The yield stress and shear thinning properties of mucus are identified as critical for ciliary coordination and mucus transport in human airways. We use here numerical simulations to explore the hydrodynamic coupling of cilia and mucus with these two properties using the Herschel–Bulkley model, in a lattice Boltzmann solver for the fluid flow. Three mucus flow regimes, i.e. a poorly organized regime, a swirly regime, and a fully unidirectional regime, are observed and analysed by parametric studies. We systematically investigate the effects of ciliary density, interaction length, Bingham number and flow index on the mucus flow regime formation. The underlying mechanism of the regime formation is analysed in detail by examining the variation of two physical quantities (polarization and integral length) and the evolution of the flow velocity, viscosity and shear-rate fields. Mucus viscosity is found to be the dominant parameter influencing the regime formation when enhancing the yield stress and shear thinning properties. The present model is able to reproduce the solid body rotation observed in experiments (Loiseau et al., Nat. Phys., vol. 16, 2020, pp. 1158–1164). A more precise prediction can be achieved by incorporating non-Newtonian properties into the modelling of mucus as proposed by Gsell et al. (Sci. Rep., vol. 10, 2020, 8405).
{"title":"Hydrodynamic coupling of a cilia–mucus system in Herschel–Bulkley flows","authors":"Q. Mao, U. D'Ortona, J. Favier","doi":"10.1017/jfm.2024.600","DOIUrl":"https://doi.org/10.1017/jfm.2024.600","url":null,"abstract":"The yield stress and shear thinning properties of mucus are identified as critical for ciliary coordination and mucus transport in human airways. We use here numerical simulations to explore the hydrodynamic coupling of cilia and mucus with these two properties using the Herschel–Bulkley model, in a lattice Boltzmann solver for the fluid flow. Three mucus flow regimes, i.e. a poorly organized regime, a swirly regime, and a fully unidirectional regime, are observed and analysed by parametric studies. We systematically investigate the effects of ciliary density, interaction length, Bingham number and flow index on the mucus flow regime formation. The underlying mechanism of the regime formation is analysed in detail by examining the variation of two physical quantities (polarization and integral length) and the evolution of the flow velocity, viscosity and shear-rate fields. Mucus viscosity is found to be the dominant parameter influencing the regime formation when enhancing the yield stress and shear thinning properties. The present model is able to reproduce the solid body rotation observed in experiments (Loiseau <jats:italic>et al.</jats:italic>, <jats:italic>Nat. Phys.</jats:italic>, vol. 16, 2020, pp. 1158–1164). A more precise prediction can be achieved by incorporating non-Newtonian properties into the modelling of mucus as proposed by Gsell <jats:italic>et al.</jats:italic> (<jats:italic>Sci. Rep.</jats:italic>, vol. 10, 2020, 8405).","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"18 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peter Lewin-Jones, Duncan A. Lockerby, James E. Sprittles
Whether colliding drops will merge with or bounce off each other is critical to numerous processes, and the physics involved is notoriously complex. In particular, experiments show that both sufficiently slow and fast head-on drop collisions lead to merging, but that there is often an intermediate regime in which bouncing is observed; these transitions in behaviour were recently discovered to be surprisingly sensitive to the radius of the drops and the ambient gas pressure. We show here that these transitions between bouncing and merging are governed by nanoscale phenomena; namely, gas-kinetic and disjoining pressure effects. To capture these crucial effects, a novel, open-source computational model is developed for the simulation of colliding drops. The model uses a hybrid approach, based on solving the Navier–Stokes equations in the drop with a lubrication approach for the unconventional physics of the gas film. Our simulations show remarkably good agreement with experiments of head-on collisions and also provide new experimentally verifiable predictions.
{"title":"Collision of liquid drops: bounce or merge?","authors":"Peter Lewin-Jones, Duncan A. Lockerby, James E. Sprittles","doi":"10.1017/jfm.2024.722","DOIUrl":"https://doi.org/10.1017/jfm.2024.722","url":null,"abstract":"Whether colliding drops will merge with or bounce off each other is critical to numerous processes, and the physics involved is notoriously complex. In particular, experiments show that both sufficiently slow and fast head-on drop collisions lead to merging, but that there is often an intermediate regime in which bouncing is observed; these transitions in behaviour were recently discovered to be surprisingly sensitive to the radius of the drops and the ambient gas pressure. We show here that these transitions between bouncing and merging are governed by nanoscale phenomena; namely, gas-kinetic and disjoining pressure effects. To capture these crucial effects, a novel, open-source computational model is developed for the simulation of colliding drops. The model uses a hybrid approach, based on solving the Navier–Stokes equations in the drop with a lubrication approach for the unconventional physics of the gas film. Our simulations show remarkably good agreement with experiments of head-on collisions and also provide new experimentally verifiable predictions.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"2 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ingu Lee, Jaehee Chang, Kiyoung Kim, Haecheon Choi
A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline1.png"/> <jats:tex-math>$Re_{bulk}= u_{bulk} D/nu _w = 5300$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline2.png"/> <jats:tex-math>$Re_{bub}= (langle u_{bub}rangle - u_{bulk}) d_{eq}/nu _w = 533unicode{x2013}1000$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, respectively, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline3.png"/> <jats:tex-math>$u_{bulk}$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the water bulk velocity, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline4.png"/> <jats:tex-math>$langle u_{bub}rangle$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the overall bubble mean velocity, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline5.png"/> <jats:tex-math>$D$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the pipe diameter and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline6.png"/> <jats:tex-math>$nu _w$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline7.png"/> <jats:tex-math>$bar {psi }(r)^{0.4}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024006529_inline8.png"/> <jats:tex-math>$bar {psi } (r)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all
{"title":"A numerical study on the turbulence characteristics in an air–water upward bubbly pipe flow","authors":"Ingu Lee, Jaehee Chang, Kiyoung Kim, Haecheon Choi","doi":"10.1017/jfm.2024.652","DOIUrl":"https://doi.org/10.1017/jfm.2024.652","url":null,"abstract":"A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline1.png\"/> <jats:tex-math>$Re_{bulk}= u_{bulk} D/nu _w = 5300$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline2.png\"/> <jats:tex-math>$Re_{bub}= (langle u_{bub}rangle - u_{bulk}) d_{eq}/nu _w = 533unicode{x2013}1000$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, respectively, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline3.png\"/> <jats:tex-math>$u_{bulk}$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the water bulk velocity, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline4.png\"/> <jats:tex-math>$langle u_{bub}rangle$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the overall bubble mean velocity, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline5.png\"/> <jats:tex-math>$D$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the pipe diameter and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline6.png\"/> <jats:tex-math>$nu _w$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline7.png\"/> <jats:tex-math>$bar {psi }(r)^{0.4}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024006529_inline8.png\"/> <jats:tex-math>$bar {psi } (r)$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all ","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"8 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Validating the theoretical work on Rayleigh–Taylor instability (RTI) through experiments with an exceptionally clean and well-characterized initial condition has been a long-standing challenge. Experiments were conducted to study the three-dimensional RTI of an SF$_6$–air interface at moderate Atwood numbers. A novel soap film technique was developed to create a discontinuous gaseous interface with controllable initial conditions. Spectrum analysis revealed that the initial perturbation of the soap film interface is half the size of an entire single-mode perturbation. The correlation between the initial interface perturbation and Atwood numbers was determined. Due to the steep and highly curved feature of the initial soap film interface, the early-time evolution of RTI exhibits significant nonlinearity. In the quasi-steady regime, various potential flow models accurately predict the late-time bubble velocities by considering the channel width as the perturbation wavelength. Differently, the late-time spike velocities are described by these potential flow models using the wavelength of the entire single-mode perturbation. These findings indicate that the bubble evolution is influenced primarily by the spatial constraint imposed by walls, while the spike evolution is influenced mainly by the initial curvature of the spike tip. Consequently, a recent potential flow model was adopted to describe the time-varying amplitude growth induced by RTI. Furthermore, the self-similar growth factors for bubbles and spikes were determined from experiments and compared with existing studies, revealing that a large amplitude in the initial soap film interface promotes the spike development.
通过实验验证雷利-泰勒不稳定性（RTI）方面的理论研究工作，并使用异常干净和特征明确的初始条件，一直是一个长期存在的挑战。实验研究了中等阿特伍德数下 SF $_6$ - 空气界面的三维 RTI。研究人员开发了一种新颖的肥皂膜技术，以创建具有可控初始条件的不连续气态界面。频谱分析表明，皂膜界面的初始扰动是整个单模扰动的一半。确定了初始界面扰动与阿特伍德数之间的相关性。由于初始皂膜界面的陡峭和高度弯曲特征，RTI 的早期时间演化表现出明显的非线性。在准稳定体系中，各种势流模型通过将通道宽度视为扰动波长，准确预测了后期的气泡速度。不同的是，这些势流模型使用整个单模扰动的波长来描述晚期尖峰速度。这些研究结果表明，气泡的演变主要受到壁的空间限制的影响，而尖峰的演变主要受到尖峰顶端初始曲率的影响。因此，采用了最新的势流模型来描述 RTI 诱导的时变振幅增长。此外，实验还确定了气泡和尖峰的自相似生长因子，并与现有研究进行了比较，结果表明初始皂膜界面的大振幅会促进尖峰的发展。
{"title":"Experimental investigation of three-dimensional Rayleigh–Taylor instability of a gaseous interface","authors":"Yu Liang, Ahmed Alkindi, Khalid Alzeyoudi, Lili Liu, Mohamed Ali, Nader Masmoudi","doi":"10.1017/jfm.2024.754","DOIUrl":"https://doi.org/10.1017/jfm.2024.754","url":null,"abstract":"Validating the theoretical work on Rayleigh–Taylor instability (RTI) through experiments with an exceptionally clean and well-characterized initial condition has been a long-standing challenge. Experiments were conducted to study the three-dimensional RTI of an SF<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007547_inline1.png\"/> <jats:tex-math>$_6$</jats:tex-math> </jats:alternatives> </jats:inline-formula>–air interface at moderate Atwood numbers. A novel soap film technique was developed to create a discontinuous gaseous interface with controllable initial conditions. Spectrum analysis revealed that the initial perturbation of the soap film interface is half the size of an entire single-mode perturbation. The correlation between the initial interface perturbation and Atwood numbers was determined. Due to the steep and highly curved feature of the initial soap film interface, the early-time evolution of RTI exhibits significant nonlinearity. In the quasi-steady regime, various potential flow models accurately predict the late-time bubble velocities by considering the channel width as the perturbation wavelength. Differently, the late-time spike velocities are described by these potential flow models using the wavelength of the entire single-mode perturbation. These findings indicate that the bubble evolution is influenced primarily by the spatial constraint imposed by walls, while the spike evolution is influenced mainly by the initial curvature of the spike tip. Consequently, a recent potential flow model was adopted to describe the time-varying amplitude growth induced by RTI. Furthermore, the self-similar growth factors for bubbles and spikes were determined from experiments and compared with existing studies, revealing that a large amplitude in the initial soap film interface promotes the spike development.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"8 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Understanding the propulsion of a swimmer in a large group of individuals holds the key to unravelling the intriguing dynamics of active matter collective motion. Here, we develop a two-dimensional (2-D) self-assembled rotor, powered by bacterial flagella. At a water–air interface, the average direction of rotation of a rotor is fixed. When the chiral rotor is put into a 2-D bacterial suspension, we examine the average and fluctuation of the angular velocity of the rotor. Remarkably, the average angular velocity of a rotor is found to increase up to 3 times when the density of surrounding bacterial suspension increases and the increase is nonlinear. In a dense suspension of bacteria, the existence of a rotor disrupts vortices in the surrounding active turbulence, and the acceleration of the rotor is independent of the activity level of the surrounding free bacteria. The nonlinear acceleration thus results from hydrodynamic interaction with surrounding crowdedness that can be quantitatively explained by hydrodynamic simulation. The simultaneity between the acceleration of rotor and free bacteria in active turbulence suggests that crowding-induced acceleration may promote the onset of instability. The result will inspire new active-matter-based microfluidic devices with improved transport properties.
{"title":"Crowding accelerates the rotation of a bacterial rotor","authors":"Haoxin Huang, Bokai Zhang, Shuo Guo","doi":"10.1017/jfm.2024.725","DOIUrl":"https://doi.org/10.1017/jfm.2024.725","url":null,"abstract":"Understanding the propulsion of a swimmer in a large group of individuals holds the key to unravelling the intriguing dynamics of active matter collective motion. Here, we develop a two-dimensional (2-D) self-assembled rotor, powered by bacterial flagella. At a water–air interface, the average direction of rotation of a rotor is fixed. When the chiral rotor is put into a 2-D bacterial suspension, we examine the average and fluctuation of the angular velocity of the rotor. Remarkably, the average angular velocity of a rotor is found to increase up to 3 times when the density of surrounding bacterial suspension increases and the increase is nonlinear. In a dense suspension of bacteria, the existence of a rotor disrupts vortices in the surrounding active turbulence, and the acceleration of the rotor is independent of the activity level of the surrounding free bacteria. The nonlinear acceleration thus results from hydrodynamic interaction with surrounding crowdedness that can be quantitatively explained by hydrodynamic simulation. The simultaneity between the acceleration of rotor and free bacteria in active turbulence suggests that crowding-induced acceleration may promote the onset of instability. The result will inspire new active-matter-based microfluidic devices with improved transport properties.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"50 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dynamics of a single highly elastic fibre settling under gravity in a very viscous fluid is studied numerically. We employ the bead model and multipole expansion of the Stokes equations, corrected for lubrication that is implemented in the precise Hydromultipole numerical codes. Four attracting regular dynamical modes of highly elastic fibres are found: two stationary shapes (one translating and the other rotating and translating), and two periodic oscillations around such shapes. The phase diagram of these modes is presented. It illustrates that the existence of each mode depends not only on the elasto-gravitation number but also on the fibre aspect ratio. Characteristic time scales, fibre deformation patterns and motion in the different modes are determined.
{"title":"Attracting dynamical modes of highly elastic fibres settling under gravity in a viscous fluid","authors":"Yevgen Melikhov, Maria L. Ekiel-Jeżewska","doi":"10.1017/jfm.2024.729","DOIUrl":"https://doi.org/10.1017/jfm.2024.729","url":null,"abstract":"The dynamics of a single highly elastic fibre settling under gravity in a very viscous fluid is studied numerically. We employ the bead model and multipole expansion of the Stokes equations, corrected for lubrication that is implemented in the precise <jats:sc>Hydromultipole</jats:sc> numerical codes. Four attracting regular dynamical modes of highly elastic fibres are found: two stationary shapes (one translating and the other rotating and translating), and two periodic oscillations around such shapes. The phase diagram of these modes is presented. It illustrates that the existence of each mode depends not only on the elasto-gravitation number but also on the fibre aspect ratio. Characteristic time scales, fibre deformation patterns and motion in the different modes are determined.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ali Arslan, Giovanni Fantuzzi, John Craske, Andrew Wynn
We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline1.png"/> <jats:tex-math>$smash { smash {{langle {delta T} rangle _h}} } geq sigma R^{-1/3} - mu$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline2.png"/> <jats:tex-math>$smash { smash {{langle {delta T} rangle _h}} }$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the average temperature difference between the bottom and top plates, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline3.png"/> <jats:tex-math>$R$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a ‘flux’ Rayleigh number and the constants <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline4.png"/> <jats:tex-math>$sigma,mu >0$</jats:tex-math> </jats:alternatives> </jats:inline-formula> depend on the geometric properties of the internal heating. This result implies that mean downward conduction (for which <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline5.png"/> <jats:tex-math>$smash { smash {{langle {delta T} rangle _h}} }< 0$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) is impossible for a range of Rayleigh numbers smaller than a critical value <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline6.png"/> <jats:tex-math>$R_0:=(sigma /mu )^{3}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The bound demonstrates that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline7.png"/> <jats:tex-math>$R_0$</jats:tex-math> </jats:alternatives> </jats:inline-formula> depends on the heating distribution and can be made arbitrarily large by concentrating the heating near the bottom plate. However, for any given fixed heating profile of the class we consider, the corresponding value of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024005901_inline8.png"/> <jats:tex-math>$R_0$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is always finite. This points to a fundamental differenc
{"title":"Internal heating profiles for which downward conduction is impossible","authors":"Ali Arslan, Giovanni Fantuzzi, John Craske, Andrew Wynn","doi":"10.1017/jfm.2024.590","DOIUrl":"https://doi.org/10.1017/jfm.2024.590","url":null,"abstract":"We consider an internally heated fluid between parallel plates with fixed thermal fluxes. For a large class of heat sources that vary in the direction of gravity, we prove that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline1.png\"/> <jats:tex-math>$smash { smash {{langle {delta T} rangle _h}} } geq sigma R^{-1/3} - mu$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline2.png\"/> <jats:tex-math>$smash { smash {{langle {delta T} rangle _h}} }$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is the average temperature difference between the bottom and top plates, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline3.png\"/> <jats:tex-math>$R$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is a ‘flux’ Rayleigh number and the constants <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline4.png\"/> <jats:tex-math>$sigma,mu >0$</jats:tex-math> </jats:alternatives> </jats:inline-formula> depend on the geometric properties of the internal heating. This result implies that mean downward conduction (for which <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline5.png\"/> <jats:tex-math>$smash { smash {{langle {delta T} rangle _h}} }< 0$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) is impossible for a range of Rayleigh numbers smaller than a critical value <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline6.png\"/> <jats:tex-math>$R_0:=(sigma /mu )^{3}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The bound demonstrates that <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline7.png\"/> <jats:tex-math>$R_0$</jats:tex-math> </jats:alternatives> </jats:inline-formula> depends on the heating distribution and can be made arbitrarily large by concentrating the heating near the bottom plate. However, for any given fixed heating profile of the class we consider, the corresponding value of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024005901_inline8.png\"/> <jats:tex-math>$R_0$</jats:tex-math> </jats:alternatives> </jats:inline-formula> is always finite. This points to a fundamental differenc","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"16 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, subcritical transition to turbulence in the quasi-two-dimensional (quasi-2-D) shear flow with strong linear friction (Camobreco <jats:italic>et al.</jats:italic>, <jats:italic>J. Fluid Mech.</jats:italic>, vol. 963, 2023, R2) has been demonstrated by the 2-D mechanism at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024007523_inline1.png"/> <jats:tex-math>$Re = 71,211$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and the nonlinear Tollmien–Schlichting (TS) waves related to the edge state were approached independently of initial optimal disturbances. For 2-D plane Poiseuille flow, transition to the fully developed turbulence requires that the Reynolds number is several times larger than the critical Reynolds number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024007523_inline2.png"/> <jats:tex-math>$Re_c$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (Markeviciute & Kerswell, <jats:italic>J. Fluid Mech.</jats:italic>, vol. 917, 2021, A57). In this paper, we observed the subcritical transitional flow in 2-D plane Poiseuille flow driven by the nonlinear TS waves by both linear and nonlinear optimal disturbances (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024007523_inline3.png"/> <jats:tex-math>$Re < Re_c$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) with different quantitative edge states. The nonlinear optimal disturbances could trigger the sustained subcritical transitional flow for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024007523_inline4.png"/> <jats:tex-math>$Re geqslant 2400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The initial energy for nonlinear optimal disturbance is more efficient than the linear optimal disturbance in reaching the subcritical transitional flow for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112024007523_inline5.png"/> <jats:tex-math>$2400 leqslant Re leqslant 5000$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Moreover, the initial energy of linear optimal disturbance is larger than the energy of its edge state. The nonlinear TS waves along the edge state are formed by the nonlinear optimal disturbances to trigger transitional flow, which agrees well with the main conclusions of Camobreco <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 963, 2023, R2), while the required <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xli
{"title":"Subcritical transitional flow in two-dimensional plane Poiseuille flow","authors":"Z. Huang, R. Gao, Y.Y. Gao, G. Xi","doi":"10.1017/jfm.2024.752","DOIUrl":"https://doi.org/10.1017/jfm.2024.752","url":null,"abstract":"Recently, subcritical transition to turbulence in the quasi-two-dimensional (quasi-2-D) shear flow with strong linear friction (Camobreco <jats:italic>et al.</jats:italic>, <jats:italic>J. Fluid Mech.</jats:italic>, vol. 963, 2023, R2) has been demonstrated by the 2-D mechanism at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007523_inline1.png\"/> <jats:tex-math>$Re = 71,211$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and the nonlinear Tollmien–Schlichting (TS) waves related to the edge state were approached independently of initial optimal disturbances. For 2-D plane Poiseuille flow, transition to the fully developed turbulence requires that the Reynolds number is several times larger than the critical Reynolds number <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007523_inline2.png\"/> <jats:tex-math>$Re_c$</jats:tex-math> </jats:alternatives> </jats:inline-formula> (Markeviciute & Kerswell, <jats:italic>J. Fluid Mech.</jats:italic>, vol. 917, 2021, A57). In this paper, we observed the subcritical transitional flow in 2-D plane Poiseuille flow driven by the nonlinear TS waves by both linear and nonlinear optimal disturbances (<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007523_inline3.png\"/> <jats:tex-math>$Re < Re_c$</jats:tex-math> </jats:alternatives> </jats:inline-formula>) with different quantitative edge states. The nonlinear optimal disturbances could trigger the sustained subcritical transitional flow for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007523_inline4.png\"/> <jats:tex-math>$Re geqslant 2400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The initial energy for nonlinear optimal disturbance is more efficient than the linear optimal disturbance in reaching the subcritical transitional flow for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0022112024007523_inline5.png\"/> <jats:tex-math>$2400 leqslant Re leqslant 5000$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Moreover, the initial energy of linear optimal disturbance is larger than the energy of its edge state. The nonlinear TS waves along the edge state are formed by the nonlinear optimal disturbances to trigger transitional flow, which agrees well with the main conclusions of Camobreco <jats:italic>et al.</jats:italic> (<jats:italic>J. Fluid Mech.</jats:italic>, vol. 963, 2023, R2), while the required <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xli","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"44 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest-growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.
{"title":"Stratified Resistive Tearing Instability","authors":"Scott J. Hopper, Toby S. Wood, Paul J. Bushby","doi":"10.1017/jfm.2024.621","DOIUrl":"https://doi.org/10.1017/jfm.2024.621","url":null,"abstract":"Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest-growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"72 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recent years have seen the emergence of new technologies that exploit nanoscale evaporation, ranging from nanoporous membranes for distillation to evaporative cooling in electronics. Despite the increasing depth of fundamental knowledge, there is still a lack of simulation tools capable of capturing the underlying non-equilibrium liquid–vapour phase changes that are critical to these and other such technologies. This work presents a molecular kinetic theory model capable of describing the entire flow field, i.e. the liquid and vapour phases and their interface, while striking a balance between accuracy and computational efficiency. In particular, unlike previous kinetic models based on the isothermal assumption, the proposed model can capture the temperature variations that occur during the evaporation process, yet does not require the computational resources of more complicated mean-field kinetic approaches. We assess the present kinetic model in three test cases: liquid–vapour equilibrium, evaporation into near-vacuum condition, and evaporation into vapour. The results agree well with benchmark solutions, while reducing the simulation time by almost two orders of magnitude on average in the cases studied. The results therefore suggest that this work is a stepping stone towards the development of an accurate and efficient computational approach to optimising the next generation of nanotechnologies based on nanoscale evaporation.
{"title":"Molecular kinetic modelling of non-equilibrium evaporative flows","authors":"Shaokang Li, Wei Su, Baochao Shan, Zuoxu Li, Livio Gibelli, Yonghao Zhang","doi":"10.1017/jfm.2024.605","DOIUrl":"https://doi.org/10.1017/jfm.2024.605","url":null,"abstract":"Recent years have seen the emergence of new technologies that exploit nanoscale evaporation, ranging from nanoporous membranes for distillation to evaporative cooling in electronics. Despite the increasing depth of fundamental knowledge, there is still a lack of simulation tools capable of capturing the underlying non-equilibrium liquid–vapour phase changes that are critical to these and other such technologies. This work presents a molecular kinetic theory model capable of describing the entire flow field, i.e. the liquid and vapour phases and their interface, while striking a balance between accuracy and computational efficiency. In particular, unlike previous kinetic models based on the isothermal assumption, the proposed model can capture the temperature variations that occur during the evaporation process, yet does not require the computational resources of more complicated mean-field kinetic approaches. We assess the present kinetic model in three test cases: liquid–vapour equilibrium, evaporation into near-vacuum condition, and evaporation into vapour. The results agree well with benchmark solutions, while reducing the simulation time by almost two orders of magnitude on average in the cases studied. The results therefore suggest that this work is a stepping stone towards the development of an accurate and efficient computational approach to optimising the next generation of nanotechnologies based on nanoscale evaporation.","PeriodicalId":15853,"journal":{"name":"Journal of Fluid Mechanics","volume":"203 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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