Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a “torpedo” shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour.     

Simulation of falling droplet by the lattice Boltzmann method

In this paper the lattice Boltzmann method (LBM) is employed to simulate deformation and breakup of a falling drop under gravity. First the two-phase LBM is applied to verify the Laplace law for static drops. In order to further verify the model, relaxation of a square droplet with two different viscosities is conducted. Then deformation and breakup of a falling drop for some range of Eotvos and Ohnesorge numbers are investigated. It is seen that at relatively low Eotvos numbers, where the surface tension force is dominant, the drop deforms slowly and reaches a steady state without breakup. At higher Eotvos numbers gravitational force prevail over the surface tension force and the drop distorts more. Breakup of the drop can be seen for a large enough Eotvos value. On the other hand the stabilizing effect of the Ohnesorge number, which is the ratio of viscous stresses and surface tension, is shown. It is found that at higher Ohnesorge values, the viscous forces are dominant and the drop tends to maintain its original shape.     

Breakup of finite fluid films

We study the dewetting process of thin fluid films that partially wet a solid surface. Using long wave (lubrication) approximation, we formulate a nonlinear partial differential equation governing the evolution of the film thickness, h. This equation includes the effects of capillarity, gravity, and additional conjoining/disjoining pressure term to account for intermolecular forces. We perform standard linear stability analysis of an infinite flat film, and identify the corresponding stable, unstable and metastable regions. Within this framework, we analyze the evolution of a semi-infinite film of length L in one direction. The numerical simulations show that for long and thin films, the dewetting fronts of the film generate a pearling process involving successive formation of ridges at the film ends and consecutive pinch-off behind these ridges. On the other hand, for shorter and thicker films, the evolution ends up by forming a single drop. The time evolution as well as the final drops pattern shows a competition between the dewetting mechanisms caused by nucleation and by free surface instability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis and experiments on the spreading dynamics of a viscoelastic drop

We study the spreading dynamics of a sessile viscoelastic drop on a horizontal surface, where a simplified Phan–Thien–Tanner (sPTT) model is considered to represent the rheology of viscoelastic drop. We have adopted a macroscopic approach to obtain the temporal evolution of the spreading drop, while to establish the efficacy of the theoretical model, we have validated the results obtained from the mathematical formulation with the experimental results for both the Newtonian (Si-oil) and viscoelastic (PDMS and aqueous solution of CMC and glycerin) drops. Following the framework of Seaver–Berg approximation, the spherical shape of the drop is assumed as a cylindrical disk here. We observe from this study that an increment in the elasticity of the fluid enhances the velocity gradient and increases the viscous dissipation in the drop volume, leading to a reduction in the spreading rate.     

不变形双滴的热毛细迁移及相互作用

对微重力下不变形双滴的非定常热毛细迁移运动进行了数值模拟,采用了有限差分方法对动量方程和能量方程进行离散,使用波前追踪法捕捉运动的不变形液滴界面．研究显示双滴的排列方式对它们的迁移规律和相互作用影响很大,其中影响任一个液滴运动的最主要的因素是另一个液滴的存在所引起的温度场的扰动．     

Octopus-shaped instabilities of evaporating drops

We report on instabilities during spreading of volatile liquids, with emphasis on the novel instability observed when isopropyl alcohol (IPA) is deposited on a monocrystaline Si wafer. This instability is characterized by emission of drops ahead of the expanding front, with each drop followed by smaller, satellite droplets, forming the structures which we nickname ‘octopi’ due to their appearance. A less volatile liquid, or a substrate of larger heat conductivity, suppress this instability. We have formulated a theoretical model that reproduces the main features of the experiment. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

搜索区域自动变更的智能水滴算法实训课排课优化

排课问题是NP完全问题,高校实训室排课需考虑实训设备配置及教学改革"走班制"专业选修课所增加的排课复杂度.将高校实训室排课问题建模为硬约束目标及软约束优化满足问题,提出了经过改进的智能水滴算法,改进算法在路径寻优过程中根据待排课程的属性与当前排课状态,结合优化目标,自动进行跳转或围绕核心点变更搜索区域,有效解决了标准智能水滴算法搜索范围固定不利于算法搜索效率提升的问题.提出了预排序策略,减轻算法后期运行的阻力,在排课资源紧张的情况下,更好地实现收敛.通过改进智能水滴算法、标准智能水滴算法、遗传算法进行排课实验对比,验证了改进智能水滴算法在排课系统中的优化效果和高效性。     

Lattice Boltzmann modeling of wall-bounded ternary fluid flows

Starting from the phase-field perspective, we first formulate a novel wetting boundary condition to describe the interactions among ternary fluids and a solid and then we propose a boundary scheme for its implementation in the framework of the lattice Boltzmann (LB) method. This scheme for three-phase fluids can preserve the reduction consistency property of the diphasic case such that it can give physically relevant results. Combining this wetting boundary scheme and the LB ternary fluid model based on multicomponent phase-field theory, we simulated several ternary fluid flow problems involving a solid substrate, including the spreading of binary drops on a substrate, the spreading of a compound drop on a substrate, the capillary intrusion of ternary fluids, and the shear of a compound liquid drop on a substrate. The numerical results are found to be good agreement with the analytical solutions and some available results. Finally, as an application, we use the LB model coupled with the present wetting boundary scheme to numerically investigate the impact of a compound drop on a solid circular cylinder. It is found that the dynamics of a compound drop can be remarkably influenced by the wettability of the solid surface and the dimensionless Weber number.     

Influence of nonisothermal effects on gas production in northern regions

The influence of mathematical model parameters on the dynamics of pressure and temperature fields at nonisothermal gas filtration is investigated in a numerical experiment. A nonlinear system of partial differential equations obtained from the energy and mass conservation laws and the Darcy law are used to describe the process, and physical and caloric equations of state are used as closing relations. The boundary conditions correspond to a given pressure drop at the bottomhole. It is shown that the influence of the temperature field on such integral characteristics as cumulative gas production is most pronounced at moderate pressure drops. The size of the zone of possible hydrate formation in a gas reservoir is determined in a particular example.     

On modeling evaporation

We develop a theoretical model for evaporation of a pure liquid drop on a thermally conductive solid substrate. We discuss a variety of effects regarding evaporation regime, the state of the liquid/gas interface and the content of gas phase. Then, we further consider two models: the one resulting from the one-sided non-equilibrium assumption and the other that assumes diffusion-limited regime and equilibrium at the liquid/gas interface. A single governing equation for the evolution of drop thickness is derived for both models. We show that although the model predicts qualitatively different temperature along liquid/gas and liquid/solid interface, the dynamics of the drops is almost the same.      

Eulerian Model of Diesel Fuel Sprays

The contribution reviews the research activities on modeling the fuel spray formation in combustion chamber of Diesel engines. A fully Eulerian code has been developed for computing the two-phase flows of drops dispersed in gaseous environment. Both the multi-component compressible gas and the drops are described using governing equations written in Eulerian coordinates. The basic laws of conservation are balanced on finite volumes with arbitrary movable boundaries. This facilitates the modeling of movable boundary problems (e.g. computations with moving engine piston). The model features full coupling between both phases in mass, momentum, and energy equations. The drop size distribution in sprays is taken into account using the multi-continua approach. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The deformation of a liquid drop by an electric field

Summary The shape and stability of an incompressible dielectric drop which is stressed by a uniform external electric field are re-examined by considering small perturbations from a prolate spheroid. Compared with the shapes predicted by other approximations it is found that, for a given field strength, the drops should be a little longer and consequently a little flatter at the equator in order to satisfy the equilibrium conditions. It is also shown that beyond a certain drop deformation the L. P. E. (Legendre polynomial expansion) method fails because the equilibrium conditions at the surface of the drop are not satisfied.     

Modeling and control of surface gravity waves in a model of a copper converter

Undesirable splashing appears in copper converters when air is injected into the molten matte to trigger the conversion process. We consider here a cylindrical container horizontally placed and containing water, where gravity waves on the liquid surface are generated due to water injection through a lateral submerged nozzle. The fluid dynamics in a transversal section of the converter is modeled by a 2-D inviscid potential flow involving a gravity wave equation with local damping on the liquid surface. Once the model is established, using a finite element method, the corresponding natural frequencies and normal modes are numerically computed in the absence of injection, and the solution of the system with injection is obtained using the spectrum. If a finite number of modes is considered, this approximation leads to a system of ordinary differential equations where the input is represented by the fluid injection. The dynamics is simulated as perturbations around a constant fluid injection solution, which is the desired operating state of the system, considering that the conversion process does not have to be stopped or seriously affected by the control. The solution is naturally unstable without control and the resulting increase of amplitude of the surface waves are assimilable to the splashing inside the converter. We show numerically that a variable flow around the operating injection is able to sensibly reduce these waves. This control is obtained by a LQG feedback law by measuring the elevation of the free surface at the point corresponding to the opposite extreme to where the nozzle injection is placed.     

Annular liquid jets in zero gravity

The equations describing the steady-state behavior of long annular liquid jets and liquid membranes in zero gravity are solved analytically as a function of the pressure difference across the jet or membrane, Weber number, and nozzle exit angle. The ranges of the parameters for which the analytical solutions are valid are determined, and analytical solutions of the mass absorption rate are obtained as a function of the Peclet and Weber numbers, nozzle exit angle, pressure difference, and thickness of the annular liquid jet. It is shown that the convergence length of annular liquid jets and liquid membranes increases as the Weber number, nozzle exit angle, and pressure coefficient are increased. It is also shown that the mass absoption rate increases as the nozzle exit angle, pressure coefficient, and Weber number are increased; however, the mass absorption rate decreases as the Peclet number and annular jet initial thickness-to-radius ratio are increased.     

Drop deformation under surfactants adsorption

The movements of free liquid drops, resulting from unbalanced surface tension gradients, in our case the adsorption of a surfactant, constitute important surface phenomena (Marangoni effect). The aim of this paper is to correlate the effect of pressure forces on the drop, with the surface coverage degree, namely with the extent to which the drop surface is covered by the surfactant. Our model shows that for a covered degree less then about 68°, these forces are negative. This means that these forces exerted by the external liquid upon the drop are oriented towards the negative direction of the normal to the drop surface, acting like a hammer. Some numerical data are given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类描述大气中重力孤立波的新模型

从两层流体浅水波方程出发,运用尺度分析与扰动方法,建立了一类新的模型(mKdV-BO模型)来描述大气中的重力孤立波。前人建立的KdV模型和BO模型适合描述经向和纬向扰动较弱时重力孤立波的生成和演化,而该模型的非线性更强,适合描述经向、纬向扰动较强时重力孤立波的生成与演化。通过运用试探函数法获得了模型的代数孤波解,并分析了孤立波的生成条件与传播速度。新模型的建立对于进一步解释大气中列队雷雨阵的形成机制,探讨大气中的强对流天气如飑线的形成等具有重要意义。 关键词：重力孤立波;试探函数法;列队雷雨阵     

An analysis of laminar boundary layers on liquid curtains

A simplified analysis of the laminar boundary layer along an isothermal liquid curtain falling under gravity is presented. The analysis uses a von Kármán-Pohlhausen integral method and includes the effects of gravity, pressure differences, surface tension and nozzle exit geometry on the convergence length of liquid curtains which have applications as chemical reactors and as protection systems in laser fusion reactors. It is shown that the effects of the surrounding gases on the curtain shape and convergence length are small, and that good approximations to the liquid curtain shape can be obtained by using inviscid flow analyses.     

Dynamics of surfactant-covered drops in linear flows

Surfactants modify interfacial properties and significantly affect drop behavior in flow. We study the dynamics of a drop, which is covered with a monolayer of insoluble surfactant, in linear viscous flows, both unbounded and in the presence of a wall. The effect of viscosity contrast is included. Analytical results in a form of expansions for weak flows and high viscosity drops are developed. Numerical results with three-dimensional boundary integral simulations are used to explore large deformations. The results show that surfactant generally enhances drop deformation, certainly under small-deformation conditions. The steady-state drop shape and surfactant distribution are independent of viscosity contrast in straining flows (e.g. hyperbolic, axisymmetric strain). The drop shape and surfactant distribution are insensitive to viscosity contrast under small deformation conditions for any linear flow; the effect of the rotational component at higher-order. The theory quantifies the effect of surfactant on drop migration away from a bounding wall as well as the rheology of dilute emulsions. It predicts non-Newtonian features such as shear thinning viscosity and normal stress. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inviscid and viscous stationary waves of gas flow through contracting-expanding nozzles

In this work we study steady states of one-dimensional viscous isentropic compressible flows through a contracting-expanding nozzle. Treating the viscosity coefficient as a singular parameter, the steady-state problem can be viewed as a singularly perturbed system. For a contracting-expanding nozzle, a complete classification of steady states is given and the existence of viscous profiles is established via the geometric singular perturbation theory. Particularly interesting is the existence of a maximal sub-to-super transonic wave and its role in the formation of other complicated transonic waves consisting of a sub-to-super portion.