# 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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### The effect of deformability on the microscale flow behavior of red blood cell suspensions

Physics of Fluids, Volume MNFC2019, Issue 1, October 2019.

Red blood cell (RBC) deformability is important for tissue perfusion and a key determinant of blood rheology. Diseases such as diabetes, sickle cell anemia, and malaria, as well as prolonged storage, may affect the mechanical properties of RBCs altering their hemodynamic behavior and leading to microvascular complications. However, the exact role of RBC deformability on microscale blood flow is not fully understood. In the present study, we extend our previous work on healthy RBC flows in bifurcating microchannels [Sherwood et al., “Viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel,” Biomech. Model. Mechanobiol. 13, 259–273 (2014); Sherwood et al., “Spatial distributions of red blood cells significantly alter local hemodynamics,” PLoS One 9, e100473 (2014); and Kaliviotis et al., “Local viscosity distribution in bifurcating microfluidic blood flows,” Phys. Fluids 30, 030706 (2018)] to quantify the effects of impaired RBC deformability on the velocity and hematocrit distributions in microscale blood flows. Suspensions of healthy and glutaraldehyde hardened RBCs perfused through straight microchannels at various hematocrits and flow rates were imaged, and velocity and hematocrit distributions were determined simultaneously using micro-Particle Image Velocimetry and light transmission methods, respectively. At low feed hematocrits, hardened RBCs were more dispersed compared to healthy ones, consistent with decreased migration of stiffer cells. At high hematocrit, the loss of deformability was found to decrease the bluntness of velocity profiles, implying a reduction in shear thinning behavior. The hematocrit bluntness also decreased with hardening of the cells, implying an inversion of the correlation between velocity and hematocrit bluntness with loss of deformability. The study illustrates the complex interplay of various mechanisms affecting confined RBC suspension flows and the impact of both deformability and feed hematocrit on the resulting microstructure.

Red blood cell (RBC) deformability is important for tissue perfusion and a key determinant of blood rheology. Diseases such as diabetes, sickle cell anemia, and malaria, as well as prolonged storage, may affect the mechanical properties of RBCs altering their hemodynamic behavior and leading to microvascular complications. However, the exact role of RBC deformability on microscale blood flow is not fully understood. In the present study, we extend our previous work on healthy RBC flows in bifurcating microchannels [Sherwood et al., “Viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel,” Biomech. Model. Mechanobiol. 13, 259–273 (2014); Sherwood et al., “Spatial distributions of red blood cells significantly alter local hemodynamics,” PLoS One 9, e100473 (2014); and Kaliviotis et al., “Local viscosity distribution in bifurcating microfluidic blood flows,” Phys. Fluids 30, 030706 (2018)] to quantify the effects of impaired RBC deformability on the velocity and hematocrit distributions in microscale blood flows. Suspensions of healthy and glutaraldehyde hardened RBCs perfused through straight microchannels at various hematocrits and flow rates were imaged, and velocity and hematocrit distributions were determined simultaneously using micro-Particle Image Velocimetry and light transmission methods, respectively. At low feed hematocrits, hardened RBCs were more dispersed compared to healthy ones, consistent with decreased migration of stiffer cells. At high hematocrit, the loss of deformability was found to decrease the bluntness of velocity profiles, implying a reduction in shear thinning behavior. The hematocrit bluntness also decreased with hardening of the cells, implying an inversion of the correlation between velocity and hematocrit bluntness with loss of deformability. The study illustrates the complex interplay of various mechanisms affecting confined RBC suspension flows and the impact of both deformability and feed hematocrit on the resulting microstructure.

Categories: Latest papers in fluid mechanics

### The effect of deformability on the microscale flow behavior of red blood cell suspensions

Physics of Fluids, Volume 31, Issue 9, September 2019.

Red blood cell (RBC) deformability is important for tissue perfusion and a key determinant of blood rheology. Diseases such as diabetes, sickle cell anemia, and malaria, as well as prolonged storage, may affect the mechanical properties of RBCs altering their hemodynamic behavior and leading to microvascular complications. However, the exact role of RBC deformability on microscale blood flow is not fully understood. In the present study, we extend our previous work on healthy RBC flows in bifurcating microchannels [Sherwood et al., “Viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel,” Biomech. Model. Mechanobiol. 13, 259–273 (2014); Sherwood et al., “Spatial distributions of red blood cells significantly alter local hemodynamics,” PLoS One 9, e100473 (2014); and Kaliviotis et al., “Local viscosity distribution in bifurcating microfluidic blood flows,” Phys. Fluids 30, 030706 (2018)] to quantify the effects of impaired RBC deformability on the velocity and hematocrit distributions in microscale blood flows. Suspensions of healthy and glutaraldehyde hardened RBCs perfused through straight microchannels at various hematocrits and flow rates were imaged, and velocity and hematocrit distributions were determined simultaneously using micro-Particle Image Velocimetry and light transmission methods, respectively. At low feed hematocrits, hardened RBCs were more dispersed compared to healthy ones, consistent with decreased migration of stiffer cells. At high hematocrit, the loss of deformability was found to decrease the bluntness of velocity profiles, implying a reduction in shear thinning behavior. The hematocrit bluntness also decreased with hardening of the cells, implying an inversion of the correlation between velocity and hematocrit bluntness with loss of deformability. The study illustrates the complex interplay of various mechanisms affecting confined RBC suspension flows and the impact of both deformability and feed hematocrit on the resulting microstructure.

Red blood cell (RBC) deformability is important for tissue perfusion and a key determinant of blood rheology. Diseases such as diabetes, sickle cell anemia, and malaria, as well as prolonged storage, may affect the mechanical properties of RBCs altering their hemodynamic behavior and leading to microvascular complications. However, the exact role of RBC deformability on microscale blood flow is not fully understood. In the present study, we extend our previous work on healthy RBC flows in bifurcating microchannels [Sherwood et al., “Viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel,” Biomech. Model. Mechanobiol. 13, 259–273 (2014); Sherwood et al., “Spatial distributions of red blood cells significantly alter local hemodynamics,” PLoS One 9, e100473 (2014); and Kaliviotis et al., “Local viscosity distribution in bifurcating microfluidic blood flows,” Phys. Fluids 30, 030706 (2018)] to quantify the effects of impaired RBC deformability on the velocity and hematocrit distributions in microscale blood flows. Suspensions of healthy and glutaraldehyde hardened RBCs perfused through straight microchannels at various hematocrits and flow rates were imaged, and velocity and hematocrit distributions were determined simultaneously using micro-Particle Image Velocimetry and light transmission methods, respectively. At low feed hematocrits, hardened RBCs were more dispersed compared to healthy ones, consistent with decreased migration of stiffer cells. At high hematocrit, the loss of deformability was found to decrease the bluntness of velocity profiles, implying a reduction in shear thinning behavior. The hematocrit bluntness also decreased with hardening of the cells, implying an inversion of the correlation between velocity and hematocrit bluntness with loss of deformability. The study illustrates the complex interplay of various mechanisms affecting confined RBC suspension flows and the impact of both deformability and feed hematocrit on the resulting microstructure.

Categories: Latest papers in fluid mechanics

### Manipulation of jet breakup length and droplet size in axisymmetric flow focusing upon actuation

Physics of Fluids, Volume 31, Issue 9, September 2019.

External sinusoidal actuation is employed in the axisymmetric flow focusing (AFF) for generating uniform droplets in the jetting mode. The perturbations propagating along the meniscus surface can modulate the rupture of the liquid jet. Experiments indicate that the jet breakup length and the resultant droplet size can be precisely controlled in the synchronized regime, which are further confirmed by the scaling law. The finding of this study can help for better understanding of the underlying physics of actuation-aided AFF, and this active droplet generation method with fine robustness, high productivity, and nice process control would be advantageous for various potential applications.

External sinusoidal actuation is employed in the axisymmetric flow focusing (AFF) for generating uniform droplets in the jetting mode. The perturbations propagating along the meniscus surface can modulate the rupture of the liquid jet. Experiments indicate that the jet breakup length and the resultant droplet size can be precisely controlled in the synchronized regime, which are further confirmed by the scaling law. The finding of this study can help for better understanding of the underlying physics of actuation-aided AFF, and this active droplet generation method with fine robustness, high productivity, and nice process control would be advantageous for various potential applications.

Categories: Latest papers in fluid mechanics

### Simulation of blood flow past a distal arteriovenous-graft anastomosis at low Reynolds numbers

Physics of Fluids, Volume 31, Issue 9, September 2019.

Patients with end-stage renal disease are usually treated by hemodialysis while waiting for a kidney transplant. A common device for vascular access is an arteriovenous graft (AVG). However, AVG failure induced by thrombosis has been plaguing dialysis practice for decades. Current studies indicate that the thrombosis is caused by intimal hyperplasia, which is triggered by the abnormal flows and forces [e.g., wall shear stress (WSS)] in the vein after AVG implant. Due to the high level of complexity, in almost all of the existing works of modeling and simulation of the blood-flow vessel-AVG system, the graft and blood vessel are assumed to be rigid and immobile. Very recently, we have found that the compliance of graft and vein can reduce flow disturbances and lower WSS [Z. Bai and L. Zhu, “Three-dimensional simulation of a viscous flow past a compliant model of arteriovenous-graft anastomosis,” Comput. Fluids 181, 403–415 (2019)]. In this paper, we apply the compliant model to investigate possible effects of several dimensionless parameters (AVG graft-vein diameter ratio [math], AVG attaching angle θ, flow Reynolds numbers Re, and native vein speed [math]) on the flow and force fields near the distal AVG anastomosis at low Reynolds numbers (up to several hundreds). Our computational results indicate that the influences of the parameters [math], θ, and Re lie largely on the graft and the influence of [math] lies largely on the vein. In any case, the WSS, wall shear stress gradient, and wall normal stress gradient and their averaged values on the graft are significantly greater than those on the vein.

Patients with end-stage renal disease are usually treated by hemodialysis while waiting for a kidney transplant. A common device for vascular access is an arteriovenous graft (AVG). However, AVG failure induced by thrombosis has been plaguing dialysis practice for decades. Current studies indicate that the thrombosis is caused by intimal hyperplasia, which is triggered by the abnormal flows and forces [e.g., wall shear stress (WSS)] in the vein after AVG implant. Due to the high level of complexity, in almost all of the existing works of modeling and simulation of the blood-flow vessel-AVG system, the graft and blood vessel are assumed to be rigid and immobile. Very recently, we have found that the compliance of graft and vein can reduce flow disturbances and lower WSS [Z. Bai and L. Zhu, “Three-dimensional simulation of a viscous flow past a compliant model of arteriovenous-graft anastomosis,” Comput. Fluids 181, 403–415 (2019)]. In this paper, we apply the compliant model to investigate possible effects of several dimensionless parameters (AVG graft-vein diameter ratio [math], AVG attaching angle θ, flow Reynolds numbers Re, and native vein speed [math]) on the flow and force fields near the distal AVG anastomosis at low Reynolds numbers (up to several hundreds). Our computational results indicate that the influences of the parameters [math], θ, and Re lie largely on the graft and the influence of [math] lies largely on the vein. In any case, the WSS, wall shear stress gradient, and wall normal stress gradient and their averaged values on the graft are significantly greater than those on the vein.

Categories: Latest papers in fluid mechanics

### Comparison of the quasi-steady-state heat transport in phase-change and classical Rayleigh-Bénard convection for a wide range of Stefan number and Rayleigh number

Physics of Fluids, Volume 31, Issue 9, September 2019.

We report the first comparative study of the phase-change Rayleigh–Bénard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height Raf is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters Raf (3.96 × 104 ≤ Raf ≤ 9.26 × 107) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate [math] vs Raf for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nuh increase with the increase in Ste and Raf. There are two distinct RB flow configurations at low Raf independent of Ste. At low and moderate Raf, the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection [math] is always greater than one. However, at higher Raf, the RB convection is turbulent, and [math] can be less than or greater than one depending on the value of Ste. The results may turn out to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.

We report the first comparative study of the phase-change Rayleigh–Bénard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height Raf is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters Raf (3.96 × 104 ≤ Raf ≤ 9.26 × 107) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate [math] vs Raf for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nuh increase with the increase in Ste and Raf. There are two distinct RB flow configurations at low Raf independent of Ste. At low and moderate Raf, the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection [math] is always greater than one. However, at higher Raf, the RB convection is turbulent, and [math] can be less than or greater than one depending on the value of Ste. The results may turn out to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.

Categories: Latest papers in fluid mechanics

### Directionally controlled open channel microfluidics

Physics of Fluids, Volume 31, Issue 9, September 2019.

Free-surface microscale flows have been attracting increasing attention from the research community in recent times, as attributable to their diverse fields of applications ranging from fluid mixing and particle manipulation to biochemical processing on a chip. Traditionally, electrically driven processes governing free surface microfluidics are mostly effective in manipulating fluids having characteristically low values of the electrical conductivity (lower than 0.085 S/m). Biological and biochemical processes, on the other hand, typically aim to manipulate fluids having higher electrical conductivities (>0.1 S/m). To circumvent the inherent limitation of traditional electrokinetic processes in manipulating highly conductive fluids in free surface flows, here we experimentally develop a novel on-chip methodology for the same by exploiting the interaction between an alternating electric current and an induced thermal field. We show that the consequent local gradients in physical properties as well as interfacial tension can be tuned to direct the flow toward a specific location on the interface. The present experimental design opens up a new realm of on-chip process control without necessitating the creation of a geometric confinement. We envisage that this will also open up research avenues on open-channel microfluidics, an area that has vastly remained unexplored.

Free-surface microscale flows have been attracting increasing attention from the research community in recent times, as attributable to their diverse fields of applications ranging from fluid mixing and particle manipulation to biochemical processing on a chip. Traditionally, electrically driven processes governing free surface microfluidics are mostly effective in manipulating fluids having characteristically low values of the electrical conductivity (lower than 0.085 S/m). Biological and biochemical processes, on the other hand, typically aim to manipulate fluids having higher electrical conductivities (>0.1 S/m). To circumvent the inherent limitation of traditional electrokinetic processes in manipulating highly conductive fluids in free surface flows, here we experimentally develop a novel on-chip methodology for the same by exploiting the interaction between an alternating electric current and an induced thermal field. We show that the consequent local gradients in physical properties as well as interfacial tension can be tuned to direct the flow toward a specific location on the interface. The present experimental design opens up a new realm of on-chip process control without necessitating the creation of a geometric confinement. We envisage that this will also open up research avenues on open-channel microfluidics, an area that has vastly remained unexplored.

Categories: Latest papers in fluid mechanics

### On gravity currents of fixed volume that encounter a down-slope or up-slope bottom

Physics of Fluids, Volume 31, Issue 9, September 2019.

We consider a gravity current released from a lock into an ambient fluid of smaller density, that, from the beginning or after some horizontal propagation X1, propagates along an inclined (up- or down-) bottom. The flow (assumed in the inertial-buoyancy regime) is modeled by the shallow-water (SW) equations with a jump condition applied at the nose (front). The behavior of the current is dominated by the slope angle, θ, but is also affected by additional dimensionless parameters: the aspect ratio of the lock x0/h0, the height ratio of the ambient to lock, H/h0, and the distance of the backwall from the beginning of the slope, X1/x0. We show that the stability of the interface, reflected by the value of the bulk Richardson number, Ri, is essential in the interpretation and modeling. In the upslope flow, Ri increases and hence entrainment/mixing effects are unimportant. In the downslope flow, the current first accelerates and Ri decreases; this enhances entrainment and drag, which then decelerate the current. We show that the accelerating-decelerating downstream current is reproduced well by a SW model combined with a simple closure for the entrainment and drag. A comparison of the theoretical results with previously published experimental data for both upslope flow and downslope flow show fair agreement.

We consider a gravity current released from a lock into an ambient fluid of smaller density, that, from the beginning or after some horizontal propagation X1, propagates along an inclined (up- or down-) bottom. The flow (assumed in the inertial-buoyancy regime) is modeled by the shallow-water (SW) equations with a jump condition applied at the nose (front). The behavior of the current is dominated by the slope angle, θ, but is also affected by additional dimensionless parameters: the aspect ratio of the lock x0/h0, the height ratio of the ambient to lock, H/h0, and the distance of the backwall from the beginning of the slope, X1/x0. We show that the stability of the interface, reflected by the value of the bulk Richardson number, Ri, is essential in the interpretation and modeling. In the upslope flow, Ri increases and hence entrainment/mixing effects are unimportant. In the downslope flow, the current first accelerates and Ri decreases; this enhances entrainment and drag, which then decelerate the current. We show that the accelerating-decelerating downstream current is reproduced well by a SW model combined with a simple closure for the entrainment and drag. A comparison of the theoretical results with previously published experimental data for both upslope flow and downslope flow show fair agreement.

Categories: Latest papers in fluid mechanics

### Cahn-Hilliard mobility of fluid-fluid interfaces from molecular dynamics

Physics of Fluids, Volume 31, Issue 9, September 2019.

The Cahn-Hilliard equation is often used to model the temporospatial evolution of multiphase fluid systems including droplets, bubbles, aerosols, and liquid films. This equation requires knowledge of the fluid-fluid interfacial mobility γ, a parameter that can be difficult to obtain experimentally. In this work, a method to obtain γ from nonequilibrium molecular dynamics is presented. γ is obtained for liquid-liquid and liquid-vapor interfaces by perturbing them from their equilibrium phase fraction spatial distributions, using molecular dynamics simulations to observe their relaxation toward equilibrium, and fitting the Cahn-Hilliard model to the transient molecular simulations at each time step. γ is then compared to a different measure of interfacial mobility, the molecular interfacial mobility M. It is found that γ is proportional to the product of M, the interface thickness, and the ratio of thermal energy to interfacial energy.

The Cahn-Hilliard equation is often used to model the temporospatial evolution of multiphase fluid systems including droplets, bubbles, aerosols, and liquid films. This equation requires knowledge of the fluid-fluid interfacial mobility γ, a parameter that can be difficult to obtain experimentally. In this work, a method to obtain γ from nonequilibrium molecular dynamics is presented. γ is obtained for liquid-liquid and liquid-vapor interfaces by perturbing them from their equilibrium phase fraction spatial distributions, using molecular dynamics simulations to observe their relaxation toward equilibrium, and fitting the Cahn-Hilliard model to the transient molecular simulations at each time step. γ is then compared to a different measure of interfacial mobility, the molecular interfacial mobility M. It is found that γ is proportional to the product of M, the interface thickness, and the ratio of thermal energy to interfacial energy.

Categories: Latest papers in fluid mechanics

### Direct methods for solving the Boltzmann equations: Comparisons with direct simulation Monte Carlo and possibilities

Physics of Fluids, Volume DSMC2019, Issue 1, November 2019.

The possibilities of direct methods for solving the Boltzmann equation in comparison with direct simulation Monte Carlo are discussed. The general features of these different methods are considered, in particular, from the point of view of application of different variants of discretization in phase space. The advantages and disadvantages of both approaches are clarified. Comparative solutions of some simple problems are given. An important issue concerns anomalous heat transfer and validation of the effect by calculations based on these two methods. The solutions of the stationary one-dimensional heat transfer problem between two infinite plates with nonclassical nonequilibrium reflection from the surface are obtained; the anomalous heat transfer with a temperature gradient and a heat flux having the same sign is observed. One-dimensional and two-dimensional (in the square domain) problems with nonequilibrium “membranelike” boundary conditions are solved numerically; the anomalous heat transfer for all the considered cases is demonstrated.

The possibilities of direct methods for solving the Boltzmann equation in comparison with direct simulation Monte Carlo are discussed. The general features of these different methods are considered, in particular, from the point of view of application of different variants of discretization in phase space. The advantages and disadvantages of both approaches are clarified. Comparative solutions of some simple problems are given. An important issue concerns anomalous heat transfer and validation of the effect by calculations based on these two methods. The solutions of the stationary one-dimensional heat transfer problem between two infinite plates with nonclassical nonequilibrium reflection from the surface are obtained; the anomalous heat transfer with a temperature gradient and a heat flux having the same sign is observed. One-dimensional and two-dimensional (in the square domain) problems with nonequilibrium “membranelike” boundary conditions are solved numerically; the anomalous heat transfer for all the considered cases is demonstrated.

Categories: Latest papers in fluid mechanics

### Direct methods for solving the Boltzmann equations: Comparisons with direct simulation Monte Carlo and possibilities

Physics of Fluids, Volume 31, Issue 9, September 2019.

The possibilities of direct methods for solving the Boltzmann equation in comparison with direct simulation Monte Carlo are discussed. The general features of these different methods are considered, in particular, from the point of view of application of different variants of discretization in phase space. The advantages and disadvantages of both approaches are clarified. Comparative solutions of some simple problems are given. An important issue concerns anomalous heat transfer and validation of the effect by calculations based on these two methods. The solutions of the stationary one-dimensional heat transfer problem between two infinite plates with nonclassical nonequilibrium reflection from the surface are obtained; the anomalous heat transfer with a temperature gradient and a heat flux having the same sign is observed. One-dimensional and two-dimensional (in the square domain) problems with nonequilibrium “membranelike” boundary conditions are solved numerically; the anomalous heat transfer for all the considered cases is demonstrated.

The possibilities of direct methods for solving the Boltzmann equation in comparison with direct simulation Monte Carlo are discussed. The general features of these different methods are considered, in particular, from the point of view of application of different variants of discretization in phase space. The advantages and disadvantages of both approaches are clarified. Comparative solutions of some simple problems are given. An important issue concerns anomalous heat transfer and validation of the effect by calculations based on these two methods. The solutions of the stationary one-dimensional heat transfer problem between two infinite plates with nonclassical nonequilibrium reflection from the surface are obtained; the anomalous heat transfer with a temperature gradient and a heat flux having the same sign is observed. One-dimensional and two-dimensional (in the square domain) problems with nonequilibrium “membranelike” boundary conditions are solved numerically; the anomalous heat transfer for all the considered cases is demonstrated.

Categories: Latest papers in fluid mechanics

### The first and second laws of thermodynamics

Physics of Fluids, Volume 31, Issue 9, September 2019.

This article summarizes an alternative approach to the formulation of the laws of thermodynamics by making use of the conservation equations of transport phenomena. The principal novel element is the inclusion of the law of conservation of momentum in the derivations. This enables one to make the statement of the first and second laws more complete by including terms describing viscous dissipation of energy.

This article summarizes an alternative approach to the formulation of the laws of thermodynamics by making use of the conservation equations of transport phenomena. The principal novel element is the inclusion of the law of conservation of momentum in the derivations. This enables one to make the statement of the first and second laws more complete by including terms describing viscous dissipation of energy.

Categories: Latest papers in fluid mechanics

### Symmetric and asymmetric coalescence of droplets on a solid surface in the inertia-dominated regime

Physics of Fluids, Volume 31, Issue 9, September 2019.

We present an investigation of symmetric and asymmetric coalescence of two droplets of equal and unequal size on a solid surface in the inertia-dominated regime. Asymmetric coalescence can result due to the coalescence of two unequal-sized droplets or coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. Based on the solution of an analytical model and lattice Boltzmann simulations, we analyze symmetric and asymmetric coalescence of two droplets on a solid surface. The analysis of coalescence of identical droplets show that the liquid bridge height grows with time as [math] for θ = 90° and [math] for θ < 90°, where t* is dimensionless time. Our analysis also yields the same scaling law for the coalescence of two unequal-sized droplets on a surface with homogeneous wettability. We also discuss the coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. We show that the prediction of bridge height with time scales as [math] irrespective of contact angles of droplet with the surface.

We present an investigation of symmetric and asymmetric coalescence of two droplets of equal and unequal size on a solid surface in the inertia-dominated regime. Asymmetric coalescence can result due to the coalescence of two unequal-sized droplets or coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. Based on the solution of an analytical model and lattice Boltzmann simulations, we analyze symmetric and asymmetric coalescence of two droplets on a solid surface. The analysis of coalescence of identical droplets show that the liquid bridge height grows with time as [math] for θ = 90° and [math] for θ < 90°, where t* is dimensionless time. Our analysis also yields the same scaling law for the coalescence of two unequal-sized droplets on a surface with homogeneous wettability. We also discuss the coalescence of two droplets having different contact angles with the surface due to a step gradient in wettability. We show that the prediction of bridge height with time scales as [math] irrespective of contact angles of droplet with the surface.

Categories: Latest papers in fluid mechanics

### Surface rheological measurements of isolated food foam systems

Physics of Fluids, Volume 31, Issue 9, September 2019.

Liquid foams represent a key component to a vast range of food industry products, from ice creams to the crema on coffee. Longevity of these foams is a highly desirable attribute; however, in order for foam stability to be effectively controlled, a better understanding of the interdependence of the bulk liquid and air-liquid interfacial rheologies is required. This study follows an increasing trend in experimental investigations made of isolated foam structures at the microscale, where the bulk and surface dynamics of a single foam liquid channel can be accurately assessed. Isolated foam channels with adjoining nodes were studied for aqueous solutions of four food grade surfactants. Existing observations of distortions to sodium dodecyl sulphate channel geometries were confirmed for solutions of Tween 20 (T20) and Tween 80 (T80) and were well described by the theory presented here. Moreover, previously unseen distortions to liquid channels were observed for polymeric surfactant systems (hydroxypropyl methylcellulose and hydrolyzed pea protein blend), which were proposed to result from their high surface viscosities. The apparent surface viscosities, μs, of surfactants tested here ranged from high (10 g/s < μs < 10−3 g/s) for polymeric surfactants to very low (10−10 g/s < μs < 10−8 g/s) for Tweens, clearly demarking the regimes of viscous and inertial dominant flows, respectively. It is recommended that further work seeks to investigate the finding of a strong correlation between μs and channel surface tension, γ, for soluble surfactant systems, which could explain the apparent non-Newtonian values of μs that were consistently measured here.

Liquid foams represent a key component to a vast range of food industry products, from ice creams to the crema on coffee. Longevity of these foams is a highly desirable attribute; however, in order for foam stability to be effectively controlled, a better understanding of the interdependence of the bulk liquid and air-liquid interfacial rheologies is required. This study follows an increasing trend in experimental investigations made of isolated foam structures at the microscale, where the bulk and surface dynamics of a single foam liquid channel can be accurately assessed. Isolated foam channels with adjoining nodes were studied for aqueous solutions of four food grade surfactants. Existing observations of distortions to sodium dodecyl sulphate channel geometries were confirmed for solutions of Tween 20 (T20) and Tween 80 (T80) and were well described by the theory presented here. Moreover, previously unseen distortions to liquid channels were observed for polymeric surfactant systems (hydroxypropyl methylcellulose and hydrolyzed pea protein blend), which were proposed to result from their high surface viscosities. The apparent surface viscosities, μs, of surfactants tested here ranged from high (10 g/s < μs < 10−3 g/s) for polymeric surfactants to very low (10−10 g/s < μs < 10−8 g/s) for Tweens, clearly demarking the regimes of viscous and inertial dominant flows, respectively. It is recommended that further work seeks to investigate the finding of a strong correlation between μs and channel surface tension, γ, for soluble surfactant systems, which could explain the apparent non-Newtonian values of μs that were consistently measured here.

Categories: Latest papers in fluid mechanics

### Homogenized model with memory for two-phase compressible flow in double-porosity media

Physics of Fluids, Volume 31, Issue 9, September 2019.

A completely averaged model of two-phase flow of compressible fluids in a medium with double porosity is developed. The variational asymptotic two-scale averaging method with splitting the nonlocality and nonlinearity is presented. Several mechanisms of delay are detected, as the nonequilibrium capillary redistribution of phases, pressure field relaxation caused by the compressibility, and the cross effects of fluid extrusion from pores due to rock compaction and fluid expansion. A generalized nonequilibrium capillary equation is obtained. All characteristic times of delay are explicitly defined as functions of saturation.

A completely averaged model of two-phase flow of compressible fluids in a medium with double porosity is developed. The variational asymptotic two-scale averaging method with splitting the nonlocality and nonlinearity is presented. Several mechanisms of delay are detected, as the nonequilibrium capillary redistribution of phases, pressure field relaxation caused by the compressibility, and the cross effects of fluid extrusion from pores due to rock compaction and fluid expansion. A generalized nonequilibrium capillary equation is obtained. All characteristic times of delay are explicitly defined as functions of saturation.

Categories: Latest papers in fluid mechanics

### Bifurcations and pattern evolutions of thermo-solutocapillary flow in rotating cylinder with a top disk

Physics of Fluids, Volume 31, Issue 9, September 2019.

The characteristics of thermosolutocapillary flow bifurcations and pattern evolutions of binary fluid in a rotating cylinder with a top disk on the free surface are investigated through three-dimensional numerical simulations. The mixture of silicon-germanium is employed as the working fluid. For the special case of the capillary ratio equal to minus one, the total thermo and solutocapillary forces are balanced. Once rotation is introduced, the balance among the driving forces is broken, and a wide variety of flow structures are presented as meridional circulations rolling in different directions. When a threshold value of the thermocapillary Reynolds number is exceeded, the stability of capillary flow is destroyed. The two-dimensional steady flow transits to the three-dimensional oscillatory state. The critical conditions for flow bifurcations are explored, and the pattern transitions are mapped. The rotation of the cylinder can suppress the flow instabilities effectively. When the disk counter-rotates with the cylinder, the critical value for the formation of instabilities increases first and then decreases. For the oscillatory flow, various patterns appear with different combinations of the thermocapillary Reynolds number, disk, and/or pool rotation rate. Without rotation, the surface concentration pattern is shown as rosebudlike wave holding still in time but oscillating in space. With the increasing disk rotation rate, the surface pattern transits from hydrosolutal waves to spiral waves, rotating waves, and superimposition of rotating and annular waves propagating in the radial direction. For counter-rotation of the disk and cylinder, a new pattern with coexistence of hydrosolutal and spiral waves traveling in opposite directions is observed.

The characteristics of thermosolutocapillary flow bifurcations and pattern evolutions of binary fluid in a rotating cylinder with a top disk on the free surface are investigated through three-dimensional numerical simulations. The mixture of silicon-germanium is employed as the working fluid. For the special case of the capillary ratio equal to minus one, the total thermo and solutocapillary forces are balanced. Once rotation is introduced, the balance among the driving forces is broken, and a wide variety of flow structures are presented as meridional circulations rolling in different directions. When a threshold value of the thermocapillary Reynolds number is exceeded, the stability of capillary flow is destroyed. The two-dimensional steady flow transits to the three-dimensional oscillatory state. The critical conditions for flow bifurcations are explored, and the pattern transitions are mapped. The rotation of the cylinder can suppress the flow instabilities effectively. When the disk counter-rotates with the cylinder, the critical value for the formation of instabilities increases first and then decreases. For the oscillatory flow, various patterns appear with different combinations of the thermocapillary Reynolds number, disk, and/or pool rotation rate. Without rotation, the surface concentration pattern is shown as rosebudlike wave holding still in time but oscillating in space. With the increasing disk rotation rate, the surface pattern transits from hydrosolutal waves to spiral waves, rotating waves, and superimposition of rotating and annular waves propagating in the radial direction. For counter-rotation of the disk and cylinder, a new pattern with coexistence of hydrosolutal and spiral waves traveling in opposite directions is observed.

Categories: Latest papers in fluid mechanics

### Significance of non-Oberbeck-Boussinesq effects augmented by power-law rheology in natural convection studies around fins

Physics of Fluids, Volume 31, Issue 9, September 2019.

The augmentation and diminution of non-Oberbeck-Boussinesq (NOB) effects due to power-law rheology cause significant changes in the results and associated implications of natural convection studies. This study focuses on the combined effect of spatial arrangement with NOB and power-law effects. Non-intuitive changes in heat transfer trends are caused by the additional effect on the shear rate distribution due to spatial arrangement of objects, represented here by an array of fins. An order of magnitude analysis was used to derive Oberbeck-Boussinesq type equations for a class of power-law fluids with all properties considered as linear functions of temperature and pressure. Significant temperature dependent properties were identified, and an explicit criterion to neglect viscous dissipation for power-law fluids in pure natural convection was derived. The identified temperature dependencies were incorporated into NOB equations and solved numerically to investigate their effect on flow field and heat transfer trends. Shear thinning significantly augmented (more than doubled) the accelerating NOB effect, while shear thickening diminished (nearly halved) it. The tendency of power-law rheology to augment or diminish NOB effects was demonstrated to considerably increase the sensitivity of results to temperature dependent properties, over and above that for the Newtonian case. Investigations to note their practical implications revealed that optimization results without NOB effects could be quite misleading for the fin array problem, due to the differing cumulative extents of augmentation. Additionally, correlation studies may be inaccurate as the nature of trends was changed fundamentally due to NOB augmentation.

The augmentation and diminution of non-Oberbeck-Boussinesq (NOB) effects due to power-law rheology cause significant changes in the results and associated implications of natural convection studies. This study focuses on the combined effect of spatial arrangement with NOB and power-law effects. Non-intuitive changes in heat transfer trends are caused by the additional effect on the shear rate distribution due to spatial arrangement of objects, represented here by an array of fins. An order of magnitude analysis was used to derive Oberbeck-Boussinesq type equations for a class of power-law fluids with all properties considered as linear functions of temperature and pressure. Significant temperature dependent properties were identified, and an explicit criterion to neglect viscous dissipation for power-law fluids in pure natural convection was derived. The identified temperature dependencies were incorporated into NOB equations and solved numerically to investigate their effect on flow field and heat transfer trends. Shear thinning significantly augmented (more than doubled) the accelerating NOB effect, while shear thickening diminished (nearly halved) it. The tendency of power-law rheology to augment or diminish NOB effects was demonstrated to considerably increase the sensitivity of results to temperature dependent properties, over and above that for the Newtonian case. Investigations to note their practical implications revealed that optimization results without NOB effects could be quite misleading for the fin array problem, due to the differing cumulative extents of augmentation. Additionally, correlation studies may be inaccurate as the nature of trends was changed fundamentally due to NOB augmentation.

Categories: Latest papers in fluid mechanics

### Holmboe instability beyond the Boussinesq approximation revisited

Physics of Fluids, Volume 31, Issue 9, September 2019.

With no use of the Boussinesq approximation, the Holmboe instability is studied in sharply stratified shear flows with arbitrary monotonic and bounded velocity profiles without inflection points, including a piecewise-linear one. Particular attention is given to the separation and analysis of contributions to instability made by the wave–wave and wave–particle interactions which are the main physical mechanisms responsible for the loss of stability. It is shown that both mechanisms are equally important for understanding the instability properties and therefore should be taken into consideration simultaneously.

With no use of the Boussinesq approximation, the Holmboe instability is studied in sharply stratified shear flows with arbitrary monotonic and bounded velocity profiles without inflection points, including a piecewise-linear one. Particular attention is given to the separation and analysis of contributions to instability made by the wave–wave and wave–particle interactions which are the main physical mechanisms responsible for the loss of stability. It is shown that both mechanisms are equally important for understanding the instability properties and therefore should be taken into consideration simultaneously.

Categories: Latest papers in fluid mechanics

### Three-dimensional flow simulations for polymer extrudate swell out of slit dies from low to high aspect ratios

Physics of Fluids, Volume 31, Issue 9, September 2019.

The impact of the slit die geometry and the polymer melt flow characteristics on the extrudate swell behavior, which is a key extrusion operating parameter, is highlighted. Three-dimensional (3D) numerical simulations based on the finite element method are compared with their conventional two-dimensional (2D) counterparts at the same apparent shear rates using ANSYS Polyflow software. The rheological behavior is described by the differential multimode Phan-Thien-Tanner constitutive model, with polypropylene as a reference. It is shown that increasing the aspect ratio of the die geometry (width/height ratio variation from 1 to 20) contributes to a significant change in the 3D extrudate deformation (relative changes of 10% in several directions; absolute changes up to 30%) and delays the equilibrium axial position (up to a factor 10). High aspect ratios induce a switch to contract flow (swell ratio <1) for the edge height swell. The 3D extrudate swell strongly deviates from the 2D simplified case due to the die effect near the wall, even for higher aspect ratios. Also a different relation with the material parameters is recorded. The initially large swell behavior is followed by a small shrinkage flow in the middle height direction which cannot be captured by the 2D counterpart. The findings are supported by a comprehensive analysis of the velocity and stress fields in and out of the slit dies.

The impact of the slit die geometry and the polymer melt flow characteristics on the extrudate swell behavior, which is a key extrusion operating parameter, is highlighted. Three-dimensional (3D) numerical simulations based on the finite element method are compared with their conventional two-dimensional (2D) counterparts at the same apparent shear rates using ANSYS Polyflow software. The rheological behavior is described by the differential multimode Phan-Thien-Tanner constitutive model, with polypropylene as a reference. It is shown that increasing the aspect ratio of the die geometry (width/height ratio variation from 1 to 20) contributes to a significant change in the 3D extrudate deformation (relative changes of 10% in several directions; absolute changes up to 30%) and delays the equilibrium axial position (up to a factor 10). High aspect ratios induce a switch to contract flow (swell ratio <1) for the edge height swell. The 3D extrudate swell strongly deviates from the 2D simplified case due to the die effect near the wall, even for higher aspect ratios. Also a different relation with the material parameters is recorded. The initially large swell behavior is followed by a small shrinkage flow in the middle height direction which cannot be captured by the 2D counterpart. The findings are supported by a comprehensive analysis of the velocity and stress fields in and out of the slit dies.

Categories: Latest papers in fluid mechanics

### Front dynamics in exchange flow of two immiscible iso-viscous fluids in two-dimensional straight and curved plane channels

Physics of Fluids, Volume 31, Issue 9, September 2019.

Exchange flow of two immiscible fluids at a low Atwood number in a straight and curved plane channel is considered in this analytical study. The fluids are considered immiscible, but practically, the results can be applied to miscible fluids for short times and in nearly horizontal channels where mixing is negligible due to strong segregation. The exchange flow and displacement flow in pipes at different inclinations with respect to vertical have been extensively studied and have many applications in industry or environmental settings. For the case of plane two-dimensional channels, however, because of the simpler geometry, it is more convenient to understand the physics of the problem and formulate the physical phenomena mathematically. An equation has been derived that describes the transient front velocity in exchange flow in a straight plane channel. The steady state front velocity in straight channels is estimated. The exchange flow in curved channels demonstrates an unstable front or a separated trail because of the curvature of the path. In the case of curved channels, some of the general behavior of the interface is predicted and validated against some experimental observations in curved pipes but quantitative analysis of the interface and the flow requires more advanced mathematical formulation and more detailed experiments for validation.

Exchange flow of two immiscible fluids at a low Atwood number in a straight and curved plane channel is considered in this analytical study. The fluids are considered immiscible, but practically, the results can be applied to miscible fluids for short times and in nearly horizontal channels where mixing is negligible due to strong segregation. The exchange flow and displacement flow in pipes at different inclinations with respect to vertical have been extensively studied and have many applications in industry or environmental settings. For the case of plane two-dimensional channels, however, because of the simpler geometry, it is more convenient to understand the physics of the problem and formulate the physical phenomena mathematically. An equation has been derived that describes the transient front velocity in exchange flow in a straight plane channel. The steady state front velocity in straight channels is estimated. The exchange flow in curved channels demonstrates an unstable front or a separated trail because of the curvature of the path. In the case of curved channels, some of the general behavior of the interface is predicted and validated against some experimental observations in curved pipes but quantitative analysis of the interface and the flow requires more advanced mathematical formulation and more detailed experiments for validation.

Categories: Latest papers in fluid mechanics

### Spectral energy transfer in a viscoelastic homogeneous isotropic turbulence

Physics of Fluids, Volume 31, Issue 9, September 2019.

Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9. Viscoelastic effects are described by the finite extensibility nonlinear elastic-Peterlin model. It is found that the presence of the polymer additives can nontrivially modify the kinetic energy dynamics by suppressing the rate of the kinetic energy transfer and altering the locality nature of this energy transfer. Spectral representation of the elastic field revealed that the elastic energy is also transferred locally through different elastic degrees of freedom via a dominantly forward energy cascade. Moreover, the elastic energy spectrum can display a power-law behavior, k−m, with the possibility of different scaling exponents depending on the Wi number. It is observed that the energy exchange between macro- and microstructures is a two-directional process: there is a dominant energy transfer from the solvent large-scale structures to the polymers alongside a weak energy transfer from polymers to the solvent small-scale structures. This energy exchange consists of three different fluxes. Two of these fluxes equally transfer a small fraction of the kinetic energy into the mean and fluctuating elastic fields. However, the main energy conversion takes place between fluctuating kinetic and elastic fields through a completely nonlocal energy transfer process.

Energy dynamics in elastoinertial turbulence is investigated by performing different direct numerical simulations of stationary, homogeneous isotropic turbulence for the range of Weissenberg numbers 0 ≤ Wi ≤ 9. Viscoelastic effects are described by the finite extensibility nonlinear elastic-Peterlin model. It is found that the presence of the polymer additives can nontrivially modify the kinetic energy dynamics by suppressing the rate of the kinetic energy transfer and altering the locality nature of this energy transfer. Spectral representation of the elastic field revealed that the elastic energy is also transferred locally through different elastic degrees of freedom via a dominantly forward energy cascade. Moreover, the elastic energy spectrum can display a power-law behavior, k−m, with the possibility of different scaling exponents depending on the Wi number. It is observed that the energy exchange between macro- and microstructures is a two-directional process: there is a dominant energy transfer from the solvent large-scale structures to the polymers alongside a weak energy transfer from polymers to the solvent small-scale structures. This energy exchange consists of three different fluxes. Two of these fluxes equally transfer a small fraction of the kinetic energy into the mean and fluctuating elastic fields. However, the main energy conversion takes place between fluctuating kinetic and elastic fields through a completely nonlocal energy transfer process.

Categories: Latest papers in fluid mechanics