# Physics of Fluids

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

*Updated:*1 hour 13 min ago

### Rock and roll: Incipient aeolian entrainment of coarse particles

Physics of Fluids, Volume 33, Issue 7, July 2021.

Aeolian transport of coarse grains is an important topic, finding applications in nature (for infrastructure exposed to wind scour) as well as industry (e.g., considering pneumatic transport). Incipient particle entrainment due to turbulent winds refers to the wind conditions where aeolian transport initiates, and as such, it is at the core of such studies. The research presented herein focuses on identifying and quantifying the dynamical processes responsible for coarse particle entrainment. Specifically designed wind tunnel experiments are conducted for a range of wind conditions near the aeolian transport thresholds. A high-resolution laser distance sensor is employed to provide information for the displacement of an exposed particle ranging from small simple rocking motions to complete entrainments (rolling). Measurements of the exposed particle's angular displacements are acquired, which allow the probabilistic study of incipient motion. The variation of statistical parameters, such as the frequency of entrainments, duration of dislodgements, magnitude of displacements, and time between displacements, is studied for a range of increasing airflow rates. The main findings from these experiments suggest that rocking can be observed only up to a limit angular displacement (equal to 0.41π for the conditions tested herein), which defines the position beyond which the resistance force can be overcome by just the mean aerodynamic forcing. Following this experimental framework to establish aeolian thresholds for a wider range of environments may be useful for the identification of the wind conditions under which aeolian transport may start occurring.

Aeolian transport of coarse grains is an important topic, finding applications in nature (for infrastructure exposed to wind scour) as well as industry (e.g., considering pneumatic transport). Incipient particle entrainment due to turbulent winds refers to the wind conditions where aeolian transport initiates, and as such, it is at the core of such studies. The research presented herein focuses on identifying and quantifying the dynamical processes responsible for coarse particle entrainment. Specifically designed wind tunnel experiments are conducted for a range of wind conditions near the aeolian transport thresholds. A high-resolution laser distance sensor is employed to provide information for the displacement of an exposed particle ranging from small simple rocking motions to complete entrainments (rolling). Measurements of the exposed particle's angular displacements are acquired, which allow the probabilistic study of incipient motion. The variation of statistical parameters, such as the frequency of entrainments, duration of dislodgements, magnitude of displacements, and time between displacements, is studied for a range of increasing airflow rates. The main findings from these experiments suggest that rocking can be observed only up to a limit angular displacement (equal to 0.41π for the conditions tested herein), which defines the position beyond which the resistance force can be overcome by just the mean aerodynamic forcing. Following this experimental framework to establish aeolian thresholds for a wider range of environments may be useful for the identification of the wind conditions under which aeolian transport may start occurring.

Categories: Latest papers in fluid mechanics

### Elastic instabilities between two cylinders confined in a channel

Physics of Fluids, Volume 33, Issue 7, July 2021.

Polymeric flow through porous media is relevant in industrial applications, such as enhanced oil recovery, microbial mining, and groundwater remediation. Biological processes, such as drug delivery and the transport of cells and particles in the body, also depend on the viscoelastic flow through the porous matrix. Large elastic stresses induced due to confined geometries can lead to elastic instability for the viscoelastic fluid flow through porous media. We have numerically studied viscoelastic flow through a channel having two closely placed cylinders to investigate pore scale elastic instabilities. We have discovered three distinct flow states in the region between the cylinders. These flow states are closely coupled with the topology of the polymeric stress field. The transition between the flow states can be identified with two critical Weissenberg numbers ([math] and [math]), where the Weissenberg number (Wi) is the ratio of elastic to viscous forces. At [math], the flow is stable, symmetric, and eddy free. For [math], eddies form in the region between the cylinders. We have measured the area occupied by the eddies for different flow conditions and fluid rheological parameters. At [math], the eddy disappears and the flow around the cylinders becomes asymmetric. We have quantified the flow asymmetry around the cylinders for different flow rates and fluid rheology. We have also studied the effect of the cylinders' diameter and separation on the eddies' size ([math]) and flow asymmetry ([math]). We have also investigated the effect of fluid rheology and cylinders' diameter and separation on the value of critical Weissenberg numbers.

Polymeric flow through porous media is relevant in industrial applications, such as enhanced oil recovery, microbial mining, and groundwater remediation. Biological processes, such as drug delivery and the transport of cells and particles in the body, also depend on the viscoelastic flow through the porous matrix. Large elastic stresses induced due to confined geometries can lead to elastic instability for the viscoelastic fluid flow through porous media. We have numerically studied viscoelastic flow through a channel having two closely placed cylinders to investigate pore scale elastic instabilities. We have discovered three distinct flow states in the region between the cylinders. These flow states are closely coupled with the topology of the polymeric stress field. The transition between the flow states can be identified with two critical Weissenberg numbers ([math] and [math]), where the Weissenberg number (Wi) is the ratio of elastic to viscous forces. At [math], the flow is stable, symmetric, and eddy free. For [math], eddies form in the region between the cylinders. We have measured the area occupied by the eddies for different flow conditions and fluid rheological parameters. At [math], the eddy disappears and the flow around the cylinders becomes asymmetric. We have quantified the flow asymmetry around the cylinders for different flow rates and fluid rheology. We have also studied the effect of the cylinders' diameter and separation on the eddies' size ([math]) and flow asymmetry ([math]). We have also investigated the effect of fluid rheology and cylinders' diameter and separation on the value of critical Weissenberg numbers.

Categories: Latest papers in fluid mechanics

### Experimental investigation of solute transport in variably saturated porous media using x-ray computed tomography

Physics of Fluids, Volume 33, Issue 7, July 2021.

Solute transport through variably saturated porous media is ubiquitous in multiple subsurface flows, piquing the geoscience community's interest. This study adopts a novel experimental approach using microfocus x-ray computed tomography for real-time imaging of a three-dimensional NaI tracer plume in a partially saturated packing column. A stabilized two-phase flow field is achievable through continuous co-injection of two-phase fluids: NaCl solvent and pump oil. Thus, the critical role of the NaCl saturation Sw and Péclet number on dispersion can be fully studied by controlling the NaCl fractional flow rate and the total flow rate from the Buckley–Leverett theory. Furthermore, we study solute transport behavior based on statistical moments, the dispersion coefficient, the dilution index, and the mean scalar dissipation rate. Experimental results indicate that the solute transport is Fickian for high Sw ≥ 0.34. In contrast, anomalous transport behavior is found for Sw < 0.34, where the concentration distribution is initially left-tailed and leptokurtic before reaching a well-dispersed regime. The dispersion coefficient is 2–10 times larger for partially saturated cases compared with the fully saturated case and shows a non-monotonical dependency on Sw. Finally, the analysis of the dilution index indicates that the overall mixing strength increases when Sw decreases, whereas the mean scalar dissipation rate reveals that the time scaling of transverse mixing is the largest at an intermediate Sw. The results can be used to elucidate the solute transport behavior in a two-phase system.

Solute transport through variably saturated porous media is ubiquitous in multiple subsurface flows, piquing the geoscience community's interest. This study adopts a novel experimental approach using microfocus x-ray computed tomography for real-time imaging of a three-dimensional NaI tracer plume in a partially saturated packing column. A stabilized two-phase flow field is achievable through continuous co-injection of two-phase fluids: NaCl solvent and pump oil. Thus, the critical role of the NaCl saturation Sw and Péclet number on dispersion can be fully studied by controlling the NaCl fractional flow rate and the total flow rate from the Buckley–Leverett theory. Furthermore, we study solute transport behavior based on statistical moments, the dispersion coefficient, the dilution index, and the mean scalar dissipation rate. Experimental results indicate that the solute transport is Fickian for high Sw ≥ 0.34. In contrast, anomalous transport behavior is found for Sw < 0.34, where the concentration distribution is initially left-tailed and leptokurtic before reaching a well-dispersed regime. The dispersion coefficient is 2–10 times larger for partially saturated cases compared with the fully saturated case and shows a non-monotonical dependency on Sw. Finally, the analysis of the dilution index indicates that the overall mixing strength increases when Sw decreases, whereas the mean scalar dissipation rate reveals that the time scaling of transverse mixing is the largest at an intermediate Sw. The results can be used to elucidate the solute transport behavior in a two-phase system.

Categories: Latest papers in fluid mechanics

### Chaotic streaklines in new exact solutions to the Navier–Stokes equations

Physics of Fluids, Volume 33, Issue 7, July 2021.

Exact solutions to the Navier–Stokes equations with time-dependent viscosity [math] are constructed. The fluid velocities [math] for these solutions are eigenvector fields for the operator curl. New exact solutions with [math] for [math], which describe dynamics of viscous fluid inside a ball and a spherical shell, have chaotic streaklines. For the derived solutions with [math] or with [math], where [math] and [math], the length of each fluid streakline is finite and, therefore, its dynamics is not chaotic. As a consequence, it is shown that all Trkalian flows with constant viscosity [math] are not chaotic.

Exact solutions to the Navier–Stokes equations with time-dependent viscosity [math] are constructed. The fluid velocities [math] for these solutions are eigenvector fields for the operator curl. New exact solutions with [math] for [math], which describe dynamics of viscous fluid inside a ball and a spherical shell, have chaotic streaklines. For the derived solutions with [math] or with [math], where [math] and [math], the length of each fluid streakline is finite and, therefore, its dynamics is not chaotic. As a consequence, it is shown that all Trkalian flows with constant viscosity [math] are not chaotic.

Categories: Latest papers in fluid mechanics

### Effects of syringe pump fluctuations on cell-free layer in hydrodynamic separation microfluidic devices

Physics of Fluids, Volume 33, Issue 7, July 2021.

Syringe pumps are widely used biomedical equipment, which offer low-cost solutions to drive and control flow through microfluidic chips. However, they have been shown to transmit mechanical oscillations resulting from their stepper motors into the flow, perturbing device performance. These detrimental effects have mostly been reported on microdroplet production, but have never been reported on hydrodynamic two-phase separation, such as in microdevices making use of cell-free layer phenomena. While various mechanisms can be used to circumvent syringe pump oscillations, it is of interest to study the oscillation effects in naïve systems, which are common in research settings. Previous fluctuation studies focused on relatively low flow rates, typically below 5 ml/h, and showed a linear decay of the relative pressure fluctuations as a function of the flow rate. In this work, we have uncovered that the relative pressure fluctuations reach a plateau at higher flow rates, typically above 5 ml/h. Using a novel low-cost coded compressive rotating mirror camera, we investigated the effect of fluctuations in a hydrodynamic microfluidic separation device based on a cell-free layer concept. We demonstrated that cell-free zone width fluctuations have the same frequency and amplitude than the syringe pump-induced pressure oscillations and illustrated the subsequent degradation of particle separation. This work provides an insight into the effect of syringe pump fluctuations on microfluidic separation, which will inform the design of microfluidic systems and improve their resilience to pulsating or fluctuating flow conditions without the use of ancillary equipment.

Syringe pumps are widely used biomedical equipment, which offer low-cost solutions to drive and control flow through microfluidic chips. However, they have been shown to transmit mechanical oscillations resulting from their stepper motors into the flow, perturbing device performance. These detrimental effects have mostly been reported on microdroplet production, but have never been reported on hydrodynamic two-phase separation, such as in microdevices making use of cell-free layer phenomena. While various mechanisms can be used to circumvent syringe pump oscillations, it is of interest to study the oscillation effects in naïve systems, which are common in research settings. Previous fluctuation studies focused on relatively low flow rates, typically below 5 ml/h, and showed a linear decay of the relative pressure fluctuations as a function of the flow rate. In this work, we have uncovered that the relative pressure fluctuations reach a plateau at higher flow rates, typically above 5 ml/h. Using a novel low-cost coded compressive rotating mirror camera, we investigated the effect of fluctuations in a hydrodynamic microfluidic separation device based on a cell-free layer concept. We demonstrated that cell-free zone width fluctuations have the same frequency and amplitude than the syringe pump-induced pressure oscillations and illustrated the subsequent degradation of particle separation. This work provides an insight into the effect of syringe pump fluctuations on microfluidic separation, which will inform the design of microfluidic systems and improve their resilience to pulsating or fluctuating flow conditions without the use of ancillary equipment.

Categories: Latest papers in fluid mechanics

### Double masking protection vs. comfort—A quantitative assessment

Physics of Fluids, Volume 33, Issue 7, July 2021.

COVID-19 has forced humankind to adopt face masks as an integral part of everyday life. This preventive measure is an effective source control technique to curb the spread of COVID-19 and other similar diseases. The virus responsible for causing COVID-19 has undergone several mutations in the recent past, including B.1.1.7, B.1.351, P.1, and N501Y, B.1.617, with a higher infectious rate. These viruses' variants are mainly responsible for the recent spike in COVID-19 cases and associated steep rise in mortality rate worldwide. Under these circumstances, the Center for Disease Control (CDC) and health experts recommend double masking, which mainly includes a surgical mask and a cotton mask for the general public. This combination provides an additional layer of protection and masks fitment to minimize the leakage of droplets expelled during coughing, sneezing, talking, and breathing. This leakage may cause airborne transmission of the virus. In the present study, we report a systematic quantitative unsteady pressure measurement supplement with flow visualization to quantify the effectiveness of a single and double mask. We have also evaluated double masking consisting of a surgical mask and an N-95 mask used by medical professionals. A simple knot improves the surgical mask fitment significantly, and hence, the leakage of droplets is minimized. The leakage of the droplets was reduced to a large extent by using a double mask combination of a two-layer cotton mask over the surgical mask with a knot. The double mask combination of surgical + N-95 and two-layer cotton + N-95 masks showed the most promising results, and no leakage of the droplets is observed in the forward direction. A double mask combination of surgical and N-95 mask offers 8.6% and 5.6% lower mean and peak pressures compared to surgical, and cotton mask. The best results are observed with cotton and N-95 masks with 54.6% and 23% lower mean and peak pressures than surgical and cotton masks; hence, this combination will offer more comfort to the wearer.

COVID-19 has forced humankind to adopt face masks as an integral part of everyday life. This preventive measure is an effective source control technique to curb the spread of COVID-19 and other similar diseases. The virus responsible for causing COVID-19 has undergone several mutations in the recent past, including B.1.1.7, B.1.351, P.1, and N501Y, B.1.617, with a higher infectious rate. These viruses' variants are mainly responsible for the recent spike in COVID-19 cases and associated steep rise in mortality rate worldwide. Under these circumstances, the Center for Disease Control (CDC) and health experts recommend double masking, which mainly includes a surgical mask and a cotton mask for the general public. This combination provides an additional layer of protection and masks fitment to minimize the leakage of droplets expelled during coughing, sneezing, talking, and breathing. This leakage may cause airborne transmission of the virus. In the present study, we report a systematic quantitative unsteady pressure measurement supplement with flow visualization to quantify the effectiveness of a single and double mask. We have also evaluated double masking consisting of a surgical mask and an N-95 mask used by medical professionals. A simple knot improves the surgical mask fitment significantly, and hence, the leakage of droplets is minimized. The leakage of the droplets was reduced to a large extent by using a double mask combination of a two-layer cotton mask over the surgical mask with a knot. The double mask combination of surgical + N-95 and two-layer cotton + N-95 masks showed the most promising results, and no leakage of the droplets is observed in the forward direction. A double mask combination of surgical and N-95 mask offers 8.6% and 5.6% lower mean and peak pressures compared to surgical, and cotton mask. The best results are observed with cotton and N-95 masks with 54.6% and 23% lower mean and peak pressures than surgical and cotton masks; hence, this combination will offer more comfort to the wearer.

Categories: Latest papers in fluid mechanics

### Fully implicit spectral boundary integral computation of red blood cell flow

Physics of Fluids, Volume 33, Issue 7, July 2021.

This paper is on an implicit time integration scheme for simulation of red blood cell (RBC) flow in an ambient fluid. The intra- and extracellular plasmas are modeled as Stokes flows and represented by boundary integral equations (BIE) written in a weakly singular form. The cell membrane is modeled as a thin elastic shell. Expressed in this way, the RBC flow model constitutes an implicit ordinary differential equation (IODE) in the cell shape. The cell shape and velocity field are discretized spatially by a spectral approach using spherical harmonic basis functions. It is then convenient to express the BIE in the Galerkin form with the spherical harmonics themselves as test functions. The key aspect in this paper is the recognition of the IODE structure of the RBC flow model and consequent application of a multi-step implicit solver for time integration. As with any implicit solver, a nonlinear equation in the cell shape is solved at each time step, for which Newton's method is applied. This requires the Jacobian of the IODE, or equivalently computation of Jacobian-vector products. An important contribution is the formulation of such Jacobian-vector products as evaluating a second BIE. The original weakly singular form is crucial in facilitating this formulation. The implicit solver employs variable order and adaptive time stepping controlled by truncation error and convergence of Newton iterations. Numerical examples show that larger time steps are possible and that the number of matrix-vector products is comparable to explicit methods. Source code is provided in the online supplementary material.

This paper is on an implicit time integration scheme for simulation of red blood cell (RBC) flow in an ambient fluid. The intra- and extracellular plasmas are modeled as Stokes flows and represented by boundary integral equations (BIE) written in a weakly singular form. The cell membrane is modeled as a thin elastic shell. Expressed in this way, the RBC flow model constitutes an implicit ordinary differential equation (IODE) in the cell shape. The cell shape and velocity field are discretized spatially by a spectral approach using spherical harmonic basis functions. It is then convenient to express the BIE in the Galerkin form with the spherical harmonics themselves as test functions. The key aspect in this paper is the recognition of the IODE structure of the RBC flow model and consequent application of a multi-step implicit solver for time integration. As with any implicit solver, a nonlinear equation in the cell shape is solved at each time step, for which Newton's method is applied. This requires the Jacobian of the IODE, or equivalently computation of Jacobian-vector products. An important contribution is the formulation of such Jacobian-vector products as evaluating a second BIE. The original weakly singular form is crucial in facilitating this formulation. The implicit solver employs variable order and adaptive time stepping controlled by truncation error and convergence of Newton iterations. Numerical examples show that larger time steps are possible and that the number of matrix-vector products is comparable to explicit methods. Source code is provided in the online supplementary material.

Categories: Latest papers in fluid mechanics

### Eddy viscosity modeling around curved boundaries through bifurcation approach and theory of rotating turbulence

Physics of Fluids, Volume 33, Issue 7, July 2021.

A novel approach to curvature effects based on the bifurcation theory and rotation turbulence energy spectrum is implemented to improve the sensitivity of the [math] two-equation turbulence model (Jones–Launder form) to curved surfaces. This is done by accounting for the vorticity tensor, which becomes more significant in curved flows, something that the standard [math] model does not originally consider. This new eddy viscosity model is based on the energy spectrum for a turbulent flow undergoing rotation and is then modeled on the bifurcation diagram in [math] phase space. The approach is demonstrated on three different test cases, 30° two-dimensional curved channel, 90° three-dimensional bend duct, and flow past cylinder, to test for the effects of convex and concave curvatures on turbulence. The results from these test cases are then contrasted against other existing eddy viscosity models as well as experimental data. The proposed approach provides better turbulence predictions along convex or concave surfaces, better memory effects, and are closer to the experimental results. For flow past cylinder, the new eddy viscosity model predicts drag coefficient that is closer to experiments with 8% difference, against 30% difference predicted by standard [math] and Pettersson models.

A novel approach to curvature effects based on the bifurcation theory and rotation turbulence energy spectrum is implemented to improve the sensitivity of the [math] two-equation turbulence model (Jones–Launder form) to curved surfaces. This is done by accounting for the vorticity tensor, which becomes more significant in curved flows, something that the standard [math] model does not originally consider. This new eddy viscosity model is based on the energy spectrum for a turbulent flow undergoing rotation and is then modeled on the bifurcation diagram in [math] phase space. The approach is demonstrated on three different test cases, 30° two-dimensional curved channel, 90° three-dimensional bend duct, and flow past cylinder, to test for the effects of convex and concave curvatures on turbulence. The results from these test cases are then contrasted against other existing eddy viscosity models as well as experimental data. The proposed approach provides better turbulence predictions along convex or concave surfaces, better memory effects, and are closer to the experimental results. For flow past cylinder, the new eddy viscosity model predicts drag coefficient that is closer to experiments with 8% difference, against 30% difference predicted by standard [math] and Pettersson models.

Categories: Latest papers in fluid mechanics

### Weakly nonlinear broadband and multi-directional surface waves on an arbitrary depth: A framework, Stokes drift, and particle trajectories

Physics of Fluids, Volume 33, Issue 7, July 2021.

Surface gravity waves in coastal waters are broadband and multi-directional, whose quadratic properties are of considerable engineering and scientific interest. Based on a Stokes expansion and an envelope-type framework, a new semi-analytical approach is proposed in this paper for the description of weakly nonlinear broadband and multi-directional surface waves. This approach proposes solving for the second-order wave fields through the separation of harmonics, by using a Fast Fourier transform and a time integration method. Different from some other methods, e.g., the High-Order Spectral method, the approach introduces a spectral shift for the superharmonic waves, leading to computationally efficient and accurate spectral predictions. The approach has been validated through comparisons with the results based on Dalzell [“A note on finite depth second-order wave–wave interactions,” Appl. Ocean Res. 21, 105–111 (1999)]. An envelope-type framework for the fast prediction of particle trajectories and Stokes drifts up to the second order in wave steepness is also derived in this paper, based on the semi-analytical approach. This paper shows that the results based on a narrowband assumption lead to underestimates of Stokes drift velocities driven by broadband unidirectional focused wave groups. The cases, examined for particle trajectories below broadband unidirectional focused wave groups, show that a larger bandwidth and water depth can enhance the differences in the net mean horizontal displacement of particles at water surface relative to these at seabed.

Surface gravity waves in coastal waters are broadband and multi-directional, whose quadratic properties are of considerable engineering and scientific interest. Based on a Stokes expansion and an envelope-type framework, a new semi-analytical approach is proposed in this paper for the description of weakly nonlinear broadband and multi-directional surface waves. This approach proposes solving for the second-order wave fields through the separation of harmonics, by using a Fast Fourier transform and a time integration method. Different from some other methods, e.g., the High-Order Spectral method, the approach introduces a spectral shift for the superharmonic waves, leading to computationally efficient and accurate spectral predictions. The approach has been validated through comparisons with the results based on Dalzell [“A note on finite depth second-order wave–wave interactions,” Appl. Ocean Res. 21, 105–111 (1999)]. An envelope-type framework for the fast prediction of particle trajectories and Stokes drifts up to the second order in wave steepness is also derived in this paper, based on the semi-analytical approach. This paper shows that the results based on a narrowband assumption lead to underestimates of Stokes drift velocities driven by broadband unidirectional focused wave groups. The cases, examined for particle trajectories below broadband unidirectional focused wave groups, show that a larger bandwidth and water depth can enhance the differences in the net mean horizontal displacement of particles at water surface relative to these at seabed.

Categories: Latest papers in fluid mechanics

### Competition between shear and biaxial extensional viscous dissipation in the expansion dynamics of Newtonian and rheo-thinning liquid sheets

Physics of Fluids, Volume 33, Issue 7, July 2021.

When a drop of fluid hits a small solid target of comparable size, it expands radially until reaching a maximum diameter and subsequently recedes. In this work, we show that the expansion process of liquid sheets is controlled by a combination of shear (on the target) and biaxial extensional (in the air) deformations. We propose an approach toward a rational description of the phenomenon for Newtonian and viscoelastic fluids by evaluating the viscous dissipation due to shear and extensional deformations, yielding a prediction of the maximum expansion factor of the sheet as a function of the relevant viscosity. For Newtonian systems, biaxial extensional and shear viscous dissipation are of the same order of magnitude. On the contrary, for thinning solutions of supramolecular polymers, shear dissipation is negligible compared to biaxial extensional dissipation and the biaxial thinning extensional viscosity is the appropriate quantity to describe the maximum expansion of the sheets. Moreover, we show that the rate-dependent biaxial extensional viscosities deduced from drop impact experiments are in good quantitative agreement with previous experimental data and theoretical predictions for various viscoelastic liquids.

When a drop of fluid hits a small solid target of comparable size, it expands radially until reaching a maximum diameter and subsequently recedes. In this work, we show that the expansion process of liquid sheets is controlled by a combination of shear (on the target) and biaxial extensional (in the air) deformations. We propose an approach toward a rational description of the phenomenon for Newtonian and viscoelastic fluids by evaluating the viscous dissipation due to shear and extensional deformations, yielding a prediction of the maximum expansion factor of the sheet as a function of the relevant viscosity. For Newtonian systems, biaxial extensional and shear viscous dissipation are of the same order of magnitude. On the contrary, for thinning solutions of supramolecular polymers, shear dissipation is negligible compared to biaxial extensional dissipation and the biaxial thinning extensional viscosity is the appropriate quantity to describe the maximum expansion of the sheets. Moreover, we show that the rate-dependent biaxial extensional viscosities deduced from drop impact experiments are in good quantitative agreement with previous experimental data and theoretical predictions for various viscoelastic liquids.

Categories: Latest papers in fluid mechanics

### Scale law analysis of the curved boundary layer evolving around a horizontal cylinder at Pr > 1

Physics of Fluids, Volume 33, Issue 7, July 2021.

The convective boundary layer flow on the external surface of an isothermally heated horizontal cylinder is investigated in this study. Numerical simulations are first carried out for a wide range of flow parameters, i.e., Rayleigh and Prandtl numbers, and scale relations quantifying the boundary layer flow are then determined from the simulation data. The numerical results suggest that the curved boundary layer experiences an initial growth state, a transitional state, and a developed state, which are essentially identical to the extensively studied flat boundary layers. Scale relations quantifying the local flow variables are obtained, and the proposed scale laws indicate that during the initial growth, the present curved boundary layer flow follows a two-dimensional growth rather than the well-known one-dimensional startup of flat boundary layers. It is further demonstrated that the characteristic velocity of the boundary layer flow maximizes at π/2, but its thickness is circumferential location independent. In the steady state, however, the maximum streamwise velocity of the boundary layer shifts to approximately 7π/9 and the thickness consistently increases with the circumferential location. It is also shown that the thickness of the inner viscous boundary layer could be obtained by properly considering the Prandtl number effect, i.e., by the term (1 + Pr−1/2)−1. The proposed scale relations could reasonably describe the curved boundary layer flow, and all regression constants are above 0.99.

The convective boundary layer flow on the external surface of an isothermally heated horizontal cylinder is investigated in this study. Numerical simulations are first carried out for a wide range of flow parameters, i.e., Rayleigh and Prandtl numbers, and scale relations quantifying the boundary layer flow are then determined from the simulation data. The numerical results suggest that the curved boundary layer experiences an initial growth state, a transitional state, and a developed state, which are essentially identical to the extensively studied flat boundary layers. Scale relations quantifying the local flow variables are obtained, and the proposed scale laws indicate that during the initial growth, the present curved boundary layer flow follows a two-dimensional growth rather than the well-known one-dimensional startup of flat boundary layers. It is further demonstrated that the characteristic velocity of the boundary layer flow maximizes at π/2, but its thickness is circumferential location independent. In the steady state, however, the maximum streamwise velocity of the boundary layer shifts to approximately 7π/9 and the thickness consistently increases with the circumferential location. It is also shown that the thickness of the inner viscous boundary layer could be obtained by properly considering the Prandtl number effect, i.e., by the term (1 + Pr−1/2)−1. The proposed scale relations could reasonably describe the curved boundary layer flow, and all regression constants are above 0.99.

Categories: Latest papers in fluid mechanics

### Experimental investigation of indoor aerosol dispersion and accumulation in the context of COVID-19: Effects of masks and ventilation

Physics of Fluids, Volume 33, Issue 7, July 2021.

The ongoing COVID-19 pandemic has highlighted the importance of aerosol dispersion in disease transmission in indoor environments. The present study experimentally investigates the dispersion and build-up of an exhaled aerosol modeled with polydisperse microscopic particles (approximately 1 μm mean diameter) by a seated manikin in a relatively large indoor environment. The aims are to offer quantitative insight into the effect of common face masks and ventilation/air purification, and to provide relevant experimental metrics for modeling and risk assessment. Measurements demonstrate that all tested masks provide protection in the immediate vicinity of the host primarily through the redirection and reduction of expiratory momentum. However, leakages are observed to result in notable decreases in mask efficiency relative to the ideal filtration efficiency of the mask material, even in the case of high-efficiency masks, such as the R95 or KN95. Tests conducted in the far field ([math] distance from the subject) capture significant aerosol build-up in the indoor space over a long duration ([math]). A quantitative measure of apparent exhalation filtration efficiency is provided based on experimental data assimilation to a simplified model. The results demonstrate that the apparent exhalation filtration efficiency is significantly lower than the ideal filtration efficiency of the mask material. Nevertheless, high-efficiency masks, such as the KN95, still offer substantially higher apparent filtration efficiencies (60% and 46% for R95 and KN95 masks, respectively) than the more commonly used cloth (10%) and surgical masks (12%), and therefore are still the recommended choice in mitigating airborne disease transmission indoors. The results also suggest that, while higher ventilation capacities are required to fully mitigate aerosol build-up, even relatively low air-change rates ([math]) lead to lower aerosol build-up compared to the best performing mask in an unventilated space.

The ongoing COVID-19 pandemic has highlighted the importance of aerosol dispersion in disease transmission in indoor environments. The present study experimentally investigates the dispersion and build-up of an exhaled aerosol modeled with polydisperse microscopic particles (approximately 1 μm mean diameter) by a seated manikin in a relatively large indoor environment. The aims are to offer quantitative insight into the effect of common face masks and ventilation/air purification, and to provide relevant experimental metrics for modeling and risk assessment. Measurements demonstrate that all tested masks provide protection in the immediate vicinity of the host primarily through the redirection and reduction of expiratory momentum. However, leakages are observed to result in notable decreases in mask efficiency relative to the ideal filtration efficiency of the mask material, even in the case of high-efficiency masks, such as the R95 or KN95. Tests conducted in the far field ([math] distance from the subject) capture significant aerosol build-up in the indoor space over a long duration ([math]). A quantitative measure of apparent exhalation filtration efficiency is provided based on experimental data assimilation to a simplified model. The results demonstrate that the apparent exhalation filtration efficiency is significantly lower than the ideal filtration efficiency of the mask material. Nevertheless, high-efficiency masks, such as the KN95, still offer substantially higher apparent filtration efficiencies (60% and 46% for R95 and KN95 masks, respectively) than the more commonly used cloth (10%) and surgical masks (12%), and therefore are still the recommended choice in mitigating airborne disease transmission indoors. The results also suggest that, while higher ventilation capacities are required to fully mitigate aerosol build-up, even relatively low air-change rates ([math]) lead to lower aerosol build-up compared to the best performing mask in an unventilated space.

Categories: Latest papers in fluid mechanics

### Active flows on curved surfaces

Physics of Fluids, Volume 33, Issue 7, July 2021.

We consider a numerical approach for a covariant generalized Navier–Stokes equation on general surfaces and study the influence of varying Gaussian curvature on anomalous vortex-network active turbulence. This regime is characterized by self-assembly of finite-size vortices into linked chains of anti-ferromagnet order, which percolate through the entire surface. The simulation results reveal an alignment of these chains with minimal curvature lines of the surface and indicate a dependency of this turbulence regime on the sign and the gradient in local Gaussian curvature. While these results remain qualitative and their explanations are still incomplete, several of the observed phenomena are in qualitative agreement with experiments on active nematic liquid crystals on toroidal surfaces and contribute to an understanding of the delicate interplay between geometrical properties of the surface and characteristics of the flow field, which has the potential to control active flows on surfaces via gradients in the spatial curvature of the surface.

We consider a numerical approach for a covariant generalized Navier–Stokes equation on general surfaces and study the influence of varying Gaussian curvature on anomalous vortex-network active turbulence. This regime is characterized by self-assembly of finite-size vortices into linked chains of anti-ferromagnet order, which percolate through the entire surface. The simulation results reveal an alignment of these chains with minimal curvature lines of the surface and indicate a dependency of this turbulence regime on the sign and the gradient in local Gaussian curvature. While these results remain qualitative and their explanations are still incomplete, several of the observed phenomena are in qualitative agreement with experiments on active nematic liquid crystals on toroidal surfaces and contribute to an understanding of the delicate interplay between geometrical properties of the surface and characteristics of the flow field, which has the potential to control active flows on surfaces via gradients in the spatial curvature of the surface.

Categories: Latest papers in fluid mechanics

### Effects of gradual flexibility and trailing edge shape on propulsive performance of pitching fins

Physics of Fluids, Volume 33, Issue 7, July 2021.

This paper addresses hydrodynamic performance of fins regarding their trailing edge convexity–concavity and flexibility distribution. The effects of trailing edge convexity–concavity on propulsive performance and vortex dynamics were investigated experimentally utilizing time-resolved particle image velocimetry and force sensors. It was found that the convex trailing edge shape always outperforms the concave shape. Wake contracting by the bent shape of the trailing edge vortex of a convex trapezoidal form resulted in higher thrust and efficiency. The results also showed that the rounded edges of fish fins did not provide additional hydrodynamic advantages. Furthermore, we found that a gradually flexible fin delivered better propulsive performance over a uniformly flexible fin. The hydrodynamic performance of the flexible fins depended on the strength and relative positions of the trailing edge vortexes shed by each fin, which were affected by the flexible deformations of the fins. In the lower Reynolds number operation (approaching, but below the first resonant mode), the fins with larger camber produced a stronger momentum footprint especially considering the far wake elements, while in the higher Reynolds number range due to resonant deformation the extent of trailing edge excursion became dominant in affecting the propulsive performance. The results showed that gradually flexible fins can improve the performance of future watercraft.

This paper addresses hydrodynamic performance of fins regarding their trailing edge convexity–concavity and flexibility distribution. The effects of trailing edge convexity–concavity on propulsive performance and vortex dynamics were investigated experimentally utilizing time-resolved particle image velocimetry and force sensors. It was found that the convex trailing edge shape always outperforms the concave shape. Wake contracting by the bent shape of the trailing edge vortex of a convex trapezoidal form resulted in higher thrust and efficiency. The results also showed that the rounded edges of fish fins did not provide additional hydrodynamic advantages. Furthermore, we found that a gradually flexible fin delivered better propulsive performance over a uniformly flexible fin. The hydrodynamic performance of the flexible fins depended on the strength and relative positions of the trailing edge vortexes shed by each fin, which were affected by the flexible deformations of the fins. In the lower Reynolds number operation (approaching, but below the first resonant mode), the fins with larger camber produced a stronger momentum footprint especially considering the far wake elements, while in the higher Reynolds number range due to resonant deformation the extent of trailing edge excursion became dominant in affecting the propulsive performance. The results showed that gradually flexible fins can improve the performance of future watercraft.

Categories: Latest papers in fluid mechanics

### Interface retaining coarsening of multiphase flows

Physics of Fluids, Volume 33, Issue 7, July 2021.

Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases, the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may, therefore, be important to retain a sharp interface for the resolved scales. Here, a process to coarsen or filter fully resolved numerical solutions for incompressible multiphase flows while retaining a sharp interface is examined. The different phases are identified by an index function that takes different values in each phase and is coarsened by solving a constant coefficient diffusion equation, while tracking the interface contour. Small flow scales of one phase, left behind when the interface is moved, are embedded in the other phase by solving another diffusion equation with a modified diffusion coefficient that is zero at the interface location to prevent diffusion across the interface, plus a pressure-like equation to enforce incompressibility of the coarse velocity field. Examples of different levels of coarsening are shown. A simulation of a coarse model, where small scales are treated as a homogeneous mixture, results in a solution that is similar to the filtered fully resolved field for the early time Rayleigh–Taylor instability.

Multiphase flows are characterized by sharp moving interfaces, separating different fluids or phases. In many cases, the dynamics of the interface determines the behavior of the flow. In a coarse, or reduced order model, it may, therefore, be important to retain a sharp interface for the resolved scales. Here, a process to coarsen or filter fully resolved numerical solutions for incompressible multiphase flows while retaining a sharp interface is examined. The different phases are identified by an index function that takes different values in each phase and is coarsened by solving a constant coefficient diffusion equation, while tracking the interface contour. Small flow scales of one phase, left behind when the interface is moved, are embedded in the other phase by solving another diffusion equation with a modified diffusion coefficient that is zero at the interface location to prevent diffusion across the interface, plus a pressure-like equation to enforce incompressibility of the coarse velocity field. Examples of different levels of coarsening are shown. A simulation of a coarse model, where small scales are treated as a homogeneous mixture, results in a solution that is similar to the filtered fully resolved field for the early time Rayleigh–Taylor instability.

Categories: Latest papers in fluid mechanics

### Bouncing dynamics of spheroidal drops on macro-ridge structure

Physics of Fluids, Volume 33, Issue 7, July 2021.

Bouncing drops on solid surfaces have gained increasing attention for various practical applications, such as self-cleaning and anti-icing strategies. Breaking the circular symmetry in bouncing dynamics on a ridge enables drop dynamics to be modified significantly and the residence time of drops on surfaces to be reduced. Here, we numerically investigate the asymmetric bouncing dynamics of oblate and prolate spheroidal drops on a superhydrophobic surface decorated with a rectangular ridge to demonstrate the feasibility of further reducing the residence time by shaping raindrop-like drops. The residence time is investigated for various aspect ratios and Weber numbers, which are discussed based on impact stages of spreading, splitting, and retraction. The underlying principle behind the residence time reduction is analyzed by quantifying the temporal variations in the widths and the axial momenta of the drops. The bouncing directions of the spheroidal drops are closely related to the momentum distributions during the retraction. We investigate how to change the residence time for ridges of different heights and widths. The symmetry-breaking bouncing of the spheroidal drops on ridge surfaces will provide fundamental and practical inspiration for the efficient control of drop mobility.

Bouncing drops on solid surfaces have gained increasing attention for various practical applications, such as self-cleaning and anti-icing strategies. Breaking the circular symmetry in bouncing dynamics on a ridge enables drop dynamics to be modified significantly and the residence time of drops on surfaces to be reduced. Here, we numerically investigate the asymmetric bouncing dynamics of oblate and prolate spheroidal drops on a superhydrophobic surface decorated with a rectangular ridge to demonstrate the feasibility of further reducing the residence time by shaping raindrop-like drops. The residence time is investigated for various aspect ratios and Weber numbers, which are discussed based on impact stages of spreading, splitting, and retraction. The underlying principle behind the residence time reduction is analyzed by quantifying the temporal variations in the widths and the axial momenta of the drops. The bouncing directions of the spheroidal drops are closely related to the momentum distributions during the retraction. We investigate how to change the residence time for ridges of different heights and widths. The symmetry-breaking bouncing of the spheroidal drops on ridge surfaces will provide fundamental and practical inspiration for the efficient control of drop mobility.

Categories: Latest papers in fluid mechanics

### Numerical investigation on the flow around an inclined prolate spheroid

Physics of Fluids, Volume 33, Issue 7, July 2021.

Numerical simulations are performed for the flow around an inclined 5:2 prolate spheroid in a uniform freestream. The Reynolds number (Re = 300, 500, 700, and 1000) and incidence angle (α = 0°–90°) are considered as significant parameters affecting the wake transitions, where α = 0° indicates flow parallel to the major axis of the prolate spheroid, and the Re is based on the inflow velocity U0 and the volume-equivalent sphere diameter De of the spheroid. In the range considered of Re and α, eight flow regimes are identified: (i) steady axisymmetric (SA) flow regime; (ii) steady planar symmetric flow regime; (iii) steady asymmetric (SAS) flow regime; (iv) periodic planar symmetric flow regime with non-zero mean lift or “Zig-zig-like” (Zz-like) mode; (v) periodic asymmetric flow regime with double-sided vortex shedding; (vi) multi-periodic asymmetric flow regime with double-sided vortex shedding and low frequency modulation (MPADL); (vii) multi-periodic asymmetric flow regime with single-sided vortex shedding and low frequency modulation (MPASL); and (viii) weakly chaotic state. Three of them are new and first reported, i.e., SAS, MPADL, and MPASL modes. The wake structure of the Zz-like mode is different from that of the zig-zig mode in the sphere/disk wake with a pair of streamwise vortices extending to the near wake. It is found that the elongated body can delay the onset of unsteadiness at small incidence angles. A flow regime map in the considered (Re, α) space is then provided. Finally, the physical mechanisms of the low-frequency phenomena observed at different wake modes are explored.

Numerical simulations are performed for the flow around an inclined 5:2 prolate spheroid in a uniform freestream. The Reynolds number (Re = 300, 500, 700, and 1000) and incidence angle (α = 0°–90°) are considered as significant parameters affecting the wake transitions, where α = 0° indicates flow parallel to the major axis of the prolate spheroid, and the Re is based on the inflow velocity U0 and the volume-equivalent sphere diameter De of the spheroid. In the range considered of Re and α, eight flow regimes are identified: (i) steady axisymmetric (SA) flow regime; (ii) steady planar symmetric flow regime; (iii) steady asymmetric (SAS) flow regime; (iv) periodic planar symmetric flow regime with non-zero mean lift or “Zig-zig-like” (Zz-like) mode; (v) periodic asymmetric flow regime with double-sided vortex shedding; (vi) multi-periodic asymmetric flow regime with double-sided vortex shedding and low frequency modulation (MPADL); (vii) multi-periodic asymmetric flow regime with single-sided vortex shedding and low frequency modulation (MPASL); and (viii) weakly chaotic state. Three of them are new and first reported, i.e., SAS, MPADL, and MPASL modes. The wake structure of the Zz-like mode is different from that of the zig-zig mode in the sphere/disk wake with a pair of streamwise vortices extending to the near wake. It is found that the elongated body can delay the onset of unsteadiness at small incidence angles. A flow regime map in the considered (Re, α) space is then provided. Finally, the physical mechanisms of the low-frequency phenomena observed at different wake modes are explored.

Categories: Latest papers in fluid mechanics

### Hydrodynamic models of astrophysical wormholes: The general concept

Physics of Fluids, Volume 33, Issue 7, July 2021.

We study the amplification of shallow-water waves in the course of their propagation in a duct of a variable cross section with a spatially inhomogeneous flow. We derive the basic set of equations for the wave propagation and present the asymptotic analysis of solutions in the neighborhood of critical points where the wave speed coincides with the speed of the current. The considered model represents a kinematic analog of astrophysical event horizons occurring in the vicinity of the black holes (BH) or white holes (WH). We study then the wave propagation in the flow with two critical points (two horizons) when the flow transits first the BH horizon and then the WH one or vice versa. In the former case, the region between the critical points mimics a wormhole in general relativity. The theoretical results are illustrated by numerical calculations of wave propagation through the critical points. It is shown that the wave amplification after passing the active zone between the horizons takes place in BH–WH arrangements only and can occur for different relationships between the subcritical and supercritical flow velocities. The frequency dependence of the amplification factor is obtained and quantified in terms of the velocity ratio within and outside the “wormhole domain.”

We study the amplification of shallow-water waves in the course of their propagation in a duct of a variable cross section with a spatially inhomogeneous flow. We derive the basic set of equations for the wave propagation and present the asymptotic analysis of solutions in the neighborhood of critical points where the wave speed coincides with the speed of the current. The considered model represents a kinematic analog of astrophysical event horizons occurring in the vicinity of the black holes (BH) or white holes (WH). We study then the wave propagation in the flow with two critical points (two horizons) when the flow transits first the BH horizon and then the WH one or vice versa. In the former case, the region between the critical points mimics a wormhole in general relativity. The theoretical results are illustrated by numerical calculations of wave propagation through the critical points. It is shown that the wave amplification after passing the active zone between the horizons takes place in BH–WH arrangements only and can occur for different relationships between the subcritical and supercritical flow velocities. The frequency dependence of the amplification factor is obtained and quantified in terms of the velocity ratio within and outside the “wormhole domain.”

Categories: Latest papers in fluid mechanics

### Vortex-induced vibration response of a cactus-inspired cylinder near a stationary wall

Physics of Fluids, Volume 33, Issue 7, July 2021.

Vortex-induced vibration (VIV) responses of a cactus-inspired cylinder near a stationary wall are numerically studied, and the effects of the height ratios (Ks/D, Ks is the height) of the cactus-inspired structure and the stationary wall on VIV response are discussed in detail. The VIV response region is usually divided into four sub-regions, namely, the initial branch (region I), the upper branch (region II), the lower branch (region III), and the desynchronization branch (region IV). The Reynolds number at which the maximum vibration amplitude occurs for the cylinder near the stationary wall is lower than that of a free-standing cylinder. The Reynolds number at which the maximum amplitude occurs decreases with an increase in the height ratio of the structure. Due to effects of the stationary wall, the critical reduced velocity at which the vortex phase jump occurs decreases. With an increase in the height ratio of the structure, the critical reduced velocity at which the vortex phase jump occurs gradually decreases. Vortex shedding is seen from the stationary wall, and the vortex moves clockwise. This vortex can weaken vortex shedding from the cylinder. Due to the large-amplitude motion, the vortex shedding from the cylinder is coupled with the stationary wall, which promotes the separation of the wall boundary layer. With an increase in the height ratio of the structure, the absolute value of vortex intensity gradually decreases, and the distance between the vortex-shedding position and the cylinder gradually increases. Therefore, the cactus-inspired structure not only changes the form of the wake vortex, but also changes the strength of the wake vortex.

Vortex-induced vibration (VIV) responses of a cactus-inspired cylinder near a stationary wall are numerically studied, and the effects of the height ratios (Ks/D, Ks is the height) of the cactus-inspired structure and the stationary wall on VIV response are discussed in detail. The VIV response region is usually divided into four sub-regions, namely, the initial branch (region I), the upper branch (region II), the lower branch (region III), and the desynchronization branch (region IV). The Reynolds number at which the maximum vibration amplitude occurs for the cylinder near the stationary wall is lower than that of a free-standing cylinder. The Reynolds number at which the maximum amplitude occurs decreases with an increase in the height ratio of the structure. Due to effects of the stationary wall, the critical reduced velocity at which the vortex phase jump occurs decreases. With an increase in the height ratio of the structure, the critical reduced velocity at which the vortex phase jump occurs gradually decreases. Vortex shedding is seen from the stationary wall, and the vortex moves clockwise. This vortex can weaken vortex shedding from the cylinder. Due to the large-amplitude motion, the vortex shedding from the cylinder is coupled with the stationary wall, which promotes the separation of the wall boundary layer. With an increase in the height ratio of the structure, the absolute value of vortex intensity gradually decreases, and the distance between the vortex-shedding position and the cylinder gradually increases. Therefore, the cactus-inspired structure not only changes the form of the wake vortex, but also changes the strength of the wake vortex.

Categories: Latest papers in fluid mechanics

### Analytic derivation of the inertial range of compressible turbulence

Physics of Fluids, Volume 33, Issue 7, July 2021.

An analytic model for steady state turbulence is employed to obtain the inertial range power spectrum of compressible turbulence. We assume that for homogeneous turbulence, the timescales controlling the energy injected at a given wavenumber from all smaller wavenumbers are equal for each spatial component. However, the longitudinal component energy is diverted into compression, so the rate controlling the energy that is transferred to all larger wavenumbers by the turbulent viscosity is reduced. The resulting inertial range is a power law with an index of −2. Indeed, such power spectra were observed in various astrophysical settings and also in numerical simulations.

An analytic model for steady state turbulence is employed to obtain the inertial range power spectrum of compressible turbulence. We assume that for homogeneous turbulence, the timescales controlling the energy injected at a given wavenumber from all smaller wavenumbers are equal for each spatial component. However, the longitudinal component energy is diverted into compression, so the rate controlling the energy that is transferred to all larger wavenumbers by the turbulent viscosity is reduced. The resulting inertial range is a power law with an index of −2. Indeed, such power spectra were observed in various astrophysical settings and also in numerical simulations.

Categories: Latest papers in fluid mechanics