C. -Y. Lai, Y. -T Sun, C. -C. Chang, Y. -Y. Chen, P. E. Arratia, J. -C. Tsai
In this fluid dynamics video, we show current findings on the morphology of an oil-water interface in a torsional flow produced by rotating the upper lid of a cylindrical tank. This video was submitted as part of the Gallery of Fluid Motion 2012 which is showcase of fluid dynamics videos.
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We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of which may prompt the transformation from a circular to a polygonal torus. Our results are discussed in the context of three experiments, a toroidal vortex ring, the hydraulic jump, and the hydraulic bump.
Interfacial instabilities in confined displacements involving non-Newtonian fluids
本文综述了受限几何中非牛顿流体驱替的界面不稳定性，重点分析毛细、黏性、弹性与摩擦力竞争驱动的图案生长机制，并展望了该领域的开放问题。
The potential fluctuation and its interfacial phenomena in molecular, micro, macro, and cosmic flow instabilities
本文提出基于质量守恒的势能波动概念，揭示流动不稳定性的起源，指出其由流体密度和速度决定且先于不稳定性发展存在，为微观至宇宙尺度的流动不稳定性理解提供突破。
Holmboe (1962) postulated that resonant interaction between two or more progressive, linear interfacial waves produces exponentially growing instabilities in idealized (broken-line profiles), homogeneous or density stratified, inviscid shear layers. In this paper, we generalize Holmboe's mechanistic picture of linear shear instabilities by (i) not initially specifying the type of the waves, and (ii) by providing the option for non-normal growth. We demonstrate the mechanism behind linear shear instabilities by proposing a purely kinematic model consisting of two linear, Doppler-shifted, progre…
On the generation of free-surface waves by instabilities in quadratic shear flows
本文研究了由Couette-Poiseuille流动不稳定性在液体层中生成自由表面波的问题，分析了不同曲率、波数和雷诺数下的稳定性边界及不同流体不稳定性类型。
Tunable self-emulsification via viscoelastic control of Marangoni-driven interfacial instabilities
研究提出利用高分子量聚合物引入粘弹性来主动调控液-液界面Marangoni驱动的自乳化现象，通过实验与理论分析揭示了聚合物浓度与破碎前指状物长度的定量关系，为软材料系统中的界面动力学控制提供了预测性框架。
Two-dimensional Stokes flow with injection and suction is investigated through a second-order, perturbative mode-coupling approach. We examine the time-dependent disturbance of an initially circular interface separating two viscous fluids, and derive a system of nonlinear differential equations describing the evolution of the interfacial perturbation amplitudes. Linear stability analysis reveals that an injection-induced expanding interface is stable, while a contracting motion driven by suction is unstable. Curiously, at the linear level this suction instability is independent of the viscosit…
The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated tip-splitting of evolving fingers. When anisotropy is present in the interfacial dynamics, the growth morphology changes to dendritic growth characterized by regular structures. We introduce anisotropy by engraving a six-fold symmetric lattice of channels on a Hele-Shaw cell. We show that the morphology transition in miscible fluids depends not only on the previously r…
The onset and development of instabilities is one of the central problems in fluid mechanics. Here we develop a connection between instabilities of free fluid interfaces and inverted pendula. When acted upon solely by the gravitational force, the inverted pendulum is unstable. This position can be stabilised by the Kapitsa phenomenon, in which high-frequency low-amplitude vertical vibrations of the base creates a fictitious force which opposes the gravitational force. By transforming the dynamical equations governing a fluid interface into an appropriate pendulum, we demonstrate how stability …
A local intermittency based Reynolds-averaged transition model for turbulent mixing induced by interfacial instabilities
本文将边界层转捩中的间歇因子 $γ$ 引入 RANS 混合模型，通过局部输运方程约束 Reynolds 应力和浮力源项，并在再冲击 RM 混合案例中验证了转捩预测能力。
We investigate the interfacial wave coupling dynamics in liquid metal batteries and their effects to the battery's operation safety. Similar to aluminum reduction cells, liquid metal batteries can be highly susceptible to magnetohydrodynamical instabilities that excite undesired interfacial waves capable to provoke short-circuits. However, in liquid metal batteries the wave dynamics is far more complex since two metal-electrolyte interfaces are present that may step into resonance. In the first part of this paper, we present a Potential analysis of coupled gravity-capillary interfacial waves i…
This fluid dynamics video is an entry for the Gallery of Fluid Motion of the 66th Annual Meeting of the APS-DFD. This work reveals new types of interfacial instabilities that occur during forced-spreading of dielectric films subjected to ionic bombardment. We demonstrated that keeping the ionic bombardment strength constant, the appearance of instability patterns dramatically changes by varying viscosity of the bombarded droplet.
Onset of thermo-convective instabilities in two-layer binary fluid systems
研究两层二元流体系统在UCST附近浮力和热毛细驱动不稳定性起始特性，采用相场方法建模并预测中性曲线，揭示参数空间变化规律。
Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural phenomena up to geological scales, to industrial and technological applications, where they represent the only way to control and promote mixing at low Reynolds numbers, well below the transition from laminar to turbulent flow. As for immiscible fluids, the onset of hydrodynamic instabilities in miscible fluids is directly related to the physics of their interfaces. The focus of this review is therefore on the general mechanisms driving the growth of disturbances at the boundary between miscible fluids, under a variety …
Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited in various microfluidic applications in order to enhance mixing, replicate well-controlled patterns or generate drops of a particular size. In this work, we study the stability and dynamics of a system of three superimposed layers of two immiscible fluids subject to a normal electric field. Following the Taylor-Melcher leaky dielectric model, the bulk remains electroneutral while a net charge accumulates on the interfaces. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic cond…
Fluid flows in liquid metal batteries can be generated by a number of effects. We start with a short overview of different driving mechanisms and then address questions specific to the metal pad role instabilities in three-layer systems. We focus on the role of the conductivity distribution in the cell, noting at the same time that interfacial tension should be considered as well for smaller cells. Following this discussion, numerical results on the excitation of interfacial waves in two-layer liquid metal systems with miscibility gaps bearing an interface normal electric current are presented…
In this paper, the interfacial motion between two immiscible viscous fluids in the confined geometry of a Hele-Shaw cell is studied. We consider the influence of a thin wetting film trailing behind the displaced fluid, which dynamically affects the pressure drop at the fluid-fluid interface by introducing a nonlinear dependence on the interfacial velocity. In this framework, two cases of interest are analyzed: The injection-driven flow (expanding evolution), and the lifting plate flow (shrinking evolution). In particular, we investigate the possibility of controlling the development of fingeri…
Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent…
Elasto-Inertial Instability in Torsional Flows of Shear-Thinning Viscoelastic Fluids
该研究针对粘弹性流体扭转流动中弹-惯性不稳定性的综合影响机制不明的问题，通过锥板实验探究多参数相空间，拓展了弯曲流线不稳定性判据，填补了纯弹性与弹-惯性不稳定性间的研究空白。
Simulating fluid-fluid displacement in a soft capillary tube: How compliance delays interfacial instability and bubble pinch-off
本文提出了一种计算模型，研究软毛细管中流体置换过程中柔顺性对界面不稳定性及气泡破裂的抑制作用。
Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low Reynolds number lubrication approximation incorporating surface tension, intermolecular effects and evaporative fluxes. Parameter ranges for evaporation- dominated and condensation-dominated regimes and a critical case are identified. Interfacial instabilities driven by the competition between the disjoining pressure and evaporative effects are studied via l…
Effect of interfacial disturbances on instabilities of buoyant/thermocapillary convective flows in rectangular cavities is studied in a series of numerical experiments. The computations are carried out for several two-liquid two-layer systems taking into account properties of liquids used in previously published experiments. Relation between the interface deformations and the Boussinesq approximation is discussed. It is shown that in some systems, including the interface disturbances in the model can alter the critical temperature difference by approximately 10%, producing either destabilizing…
Flow driven interfacial waves: an inviscid asymptotic study
本文用渐近方法研究风与水流联合驱动的短波界面波演化，求解Rayleigh方程并构造一致有效近似，给出任意剪切流下Miles和rippling不稳定性的增长率表达式。
The traditional approach in the study of hydrodynamic stability of stratified fluids includes the stick boundary conditions between layers. However, this rule may be violated in polymer systems and as a consequence various instabilities may arise. The main objective of this paper is to analyze theoretically the influence of slip boundary conditions on the hydrodynamic stability of the interface between two immiscible viscous layers subjected to simple shear flow. It is found that the growth rate of long-wave disturbances is fairly sensitive to the slip at the interface between layers as well a…
The process of one fluid pushing another is universally common while involving complex interfacial instabilities. Particularly, occurring in a myriad of natural and industrial processes, wavy fingering patterns frequently emerge when a less viscous fluid pushes another more viscous one, such as water invading oil, in a porous medium. Such finger-shaped interfaces producing partial displacement significantly affect the efficiency of numerous applications, for example, chromatography, printing devices, coating flows, oil-well cementing, as well as large-scale technologies of groundwater and enha…
The stratified inclined duct (SID) sustains an exchange flow in a long, gently sloping duct as a model for continuously-forced density-stratified flows such as those found in estuaries. Experiments have shown that the emergence of interfacial waves and their transition to turbulence as the tilt angle is increased appears linked to a threshold in the exchange flow rate given by inviscid two-layer hydraulics. We uncover these hydraulic mechanisms with (i) recent direct numerical simulations (DNS) providing full flow data in the key flow regimes (Zhu & Atoufi et al., arXiv:2301.09773, 2023), (ii)…
A pressure-driven two-layer channel flow of a Newtonian fluid with constant viscosity (top layer) and a fluid with a time-dependent viscosity (bottom layer) is numerically investigated. The bottom layer goes through an aging process in which its viscosity increases due to the formation of internal structure, which is represented by a Coussot-type relationship. The resultant flow dynamics is the consequence of the competition between structuration and destructuration, as characterized by the dimensionless timescale for structuration (tau) and the dimensionless material property (beta) of the bo…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the non-linear description is performed and analyzed in a wide range of physical situations. The differential equations of the interfacial motion thus obtained may be useful in research of the non-linear development of the classical hydrodynamic instabilities. They should play an important role in the understanding of the hydrodynamic phenomena associated with the fl…
Superhydrophobic surfaces have been shown to produce significant drag reduction in both laminar and turbulent flows by introducing an apparent slip velocity along an air-water interface trapped within the surface roughness. In the experiments presented within this study, we demonstrate the existence of a surface tension gradient associated with the resultant Marangoni flow along an air-water interface that causes the slip velocity and slip length to be significantly reduced. In this study, the slip velocity along a millimeter-sized air-water interface was investigated experimentally. This larg…
Using air to displace a viscous fluid contained in Hele-Shaw cell can create a fingering pattern at the interface between the fluids, if the capillary number exceeds a critical value. This Saffman-Taylor instability is revisited for the inverse case of a viscous fluid displacing air, when partially wettable hydrophilic particles are lying on the walls. Though the inverse case is otherwise stable, the presence of the particles results in a fingering instability at low capillary number. This capillary-driven instability is driven-by the integration of particles into the interface which results f…
A highly sheared dense aqueous suspension of granular cornstarch particles displays rich nonlinear rheology. We had previously demonstrated the growth and onset of interfacial instabilities when shear-thinning cornstarch suspensions were displaced by a Newtonian fluid, and had suggested methods to maximise displacement efficiency [Palak, R. Sathayanath, S. K. Kalpathy and R. Bandyopadhyay, Colloids Surf. A Physicochem. Eng. Asp., 629 (2021) 127405]. In the present work, we explore the miscible displacement of a dense aqueous cornstarch suspension in its discontinuous shear-thickening regime in…
Stability of surfactant-laden double-layered viscoelastic fluids flowing over an inclined plane
本文研究含不溶性表面活性剂的双层弱黏弹性流体沿斜面流动的稳定性，推导Orr-Sommerfeld型边值问题并数值求解，揭示三种失稳模式及上下层黏弹性对各模式的差异化影响规律。
Nonlinear stages of the recently uncovered instability due to insoluble surfactant at the interface between two fluids are investigated for the case of a creeping plane Couette flow with one of the fluids a thin film and the other one a much thicker layer. Numerical simulation of strongly nonlinear longwave evolution equations which couple the film thickness and the surfactant concentration reveals that in contrast to all similar instabilities of surfactant-free flows, no amount of the interfacial shear rate can lead to a small-amplitude saturation of the instability. Thus, the flow is stable …
When a soft glassy colloidal suspension is displaced by a Newtonian fluid in a radial Hele-Shaw geometry, the pattern morphology that develops at the interface is determined by the complex rheology of the former. We had reported in an earlier work [Palak, V. R. S. Parmar, D. Saha and R. Bandyopadhyay, JCIS Open, 6 (2022) 100047] that a range of interfacial patterns can be formed by controlling the elasticity of the displaced suspension, the flow rate of the displacing fluid and the interfacial tension of the fluid pair. Interestingly, all the different morphological features can be distinguish…
Direct numerical simulation of compressible interfacial multiphase flows using a mass-momentum-energy consistent volume-of-fluid method
本研究开发了一种质量-动量-能量一致的VOF方法，用于可压缩界面多相流的直接数值模拟，该方法能精确解析激波与界面，并验证了其捕捉粘性和毛细效应的能力。
A spectral boundary integral method for simulating electrohydrodynamic flows in viscous drops
提出一种谱边界积分方法，利用球谐展开和综合电荷输运模型模拟均匀电场中液滴的电流体动力学，通过加权球谐展开解决低粘度液滴的数值振铃问题，并在Taylor和Quincke电旋转区域验证了其有效性。
Sidewall effects on the onset of interfacial Holmboe waves in stratified exchange flows at high Schmidt number
研究高施密特数下分层交换流中界面霍尔姆博厄波起始的侧壁效应，用长管道、锐界面渐近理论确定受限调整弗劳德数\(Fr^*\)，通过线性稳定性分析等方法，表明\(Fr^*\)近似恒定临界值可准确预测波起始，调和差异并确立横向受限的控制作用。
This work focuses on the interfacial dynamics with interfacial mass flux in the presence of acceleration and surface tension. We employ the general matrix method to find the fundamental solutions for the linearized boundary value problem conserving mass, momentum and energy. We find that the dynamics can be stable or unstable depending on the values of the acceleration, the surface tension and the density ratio. In the stable regime, the flow has the non-perturbed fields in the bulk, is shear-free at the interface, and has the constant interface velocity. The dynamics is unstable only when it …
The stability of liquid films coating the walls of a parallel-plate channel and sheared by a pressure-driven gas flow along the channel centre is studied. The films are susceptible to a long-wavelength instability, whose dynamic behaviour is found - for sufficiently low Reynolds numbers and thick gas layers - to be described by two coupled non-linear partial differential equations. To the best of our knowledge, such coupled fully non-linear equations for the film thicknesses have not been derived previously. A linear stability analysis conducted under the condition that the material properties…
Previous studies have shown that intermediate surface tension has a counterintuitive destabilizing effect on 2-phase planar jets. Here, the transition process in confined 2D jets of two fluids with varying viscosity ratio is investigated using DNS. Neutral curves for persistent oscillations are found by recording the norm of the velocity residuals in DNS for over 1000 nondimensional time units, or until the signal has reached a constant level in a logarithmic scale - either a converged steady state, or a "statistically steady" oscillatory state. Oscillatory final states are found for all visco…
Front-propagating systems provide some of the most fundamental physical examples of interfacial instability and pattern formation. However, their nonlinear dynamics are rarely addressed. Here, we present an experimental study of air displacing a viscous fluid within a collapsed, compliant channel - a model system for pulmonary airway reopening. We show that compliance induces fingering instabilities absent in the rigid channel and we present the first experimental observations of the counter-intuitive 'pushing' behaviour previously predicted numerically, for which a reduction in air pressure r…
Interfacial activity dynamics of confined active droplets
本文通过双通道显微实验与 Brinkman squirmer 模型，研究受限活性油滴的界面活性动力学，揭示了随液滴半径增大出现的涡流迁移、偶极-四极双稳态及多极模态转变，并阐明其源于胶束慢扩散与分子快扩散之间的时间尺度竞争。
Instabilities arise in a number of flow configurations. One such manifestation is the development of interfacial waves in multiphase flows, such as those observed in the falling liquid film problem. Controlling the development of such instabilities is a problem of both academic and industrial interest. However, this has proven challenging in most cases due to the strong nonlinearity and high dimensionality of the underlying equations. In the present work, we successfully apply Deep Reinforcement Learning (DRL) for the control of the one-dimensional (1D) depth-integrated falling liquid film. In…
Simulating interfacial flows: a farewell to planes
针对现有VOF方法依赖分段线性界面表示导致曲率估计精度低的问题，本文提出三维分段抛物界面重构方法并应用于VOF框架，实现界面重构与曲率估计单步完成，经测试其精度与稳定性优于经典PLIC-VOF方法。
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasi-stationary states of free interface in fluid dynamical systems subject to vibrations, revealed existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously …
A Vortex Damping Outflow Forcing for Multiphase Flows with Sharp Interfacial Jumps
本文提出一种涡旋阻尼出流强迫项，用于抑制多相流出口处因尖锐界面跳变产生的扰动，可耦合固定压力边界模拟沸腾问题，并在Flash-X上验证了其准确性与稳定性。
Interfacial instability as a trigger for dryout inception in two-phase CO2 flow
研究通过分析两相环形流中界面不稳定性的触发机制，揭示干熄现象的起因，利用数学模型和线性理论探讨界面稳定性，通过数值计算验证临界蒸汽质量与实验数据一致。
For the past two hundred years, parametric instabilities have been studied in various physical systems, such as fluids, mechanical devices and even inflationary cosmology. It was not until a few decades ago that this subharmonic unstable response arose as a central mechanism for the thermalisation of the Early Universe, in a theory known as preheating. Here we study a parametrically driven two-fluid interface to simulate the key aspects of inflationary preheating dynamics through the onset of nonlinear Faraday waves. We present a detailed analysis of the effective field theory description for …
In this paper, the instability of layered two-phase flows caused by the presence of a soluble surfactant (or a surface active solute) is studied. The fluids have different viscosities, but are density matched to focus on Marangoni effects. The fluids flow between two flat plates, which are maintained at different solute concentrations. This establishes a constant flux of solute from one fluid to the other in the base state. A linear stability analysis is performed, using a combination of asymptotic and numerical methods. In the creeping flow regime, Marangoni stresses destabilize the flow, pro…
Exploitation-exploration transition in the physics of fluid-driven branching
本文通过在Hele-Shaw电池中注入染料实验，发现屈服应力流体中随注入速率变化发生从直接路径到分支形态的开发-探索转变，并揭示了突破所需流体量最小及速度与准确性权衡的流体计算具身范式。
Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to specify the physics of the waves in advance. Wave interactions may lead to instabilities, which may or may not be of the familiar "normal-mode" type. Contrary to intuition, the underlying dynamical system describing linear wave interactions is found to be non-linear. Specifically, a saw-tooth jet profile with three interfaces possessing kinematic and geometric sy…
Dynamics of thin film flows on a vertical fibre with vapor absorption
本文研究吸水硅油在垂直纤维上吸收水蒸气时的薄膜流动动力学，提出单侧薄膜型非线性偏微分方程耦合模型，并通过稳定性分析与数值模拟揭示了吸收引发的界面不稳定性、波纹形成及液滴合并的参数条件。
On buoyancy in disperse two-phase flow and its impact on the well-posedness of two-fluid models
本文探讨了分散两相流中浮力的分解及其对两流体模型正则性的影响，推导了新的闭合关系，表明除雷诺应力外，所有应力和伪应力均贡献于浮力背景流，并具有低通滤波特性，防止哈达玛不稳定性。
Culinary fluid mechanics and other currents in food science
本文综述了流体动力学进展如何改变食品科学，以菜单结构探讨多相流、复杂流体等烹饪流体力学主题，评估最新知识、未解问题及未来方向。
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