Motion,deformation, and coalescence of ferrofluid droplets subjected to a uniform magnetic field

In this article, we present the motion, deformation, and coalescence of ferrofluid droplets suspended in a nonmagnetic fluid, subjected to a uniform magnetic field in both vertical and horizontal directions. A coupling between the simplified multiphase lattice Boltzmann method and the self-correcting scheme is constructed to numerically solve the two-dimensional flow field and the magnetostatics equations, respectively. The Cahn-Hilliard equation is employed to seize the diffuse interface between magnetic and nonmagnetic fluids. In order to validate the model, deformation of a ferrofluid droplet suspended in nonmagnetic fluid is simulated as a test case and the results are compared with numerical and experimental results. Furthermore, a detailed analysis on the behavior of falling ferrofluid droplets and the coalescence between a pair of ferrofluid droplets under the effect of different magnetic fields and different droplets configurations are also presented in this article. The results provide significant insight and a better understanding of these phenomena. It is found that for higher values of magnetic bond number and susceptibility, the droplet deformation is significant and the falling process is faster while a reverse behavior is observed for higher values of Eötvös number. Moreover, the magnetic energy density exhibits an interesting behavior in the vicinity of the droplets. It is concentrated between the droplets with a nonuniform distribution when the droplets are close to each other.     

Parametric modulation in the Taylor-Couette ferrofluid flow

A parametric instability of the Taylor-Couette ferrofluid flow excited by a periodically oscillating magnetic field, has been investigated numerically. The Floquet analysis has been employed. It has been found that the modulation of the applied magnetic field affects the stability of the basic flow. The instability response has been found to be synchronous with respect to the frequency of periodically oscillating magnetic field.     

The effects of local thermal nonequilibrium and MFD viscosity on the onset of Brinkman ferroconvection

The simultaneous effect of local thermal nonequilibrium (LTNE) and magnetic field dependent (MFD) viscosity on thermal convective instability in a horizontal ferrofluid saturated Brinkman porous layer in the presence of a uniform vertical magnetic field is studied analytically. The results indicate that the onset of Brinkman ferroconvection is delayed with increasing MFD viscosity parameter but the critical wave number is found to be independent of this parameter. When compared to the simultaneous presence of buoyancy and magnetic forces, it is observed that the onset of Brinkman ferroconvection is delayed more when the magnetic forces alone are present. Asymptotic solutions for both small and large values of scaled inter-phase heat transfer coefficient H _t are compared with those computed numerically and good agreement is found between them. Besides, the influence of magnetic and LTNE parameters on the stability characteristics of the system is also discussed. The available results in the literature are recovered as particular cases from the present study.     

Oscillations of a gas bubble in a non-Newtonian liquid under the action of an acoustic field

The evolution of the radius of a spherical cavitation bubble in an incompressible non-Newtonian liquid under the action of an external acoustic field is investigated. Non-Newtonian liquids having relaxation properties and also pseudoplastic and dilatant liquids with powerlaw equation of state are studied. The equations for the oscillation of the gas bubble are derived, the stability of its radial oscillation and its spherical form are investigated, and formulas are given for the characteristic frequency of oscillations of the cavitation hollow in a relaxing liquid. The equations are integrated numerically. It is shown that in a relaxing non-Newtonian liquid the viscosity may lead to the instability of the radial oscillations and the spherical form of the bubble. The results obtained here are compared with the behavior of a gas bubble in a Newtonian liquid.     

Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schr6dinger equations （1-NLS） with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoret- ically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.     

Suppression or enhancement of interfacial instability in two-layer plane Couette flow of FENE-P fluids past a deformable solid layer

The linear stability of two-layer plane Couette flow of FENE-P fluids past a deformable solid layer is analyzed in order to examine the effect of solid deformability on the interfacial instability due to elasticity and viscosity stratification at the two-fluid interface. The solid layer is modeled using both linear viscoelastic and neo-Hookean constitutive equations. The limiting case of two-layer flow of upper-convected Maxwell (UCM) fluids is used as a starting point, and results for the FENE-P case are obtained by numerically continuing the UCM results for the interfacial mode to finite values of the chain extensibility parameter. For the case of two-layer plane Couette flow past a rigid solid surface, our results show that the finite extensibility of the polymer chain significantly alters the neutral stability boundaries of the interfacial instability. In particular, the two-layer Couette flow of FENE-P fluids is found to be unstable in a larger range of nondimensional parameters when compared to two-layer flow of UCM fluids. The presence of the deformable solid layer is shown to completely suppress the interfacial instability in most of the parameter regimes where the interfacial mode is unstable, while it could have a completely destabilizing effect in other parameter regimes even when the interfacial mode is stable in rigid channels. When compared with two-layer UCM flow, the two-layer FENE-P case is found in general to require solid layers with relatively lower shear modulii in order to suppress the interfacial instability. The results from the linear elastic solid model are compared with those obtained using the (more rigorous) neo-Hookean model for the solid, and good agreement is found between the two models for neutral stability curves pertaining to the two-fluid interfacial mode. The present study thus provides an important extension of the earlier analysis of two-layer UCM flow [V. Shankar, Stability of two-layer viscoelastic plane Couette flow past a deformable solid layer: implications of fluid viscosity stratification, J. Non-Newtonian Fluid Mech. 125 (2005) 143–158] to more accurate constitutive models for the fluid and solid layers, and reaffirms the central conclusion of instability suppression in two-layer flows of viscoelastic fluids by soft elastomeric coatings in more realistic settings.     

Numerical simulation of nucleate pool boiling on the horizontal surface for ferrofluid under the effect of non-uniform magnetic field

Nucleate pool boiling heat transfer of ferrofluid on a horizontal plate; has been explored numerically. Extra necessary equations have been used in this model to simulate mass transfer and effect of magnetic field that had not considered in previous researches using mixture model. Also effect of negative and positive gradient of magnetic field on the heat transfer rate and bubble shape has been investigated. Results are in good agreement with experimental data.     

Effect of temperature dependent viscosity on revolving axi-symmetric ferrofluid flow with heat transfer

The prime objective of the present study is to examine the effect of temperature dependent viscosity μ(T) on the revolving axi-symmetric laminar boundary layer flow of an incompressible, electrically non-conducting ferrofluid in the presence of a stationary plate subjected to a magnetic field and maintained at a uniform temperature. To serve this purpose, the non-linear coupled partial differential equations are firstly converted into the ordinary differential equations using well-known similarity transformations. The popular finite difference method is employed to discretize the non-linear coupled differential equations. These discretized equations are then solved using the Newton method in MATLAB, for which an initial guess is made with the help of the Flex PDE Solver. Along with the velocity profiles, the effects of temperature dependent viscosity are also examined on the skin friction, the heat transfer, and the boundary layer displacement thickness. The obtained results are presented numerically as well as graphically.     

STABILITY OF ULTRATHIN LIQUID FILM EVOLUTION WITH SURFACTANT

针对固体基底上厚度小于100 nm的含活性剂超薄液膜演化过程, 基于润滑理论推导出包含分离压影响的液膜厚度和活性剂浓度的演化方程, 采用正则模态法导出了描述液膜线性稳定性的特征方程, 分析了多个特征参数对线性稳定性的影响, 数值模拟了液膜厚度和活性剂浓度演化历程, 对比了模拟所得非线性结果与线性分析预测结果的一致性.结果表明:范德华力具有促进扰动增长的作用, 较强的玻恩斥力促使扰动衰减, 使液膜趋于稳定;较小的毛细力数易使液膜凹陷处发生二次失稳, 并最终导致去润湿现象发生;液膜厚度和溶于液膜内部的活性剂浓度初值越大, 液膜稳定性越强, 液膜表面活性剂浓度影响则相反;增大吸附系数不利于液膜稳定性.     

Sharp-Interface Nematic-Isotropic Phase Transformations With Flow

We develop a sharp-interface theory for phase transformations between the isotropic and uniaxial nematic phases of a flowing liquid crystal. Aside from conventional evolution equations for the bulk phases and corresponding interface conditions, the theory includes a supplemental interface condition expressing the balance of configurational momentum. As an idealized illustrative application of the theory, we consider the problem of an evolving spherical droplet of the isotropic phase surrounded by the nematic phase in a radially-oriented state. For this problem, the bulk and interfacial equations collapse to a single nonlinear second-order ordinary differential equation for the radius of the droplet—an equation which, in essence, expresses the balance of configurational momentum on the interface. This droplet evolution equation, which closely resembles a previously derived and extensively studied equation for the expansion of contraction of a spherical gas bubble in an incompressible viscous liquid, includes terms accounting for the curvature elasticity and viscosity of the nematic phase, interfacial energy, interfacial viscosity, and the ordering kinetics of the phase transformation. We determine the equilibria of this equation and study their stability. Additionally, we find that motion of the interface generates a backflow, without director reorientation, in the nematic phase. Our analysis indicates that a backflow measurement has the potential to provide an independent means to determine the density difference between the isotropic and uniaxial nematic phases.     

Orientational phase transitions in systems of axially symmetric particles in steady elongational flow combined with potential fields

Effects of uniaxial elongational flow combined with an external potential field (electric, magnetic) on the isotropic-to-nematic phase transition are considered basing on the Onsager free energy approach and self-consistent field theory. Ellipsoidal particles of uniaxial symmetry subjected to dipole and quadruple fields are assumed. Mean-field potential of the interparticle interactions accounting for dipole and quadruple contributions is considered.The self-consistency equations include dipole and quadruple contributions of the external and mean-field potentials. The equilibrium thermodynamic potentials, critical conditions of phase instability, and phase equilibria are discussed.Example computations indicate that orientation of rigid, prolate particles in the elongational flow and/or an external potential field results in narrowing the range of phase instability, reducing the difference in orientational order between the phases in equilibrium, and shifting phase equilibria to smaller values of the interparticle interactions parameter.Uniaxial elongational flow contributes a potential with quadruple symmetry, additive to other quadruple terms of the external potential. Specific nature of the flow potential, different to the non-hydrodynamic potentials, is evident in the behaviour of internal energy and entropy. At the phase transitions, the flow contributes to the discontinuity of internal energy and entropy, a term originated from the activation energy of viscous motion.     

Hydrodynamic stability of dense plasma in a corrugated magnetic field

The hydrodynamic stability of plasma in a corrugated magnetic field is considered. A stability criterion is established for flute oscillations; it is valid for arbitrary values of β = 8πp/B². In a fairly long system unstable flute perturbations with a wavelength much greater that the period of corrugation always exist. The equations of motion are solved for these most dangerous perturbations, and the instability increments are derived for the case of an ideal plasma and also with due allowance for viscosity. The viscosity is considerable for large β and may lead to a reduction by a factor of ～ √β in the increments.     

A comparison of the magnetorheology of two ferrofluids with different magnetic field-dependent chaining behavior

The effect of magnetic field-induced particle chaining on the magnetorheology of commercial iron oxide-based ferrofluids was investigated by comparison of a ferrofluid with particles that resist chaining and a ferrofluid with particles that interact when a field is applied, forming chain-like aggregates. This difference between the two ferrofluids was confirmed by optical microscopy and dynamic light scattering in an applied magnetic field. Both fluids had similar magnetic particle fraction, but showed different magnetorheological behavior. Chaining resulted in a stronger magnetic field-dependent viscosity enhancement and the appearance of an elastic modulus. The magnetorheology of these two fluids was described using the Mason number (Mn), resulting in two distinct Mn power law slopes at intermediate and small Mn values for the ferrofluid with magnetic field-induced aggregation. The commonly used magnetic coupling parameter failed to distinguish the behavior of the two ferrofluids.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.     

Influence of a homogeneous axial magnetic field on Taylor–Couette flow of ferrofluids with low particle–particle interaction

Experimental results concerning the stability of Couette flow of ferrofluids under magnetic field influence are presented. The fluid cell of the Taylor–Couette system is subject to a homogeneous axial magnetic field and the axial flow profiles are measured by ultrasound Doppler velocimetry. It has been found that an axial magnetic field stabilizes the Couette flow. This effect decreases with a rotating outer cylinder. Moreover, it could be observed that lower axial wave numbers are more stable at a higher axial magnetic field strength. Since the used ferrofluid shows a negligible particle–particle interaction, the observed effects are considered to be solely based on the hindrance of free particle rotation.     

采用不同黏性处理方法的宽无叶扩压器不稳定流动研究

径向无叶扩压器的全局稳定性可能受到核心主流失稳,出口回流与壁面边界层分离等因素影响,对于宽无叶扩压器,无黏核心主流与壁面边界层流动对不稳定扰动诱发的作用机理是当前研究的重点.本文首先通过数值计算获得了大宽度比孤立无叶扩压器平均流动,然后基于小扰动理论和周向均质假设,分别对欧拉方程与 Navier-Stokes 方程进行线性化,建立了基于无黏核心流动的稳定性分析方法,以及基于涡黏性与分子黏性的混合稳定性分析方法;通过与实验结果的对比,验证了混合稳定性分析方法预测所得流动失稳频率和全局直接模态的准确性;最后基于伴随方法获得了特征值的结构敏感性,揭示了不同黏性处理条件下宽无叶扩压器内全局不失稳扰动的源发区域.在只考虑核心主流的无黏条件下,宽无叶扩压器内流动不稳定扰动来源于流场中部,为二维的离心失稳;在同时考虑核心主流与边界层的作用时,宽无叶扩压器不稳定扰动不仅来源于扩压器流场中部的核心主流,壁面回流对于不稳定扰动的产生了重要影响.      

受径向振荡激励的黏弹性液滴稳定性分析

当液滴受到外部周期性的径向激励时, 在其表面会形成驻波模式的不稳定, 这就是在球面上的Faraday不稳定问题. 不稳定的表面波的振荡频率根据流体物性参数和所施加激励条件的不同呈现为谐波或是亚谐波模式的振荡. 本文基于线性小扰动理论, 研究了受径向振荡体积力的黏弹性液滴表面波的不稳定性. 振荡的体积力导致动量方程为含有时间周期系数的Mathieu方程, 系统因此变成参数不稳定问题, 采用Floquet理论进行求解. 本模型中将黏弹性的特征处理为与流变模型参数相关的等效黏度, 从而简化了问题的求解. 基于对中性稳定曲线及增长率的分析, 研究了黏弹性参数对液滴稳定性的影响. 结果表明零剪切黏度和应变驰豫时间的增加具有抑制液滴表面波增长的作用, 提高了使液滴表面发生谐波不稳定的激励幅值. 随着振荡幅值的增加, 增长率不稳定的区域减少, 且随着振荡频率的增加, 液滴表面波增长率减小. 通过对增长率的分析可以得出, 应力松弛时间的增加使得增长率增加, 从而促进了液滴表面波的增长.      

A model for droplet entrainment in heated annular flow

The ability to accurately predict droplet entrainment in annular two-phase flow is required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. Most annular flow entrainment models in the open literature are formulated in terms of dimensionless groups, which do not directly account for interfacial instabilities. However, many researchers agree that there is a clear presence of interfacial instability phenomena having a direct impact on droplet entrainment. The present study proposes a model for droplet entrainment, based on the underlying physics of droplet entrainment from upward co-current annular film flow that is characteristic to light water reactor safety analysis. The model is developed based on a force balance and stability analysis that can be implemented into a transient three-field (continuous liquid, droplet, and vapor) two-phase heat transfer and fluid flow systems analysis computer code.     

含气泡油滴撞击油膜壁面时气泡的变形与破裂

油--气润滑过程中润滑油液滴受高速气流扰动易形成含气泡油滴,微气泡将对油滴撞击壁面时的运动过程以及壁面油膜 层的形成质量产生重要影响. 基于耦合的水平集--体积分数 方法,对含气泡油滴撞击油膜壁面行为进行数值模拟研究, 考察含气泡油滴撞击油膜壁面时气泡的变形运动过程,探讨气泡破裂的动力学机制,分析气泡大小、碰撞速度和液体黏度等因素对含气 泡油滴撞壁过程中气泡变形特征参数的影响规律. 研究表明:含气泡油滴撞击油膜壁面后气泡会发生变形,并破裂形成膜液滴;气泡随同 液滴运动过程中,气泡内外压力和速度梯度变化是使气泡发生破裂的主要诱因. 气泡大小对气泡破裂方式影响较大,气泡较小时发生单 点破裂,而气泡较大时更容易发生多处破裂. 不同大小气泡受力差异较大,气泡大小与破裂发生时刻没有明显相关性. 碰撞速度和液体 黏度对气泡的变形、破裂和破裂发生时刻都具有一定的影响. 碰撞速度越大,油滴动能越大,更容易产生气泡变形和破裂现象. 液体黏 度增大,在油滴撞壁运动前期促进气泡变形,而在运动后期可以阻延气泡破裂行为发生.      

On the stability of multi-layered fluids. Part I: analysis

The linear stability of the Poiseuille flow of multi-layered different fluids, described mathematically by a system of Orr-Somerfeld differential equations, is investigated. A spectral method is used to rewrite this system into a generalized eigenvalue problem, which can be solved with the QZ-algorithm. Special attention is paid to the tractibility of the interfacial conditions of the stability problem. Since we will limit ourselves to a linear stability analysis, the analytical treatment of the interfacial conditions is simplified. Some results related to simple flow configurations are presented. The origin of certain regions of interfacial instability is explained by simple analytical reasoning.