau constitutive equation. Our results show that the swirling flow can either increase or decrease the speed of the squirmer depending on the Carreau number. In contrast to swimming in a viscoelastic fluid, the speed of a swirling squirmer in a shear-thinning fluid does not go beyond the Newtonian value in a wide range of parameters considered. We also elucidate how the coupling of the azimuthal flow with shear-thinning viscosity can produce the rotational motion of a swirling pusher or puller.

Micro-organisms and artificial microswimmers often move in biological fluids displaying complex rheological behaviors, including viscoelasticity and shear-thinning viscosity. A comprehensive understanding of the effectiveness of different swimming gaits in various types of complex fluids remains elusive. The squirmer model has been commonly used to represent different types of swimmers and probe the effects of different types of complex rheology on locomotion. While many studies focused only on squirmers with surface velocities in the polar direction, a recent study has revealed that a squirmer with swirling motion can swim faster in a viscoelastic fluid than in Newtonian fluids [Binagia et al., J. Fluid Mech. 900, A4, (2020)]. Here, we consider a similar setup but focus on the sole effect due to shear-thinning viscosity. We use asymptotic analysis and numerical simulations to examine how the swirling flow affects the swimming performance of a squirmer in a shear-thinning but inelastic fluid described by the Carreau constitutive equation. Our results show that the swirling flow can either increase or decrease the speed of the squirmer depending on the Carreau number. In contrast to swimming in a viscoelastic fluid, the speed of a swirling squirmer in a shear-thinning fluid does not go beyond the Newtonian value in a wide range of parameters considered. We also elucidate how the coupling of the azimuthal flow with shear-thinning viscosity can produce the rotational motion of a swirling pusher or puller.

Categories: Latest papers in fluid mechanics

### Inertial migration of oblate spheroids in a plane channel

Physics of Fluids, Volume 32, Issue 11, November 2020.

We discuss an inertial migration of oblate spheroids in a plane channel, where the steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius a. By analyzing the inertial lift force, we argue that this force is proportional to a3b, where b is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on b and is equal to that of the sphere of radius a.

We discuss an inertial migration of oblate spheroids in a plane channel, where the steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius a. By analyzing the inertial lift force, we argue that this force is proportional to a3b, where b is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on b and is equal to that of the sphere of radius a.

Categories: Latest papers in fluid mechanics

### Natural circulation pump with asymmetrical heat transfer wall as the element of Büttiker–Landauer thermal ratchet

Physics of Fluids, Volume 32, Issue 11, November 2020.

Technology that makes use of waste heat or low-grade energy is important for addressing worldwide energy security concerns. This study proposes the application of a natural circulation pump employing an asymmetrical heat transfer wall as the element of a Büttiker–Landauer (BL) thermal ratchet powered by waste heat. Furthermore, experiments for evaluating the proposed arrangement’s performance were conducted. We demonstrated experimentally that we can realize water circulation in a channel owing to the localized non-equilibrium nature of the pump’s asymmetrical heat transfer wall. In addition, we propose a framework for evaluating the pump’s performance. Our proposal is expected to result in the uptake of practical applications for BL ratchets.

Technology that makes use of waste heat or low-grade energy is important for addressing worldwide energy security concerns. This study proposes the application of a natural circulation pump employing an asymmetrical heat transfer wall as the element of a Büttiker–Landauer (BL) thermal ratchet powered by waste heat. Furthermore, experiments for evaluating the proposed arrangement’s performance were conducted. We demonstrated experimentally that we can realize water circulation in a channel owing to the localized non-equilibrium nature of the pump’s asymmetrical heat transfer wall. In addition, we propose a framework for evaluating the pump’s performance. Our proposal is expected to result in the uptake of practical applications for BL ratchets.

Categories: Latest papers in fluid mechanics

### Unsteady magnetohydrodynamic flow of generalized second grade fluid through porous medium with Hall effects on heat and mass transfer

Physics of Fluids, Volume 32, Issue 11, November 2020.

This work investigates the unsteady magnetohydrodynamic flow of generalized second grade fluid through a porous medium with Hall effects on heat and mass transfer. The second grade fluid with a fractional derivative is used for the constitutive equation. A second-order fractional backward difference formula in the temporal direction and a spectral collocation method in the spatial direction are proposed to solve the model numerically. In the numerical implementation, a fast method is applied to decrease the memory requirement and computational cost. The velocity, temperature, and concentration profiles are discussed through graphs. The effects of various parameters on the velocity profiles, temperature field, and concentration field are shown. Results indicate that as the fractional derivative γ increases and the Hall parameter m decreases, the amplitudes of the velocity components decrease.

This work investigates the unsteady magnetohydrodynamic flow of generalized second grade fluid through a porous medium with Hall effects on heat and mass transfer. The second grade fluid with a fractional derivative is used for the constitutive equation. A second-order fractional backward difference formula in the temporal direction and a spectral collocation method in the spatial direction are proposed to solve the model numerically. In the numerical implementation, a fast method is applied to decrease the memory requirement and computational cost. The velocity, temperature, and concentration profiles are discussed through graphs. The effects of various parameters on the velocity profiles, temperature field, and concentration field are shown. Results indicate that as the fractional derivative γ increases and the Hall parameter m decreases, the amplitudes of the velocity components decrease.

Categories: Latest papers in fluid mechanics